To summarize professor Pei9s experience in treating globus hystericus.Methods:Learn from your teacher.Results:Professor Pei had been suffering from the disease for more than 30 years and had her unique views on the tr...To summarize professor Pei9s experience in treating globus hystericus.Methods:Learn from your teacher.Results:Professor Pei had been suffering from the disease for more than 30 years and had her unique views on the treatment of globus hystericus,which are mostly for emotional dysfunction,liver Qi is not comfortable,functioning of Qi is not adjusted,Yin and Yang imbalance.The basic principle of treatment is to grasp the core pathogenesis,take harmony as the method and balance as the duration,harmonize Qi,regulate Yin and Yang,use drugs to disperse the liver and rectify Qi,as well as auxiliary treatment with products to promote blood circulation,remove blood stasis,dryness and dampness,and clear heat.展开更多
Minor Bupleurum Decoction is a common TCM compound and a classic prescription that can best reflect the"harmonizing method',of TCM.But there are many differences on the usage and dosage of Minor Bupleurum Dec...Minor Bupleurum Decoction is a common TCM compound and a classic prescription that can best reflect the"harmonizing method',of TCM.But there are many differences on the usage and dosage of Minor Bupleurum Decoction.Combined with the clinical treatment experience,this paper summarizes the experience of Minor Bupleurum Decoction in the clinical treatment of diseases.It is hoped that relevant suggestions can be provided for clinicians to improve the clinical therapeutic effect of Minor Bupleurum Decoction.展开更多
The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The a...The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.展开更多
A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A ...A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.展开更多
The time domain harmonic balance method is an attractive reduced order method of analyzing unsteady flow for turbomachines. However, the method can admit non-physical solutions. Non-physical solutions were encountered...The time domain harmonic balance method is an attractive reduced order method of analyzing unsteady flow for turbomachines. However, the method can admit non-physical solutions. Non-physical solutions were encountered from a three-blade-row compressor configuration in a time domain harmonic balance analysis. This paper aims to investigate the root cause of the non-physical solutions. The investigation involves several strategies, which include increasing the number of harmonics, increasing the number of time instants, including scattered modes,including the rotor-rotor interaction, and the use of a new method-the approximate time domain nonlinear harmonic method. Numerical analyses pertinent to each strategy are presented to reveal the root cause of the non-physical solution. It is found that the nonlinear interaction of unsteady flow components with different fundamental frequencies is the cause of the non-physical solution. The non-physical solution can be eliminated by incorporating extra scattered modes or using the approximate time domain nonlinear harmonic method.展开更多
Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time(HB-AFT) domain technique has some advantages in dealing with nonlinear probl...Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time(HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.展开更多
Dielectric elastomer(DE) is suitable in soft transducers for broad applications,among which many are subjected to dynamic loadings, either mechanical or electrical or both. The tuning behaviors of these DE devices cal...Dielectric elastomer(DE) is suitable in soft transducers for broad applications,among which many are subjected to dynamic loadings, either mechanical or electrical or both. The tuning behaviors of these DE devices call for an efficient and reliable method to analyze the dynamic response of DE. This remains to be a challenge since the resultant vibration equation of DE, for example, the vibration of a DE balloon considered here is highly nonlinear with higher-order power terms and time-dependent coefficients. Previous efforts toward this goal use largely the numerical integration method with the simple harmonic balance method as a supplement. The numerical integration and the simple harmonic balance method are inefficient for large parametric analysis or with difficulty in improving the solution accuracy. To overcome the weakness of these two methods,we describe formulations of the incremental harmonic balance(IHB) method for periodic forced solutions of such a unique system. Combined with an arc-length continuation technique, the proposed strategy can capture the whole solution branches, both stable and unstable, automatically with any desired accuracy.展开更多
According to the rotor vortex theory,the rotor circulation and the rotorinduced velocity are developed into Fourier series.The circulation distributionalong blade spanwise is expressed in terms of segment-by-segment l...According to the rotor vortex theory,the rotor circulation and the rotorinduced velocity are developed into Fourier series.The circulation distributionalong blade spanwise is expressed in terms of segment-by-segment linearfunctions.In consequence the induced velocity equations and the circulationequations are derived.The engineering application of the rotor vortex theoryis provided.Then the induced velocity and its harmonic components are obtainedto provide a quantitative basis for the vortex model.For calculatingeach harmonic component of the induced velocity a simplified method is putforward which considers the effects of each order circulation with neglectingthose of higher order.The method saves the computer time and is of significantbenefit.展开更多
The coupling vibration of a hydraulic pipe system consisting of two pipes is studied.The pipes are installed in parallel and fixed at their ends,and are restrained by clips to one bracket at their middle points.The pi...The coupling vibration of a hydraulic pipe system consisting of two pipes is studied.The pipes are installed in parallel and fixed at their ends,and are restrained by clips to one bracket at their middle points.The pipe subjected to the basement excitation at the left end is named as the active pipe,while the pipe without excitation is called the passive pipe.The clips between the two pipes are the bridge for the vibration energy.The adjacent natural frequencies will enhance the vibration coupling.The governing equation of the coupled system is deduced by the generalized Hamilton principle,and is discretized to the modal space.The modal correction is used during the discretization.The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket.The harmonic balance method(HBM)is used to study the responses in the adjacent natural frequency region.The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket,while the locations of them are not node points.The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes.The stiffness of the clip and bracket can release the vibration coupling.It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough.In this way,the vibration energy is reflected by the almost rigid bracket,and is hard to transfer to the passive pipe via a soft clip.The best choice is to set the clips at the pipe node points.The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system.展开更多
In this study,a coupling model of fluid-conveying pipes made of functionally graded materials(FGMs)with NiTiNOL-steel(NiTi-ST)for vibration absorption is investigated.The vibration responses of the FGM fluid-conveying...In this study,a coupling model of fluid-conveying pipes made of functionally graded materials(FGMs)with NiTiNOL-steel(NiTi-ST)for vibration absorption is investigated.The vibration responses of the FGM fluid-conveying pipe with NiTi-ST are studied by the Galerkin truncation method(GTM)and harmonic balance method(HBM).The harmonic balance solutions and the numerical results are consistent.Also,the linearized stability of the structure is determined.The effects of the structure parameters on the absorption performance are also studied.The results show that the NiTi-ST is an effective means of vibration absorption.Furthermore,in studying the effect of the NiTi-ST,a closed detached response(CDR)is first observed.It is noteworthy that the CDR may dramatically change the vibration amplitude and that the parameters of the NiTi-ST may determine the emergence or disappearance of the CDR.This vibration absorption device can be extended to offer more general vibration control in engineering applications.展开更多
The revelation of thermal energy exchange mechanism of human body is challenging yet worthwhile,because it can clearly explain the changes in human symptoms and health status.Understanding,the heat transfer of the ski...The revelation of thermal energy exchange mechanism of human body is challenging yet worthwhile,because it can clearly explain the changes in human symptoms and health status.Understanding,the heat transfer of the skin is significant because the skin is the foremost organ for the energy exchange between the human body and the environment.In order to diagnose the physiological conditions of human skin without causing any damage,it is necessary to use a non-invasive measurement technique by means of a conformal flexible sensor.The harmonic method can minimize the thermal-induced injury to the skin due to its low heat generating properties.A novel type of computational theory assessing skin thermal conductivity,blood perfusion rate of capillaries in the dermis,and superficial subcutaneous tissues was formed by combining the multi-medium thermal diffusion model and the bio-thermal model(Pennes equation).The skins of the hand back of six healthy subjects were measured.It was found that the results revealed no consistent changes in thermal conductivity were observed across genders and ages.The measured blood perfusion rates were within the range of human capillary flow.It was found that female subjects had a higher perfusion rate range(0.0058-0.0061 s^(-1))than male subjects(0.0032-0.0049 s^(-1)),which is consistent with invasive medical studies about the gender difference in blood flow rates and stimulated effects in relaxation situations.展开更多
Epidemics spread quickly and are highly contagious.And there has been a profound understanding of etiology,pathogenesis,prevention,and treatment of these diseases in traditional Chinese medicine(TCM).Coronavirus disea...Epidemics spread quickly and are highly contagious.And there has been a profound understanding of etiology,pathogenesis,prevention,and treatment of these diseases in traditional Chinese medicine(TCM).Coronavirus disease 2019(COVID-19)falls into the category of“epidemic dampness”,and the core pathogenesis is that latency of externally-contracted dampness turbidity and epidemic toxin in pleurodiaphragmatic interspace provokes Shaoyang ministerial fire and causes concomitant attack of external and internal pathogens,resulting in wood fire tormenting metal and the upward rushing of dampness fire(toxin),ultimately leading to a syndrome of epidemic toxin blocking the lung.Throughout the treatment of COVID-19,Professor Shiyun Yan uses the“harmonizing”method and sticks to the basic principles of“protecting middle qi,pectoral qi and yin fluid”to consolidate the root,dispersing externally and clearing internally and using in combination drugs cold and warm in property.The specific treatment approaches include ventilating lung and expelling pathogens,clearing heat and removing the toxin,tonifying qi and nourishing yin,activating blood and resolving stasis,resolving dampness,and dredging collaterals,to prevent the patient’s condition from getting worse and save the dying.展开更多
Epidemics spread quickly and are highly contagious.And there has been a profound understanding of etiology,pathogenesis,prevention,and treatment of these diseases in traditional Chinese medicine(TCM).Coronavirus disea...Epidemics spread quickly and are highly contagious.And there has been a profound understanding of etiology,pathogenesis,prevention,and treatment of these diseases in traditional Chinese medicine(TCM).Coronavirus disease 2019(COVID‑19)falls into the category of“epidemic dampness”,and the core pathogenesis is that latency of externally‑contracted dampness turbidity and epidemic toxin in pleurodiaphragmatic interspace provokes Shaoyang ministerial fire and causes concomitant attack of external and internal pathogens,resulting in wood fire tormenting metal and the upward rushing of dampness fire(toxin),ultimately leading to a syndrome of epidemic toxin blocking the lung.Throughout the treatment of COVID‑19,Professor Shiyun Yan uses the“harmonizing”method and sticks to the basic principles of“protecting middle qi,pectoral qi and yin fluid”to consolidate the root,dispersing externally and clearing internally and using in combination drugs cold and warm in property.The specific treatment approaches include ventilating lung and expelling pathogens,clearing heat and removing the toxin,tonifying qi and nourishing yin,activating blood and resolving stasis,resolving dampness,and dredging collaterals,to prevent the patient’s condition from getting worse and save the dying.展开更多
In this study,the first-order shear deformation theory(FSDT)is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC).The vi...In this study,the first-order shear deformation theory(FSDT)is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC).The vibration analyses of the FG-GPLRC truncated conical shell are presented.Considering the graphene platelets(GPLs)of the FG-GPLRC truncated conical shell with three different distribution patterns,the modified Halpin-Tsai model is used to calculate the effective Young’s modulus.Hamilton’s principle,the FSDT,and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell.The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell.Then,the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method.The effects of the weight fraction and distribution pattern of the GPLs,the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed.This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.展开更多
A broadband adaptive vibration control strategy with high reliability and flexible versatility is proposed.The high vibration damping performance of nonlinear energy sink(NES)has attracted attention.However,targeted e...A broadband adaptive vibration control strategy with high reliability and flexible versatility is proposed.The high vibration damping performance of nonlinear energy sink(NES)has attracted attention.However,targeted energy transfer may cause severe vibration of NES.Besides,it is difficult to realize pure nonlinear stiffness without the linear part.As a result,the reliability of NES is not high.The low reliability of NES has hindered its application in engineering.In addition,the performance of NES depends on its mass ratio of the primary system,and NES lacks versatility for different vibration systems.Therefore,this paper proposes the concept of NES cell.The advantages of the adaptive vibration control of NES are applied to cellular NES.By applying a large number of NES cells in parallel,the reliability of NES and its versatility to complex vibration structures are improved.An elastic beam is used as the primary vibration structure,and a limited NES is used as the cell.The relationship between the vibration suppression effect of NES cells and the number of NES cell is studied.In addition,the effect of the distribution of NES cells on the multi-mode resonance suppression of the beam is also studied.In summary,the mode of the primary structure can be efficiently controlled by a large number of lightweight NES cell.Therefore,the lightweight NES cell is flexible for vibration control of complex structures.In addition,it improves the reliability of NES applications.Therefore,the distributed application of NES cells proposed in this paper is a valuable vibration suppression strategy.展开更多
A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance.In this paper,a generalized vibration isolation system is established with nonlinear stiffness,nonlinear ...A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance.In this paper,a generalized vibration isolation system is established with nonlinear stiffness,nonlinear viscous damping,and Bouc-Wen(BW)hysteretic damping.An approximate analytical analysis is performed based on a harmonic balance method(HBM)and an alternating frequency/time(AFT)domain technique.To evaluate the damping effect,a generalized equivalent damping ratio is defined with the stiffness-varying characteristics.A comprehensive comparison of different kinds of damping is made through numerical simulations.It is found that the damping ratio of the linear damping is related to the stiffness-varying characteristics while the damping ratios of two kinds of nonlinear damping are related to the responding amplitudes.The linear damping,hysteretic damping,and nonlinear viscous damping are suitable for the small-amplitude,medium-amplitude,and large-amplitude conditions,respectively.The hysteretic damping has an extra advantage of broadband isolation.展开更多
This paper is focused on the post-buckling behavior of the fixed laminated composite beams with effects of axial compression force and the shear deformation.The analytical solutions are established for the original co...This paper is focused on the post-buckling behavior of the fixed laminated composite beams with effects of axial compression force and the shear deformation.The analytical solutions are established for the original control equations(that is not simplified)by applying the Maclaurin series expansion,Chebyshev polynomials,the harmonic balance method and the Newton’s method.The validity of the present method is verified via comparing the analytical approximate solutions with the numerical ones which are obtained by the shooting method.The present third analytical approximate solutions can give excellent agreement with the numerical solutions for a wide range of the deformation amplitudes.What’s more,the effect of shear deformation on the post-bucking configuration of the sandwich beam is also proposed.It can be found that the shear angle has a great influence on the post-buckling load of composite beams.Therefore,the model simplifying the shear formation term as small quantity is not accurate for the case of sandwich beam with soft core.展开更多
The subharmonic resonance and bifurcations of a clamped-clamped buckled beam under base harmonic excitations are investigated.The nonlinear partial integrodifferential equation of the motion of the buckled beam with b...The subharmonic resonance and bifurcations of a clamped-clamped buckled beam under base harmonic excitations are investigated.The nonlinear partial integrodifferential equation of the motion of the buckled beam with both quadratic and cubic nonlinearities is given by using Hamilton’s principle.A set of second-order nonlinear ordinary differential equations are obtained by spatial discretization with the Galerkin method.A high-dimensional model of the buckled beam is derived,concerning nonlinear coupling.The incremental harmonic balance(IHB)method is used to achieve the periodic solutions of the high-dimensional model of the buckled beam to observe the nonlinear frequency response curve and the nonlinear amplitude response curve,and the Floquet theory is used to analyze the stability of the periodic solutions.Attention is focused on the subharmonic resonance caused by the internal resonance as the excitation frequency near twice of the first natural frequency of the buckled beam with/without the antisymmetric modes being excited.Bifurcations including the saddle-node,Hopf,perioddoubling,and symmetry-breaking bifurcations are observed.Furthermore,quasi-periodic motion is observed by using the fourth-order Runge-Kutta method,which results from the Hopf bifurcation of the response of the buckled beam with the anti-symmetric modes being excited.展开更多
The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of different analytical approximate approaches.The forced vibratio...The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of different analytical approximate approaches.The forced vibration of snap-through mechanism is treated as a quadratic nonlinear oscillator.The Lindstedt-Poincar′e method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses.It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method.The analytical approximations are compared with the numerical integrations in terms of the frequency response curves and the phase portraits.Supported by the numerical results, the harmonic balance method predicts that the quadratic nonlinearity bends the frequency response curves to the left.If the excitation amplitude is a second-order small quantity of the bookkeeping parameter,the steady-state responses predicted by the second-order approximation of the LindstedtPoincar′e method and the multiple-scale method agree qualitatively with the numerical results.It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.展开更多
Soft nonlinear support is a major engineering project,but there are few relevant studies.In this paper,a dynamic pipeline model with soft nonlinear supports at both ends is established.By considering the influence of ...Soft nonlinear support is a major engineering project,but there are few relevant studies.In this paper,a dynamic pipeline model with soft nonlinear supports at both ends is established.By considering the influence of the Coriolis force and centrifugal force,the dynamical coupling equation of fluid-structure interaction is derived with extended Hamilton’s principle.Then,the approximate analytical solutions are sought via the harmonic balance method.The amplitude-frequency response curves show that different effects can be determined by approximate analysis.It is demonstrated that the increase in the fluid velocity can increase the amplitude of the pipeline system.The frequency range of unstable response increases when the fluid pressure raises.The combination of the soft nonlinear clamp and the large geometrical deformation of the pipeline affects the nonlinear vibration characteristic of the system,and the external excitation force and damping have significant effects on the stability.展开更多
文摘To summarize professor Pei9s experience in treating globus hystericus.Methods:Learn from your teacher.Results:Professor Pei had been suffering from the disease for more than 30 years and had her unique views on the treatment of globus hystericus,which are mostly for emotional dysfunction,liver Qi is not comfortable,functioning of Qi is not adjusted,Yin and Yang imbalance.The basic principle of treatment is to grasp the core pathogenesis,take harmony as the method and balance as the duration,harmonize Qi,regulate Yin and Yang,use drugs to disperse the liver and rectify Qi,as well as auxiliary treatment with products to promote blood circulation,remove blood stasis,dryness and dampness,and clear heat.
文摘Minor Bupleurum Decoction is a common TCM compound and a classic prescription that can best reflect the"harmonizing method',of TCM.But there are many differences on the usage and dosage of Minor Bupleurum Decoction.Combined with the clinical treatment experience,this paper summarizes the experience of Minor Bupleurum Decoction in the clinical treatment of diseases.It is hoped that relevant suggestions can be provided for clinicians to improve the clinical therapeutic effect of Minor Bupleurum Decoction.
基金Project supported by the National Natural Science Foundation of China(Nos.11972129 and12372008)the National Major Science and Technology Projects of China(No.2017-IV-0008-0045)+3 种基金the Natural Science Foundation of Heilongjiang Province of China(No.YQ2022A008)the Fundamental Research Funds for the Central Universities of China(No.HIT.OCEF.2023006)the Polish National Science Centre of Poland under the OPUS 18 grant(No.2019/35/B/ST8/00980)the Tianjin University Independent Innovation Foundation of China(No.2023XJS-0038)。
文摘The harmonic balance method(HBM)is one of the most widely used methods in solving nonlinear vibration problems,and its accuracy and computational efficiency largely depend on the number of the harmonics selected.The adaptive harmonic balance(AHB)method is an improved HBM method.This paper presents a modified AHB method with the asymptotic harmonic selection(AHS)procedure.This new harmonic selection procedure selects harmonics from the frequency spectra of nonlinear terms instead of estimating the contribution of each harmonic to the whole nonlinear response,by which the additional calculation is avoided.A modified continuation method is proposed to deal with the variable size of nonlinear algebraic equations at different values of path parameters,and then all solution branches of the amplitude-frequency response are obtained.Numerical experiments are carried out to verify the performance of the AHB-AHS method.Five typical nonlinear dynamic equations with different types of nonlinearities and excitations are chosen as the illustrative examples.Compared with the classical HBM and Runge-Kutta methods,the proposed AHB-AHS method is of higher accuracy and better convergence.The AHB-AHS method proposed in this paper has the potential to investigate the nonlinear vibrations of complex high-dimensional nonlinear systems.
基金support from the Youth Innovation Promotion Association of Chinese Academy of Sciences (Grant No.2019319)support from the Start-up Foundation of Suzhou Institute of Nano-Tech and Nano-Bionics,CAS,Suzhou (Grant No.Y9AAD110)。
文摘A Josephson traveling wave parametric amplifier(JTWPA),which is a quantum-limited amplifier with high gain and large bandwidth,is the core device of large-scale measurement and control systems for quantum computing.A typical JTWPA consists of thousands of Josephson junctions connected in series to form a transmission line and hundreds of shunt LC resonators periodically loaded along the line for phase matching.Because the variation of these capacitors and inductors can be detrimental to their high-frequency characteristics,the fabrication of a JTWPA typically necessitates precise processing equipment.To guide the fabrication process and further improve the design for manufacturability,it is necessary to understand how each electronic component affects the amplifier.In this paper,we use the harmonic balance method to conduct a comprehensive study on the impact of nonuniformity and fabrication yield of the electronic components on the performance of a JTWPA.The results provide insightful and scientific guidance for device design and fabrication processes.
基金National Natural Science Foundation of China(51976172)National Science and Technology Major Project (2017-II-0009-0023)+1 种基金China’s 111 project(B17037)Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University(CX2023056)。
文摘The time domain harmonic balance method is an attractive reduced order method of analyzing unsteady flow for turbomachines. However, the method can admit non-physical solutions. Non-physical solutions were encountered from a three-blade-row compressor configuration in a time domain harmonic balance analysis. This paper aims to investigate the root cause of the non-physical solutions. The investigation involves several strategies, which include increasing the number of harmonics, increasing the number of time instants, including scattered modes,including the rotor-rotor interaction, and the use of a new method-the approximate time domain nonlinear harmonic method. Numerical analyses pertinent to each strategy are presented to reveal the root cause of the non-physical solution. It is found that the nonlinear interaction of unsteady flow components with different fundamental frequencies is the cause of the non-physical solution. The non-physical solution can be eliminated by incorporating extra scattered modes or using the approximate time domain nonlinear harmonic method.
基金supported by the National Natural Science Foundation of China(No.10632040)
文摘Comparisons of the common methods for obtaining the periodic responses show that the harmonic balance method with alternating frequency/time(HB-AFT) domain technique has some advantages in dealing with nonlinear problems of fractional exponential models. By the HB-AFT method, a rigid rotor supported by ball bearings with nonlinearity of Hertz contact and ball passage vibrations is considered. With the aid of the Floquet theory, the movement characteristics of interval stability are deeply studied. Besides, a simple strategy to determine the monodromy matrix is proposed for the stability analysis.
基金the National Natural Science Foundation of China(Nos.11702215 and11972277)the Natural Science Basic Research Plan in Shaanxi Province of China(Nos.2017JQ5062 and 2018JQ1029)。
文摘Dielectric elastomer(DE) is suitable in soft transducers for broad applications,among which many are subjected to dynamic loadings, either mechanical or electrical or both. The tuning behaviors of these DE devices call for an efficient and reliable method to analyze the dynamic response of DE. This remains to be a challenge since the resultant vibration equation of DE, for example, the vibration of a DE balloon considered here is highly nonlinear with higher-order power terms and time-dependent coefficients. Previous efforts toward this goal use largely the numerical integration method with the simple harmonic balance method as a supplement. The numerical integration and the simple harmonic balance method are inefficient for large parametric analysis or with difficulty in improving the solution accuracy. To overcome the weakness of these two methods,we describe formulations of the incremental harmonic balance(IHB) method for periodic forced solutions of such a unique system. Combined with an arc-length continuation technique, the proposed strategy can capture the whole solution branches, both stable and unstable, automatically with any desired accuracy.
文摘According to the rotor vortex theory,the rotor circulation and the rotorinduced velocity are developed into Fourier series.The circulation distributionalong blade spanwise is expressed in terms of segment-by-segment linearfunctions.In consequence the induced velocity equations and the circulationequations are derived.The engineering application of the rotor vortex theoryis provided.Then the induced velocity and its harmonic components are obtainedto provide a quantitative basis for the vortex model.For calculatingeach harmonic component of the induced velocity a simplified method is putforward which considers the effects of each order circulation with neglectingthose of higher order.The method saves the computer time and is of significantbenefit.
基金Project supported by the National Natural Science Foundation of China(No.12002195)the Pujiang Project of Shanghai Science and Technology Commission of China(No.20PJ1404000)。
文摘The coupling vibration of a hydraulic pipe system consisting of two pipes is studied.The pipes are installed in parallel and fixed at their ends,and are restrained by clips to one bracket at their middle points.The pipe subjected to the basement excitation at the left end is named as the active pipe,while the pipe without excitation is called the passive pipe.The clips between the two pipes are the bridge for the vibration energy.The adjacent natural frequencies will enhance the vibration coupling.The governing equation of the coupled system is deduced by the generalized Hamilton principle,and is discretized to the modal space.The modal correction is used during the discretization.The investigation on the natural characters indicates that the adjacent natural frequencies can be adjusted by the stiffness of the two clips and bracket.The harmonic balance method(HBM)is used to study the responses in the adjacent natural frequency region.The results show that the vibration energy transmits from the active pipe to the passive pipe swimmingly via the clips together with a flexible bracket,while the locations of them are not node points.The adjacent natural frequencies may arouse wide resonance curves with two peaks for both pipes.The stiffness of the clip and bracket can release the vibration coupling.It is suggested that the stiffness of the clip on the passive pipe should be weak and the bracket should be strong enough.In this way,the vibration energy is reflected by the almost rigid bracket,and is hard to transfer to the passive pipe via a soft clip.The best choice is to set the clips at the pipe node points.The current work gives some suggestions for weakening the coupled vibration during the dynamic design of a coupled hydraulic pipe system.
基金Project supported by the National Natural Science Foundation of China(Nos.12272240 and12022213)。
文摘In this study,a coupling model of fluid-conveying pipes made of functionally graded materials(FGMs)with NiTiNOL-steel(NiTi-ST)for vibration absorption is investigated.The vibration responses of the FGM fluid-conveying pipe with NiTi-ST are studied by the Galerkin truncation method(GTM)and harmonic balance method(HBM).The harmonic balance solutions and the numerical results are consistent.Also,the linearized stability of the structure is determined.The effects of the structure parameters on the absorption performance are also studied.The results show that the NiTi-ST is an effective means of vibration absorption.Furthermore,in studying the effect of the NiTi-ST,a closed detached response(CDR)is first observed.It is noteworthy that the CDR may dramatically change the vibration amplitude and that the parameters of the NiTi-ST may determine the emergence or disappearance of the CDR.This vibration absorption device can be extended to offer more general vibration control in engineering applications.
基金support from the National Natural Science Foundation of China(Nos.52222602,52201261)Beijing Nova Program(No.20220484170)+1 种基金Ningbo 3315 Innovative Teams Program(No.2019A-14-C)Fundamental Research Funds for the Central Universities(Nos.FRF-TP-22-001C1,FRF-EYIT-23-05).
文摘The revelation of thermal energy exchange mechanism of human body is challenging yet worthwhile,because it can clearly explain the changes in human symptoms and health status.Understanding,the heat transfer of the skin is significant because the skin is the foremost organ for the energy exchange between the human body and the environment.In order to diagnose the physiological conditions of human skin without causing any damage,it is necessary to use a non-invasive measurement technique by means of a conformal flexible sensor.The harmonic method can minimize the thermal-induced injury to the skin due to its low heat generating properties.A novel type of computational theory assessing skin thermal conductivity,blood perfusion rate of capillaries in the dermis,and superficial subcutaneous tissues was formed by combining the multi-medium thermal diffusion model and the bio-thermal model(Pennes equation).The skins of the hand back of six healthy subjects were measured.It was found that the results revealed no consistent changes in thermal conductivity were observed across genders and ages.The measured blood perfusion rates were within the range of human capillary flow.It was found that female subjects had a higher perfusion rate range(0.0058-0.0061 s^(-1))than male subjects(0.0032-0.0049 s^(-1)),which is consistent with invasive medical studies about the gender difference in blood flow rates and stimulated effects in relaxation situations.
文摘Epidemics spread quickly and are highly contagious.And there has been a profound understanding of etiology,pathogenesis,prevention,and treatment of these diseases in traditional Chinese medicine(TCM).Coronavirus disease 2019(COVID-19)falls into the category of“epidemic dampness”,and the core pathogenesis is that latency of externally-contracted dampness turbidity and epidemic toxin in pleurodiaphragmatic interspace provokes Shaoyang ministerial fire and causes concomitant attack of external and internal pathogens,resulting in wood fire tormenting metal and the upward rushing of dampness fire(toxin),ultimately leading to a syndrome of epidemic toxin blocking the lung.Throughout the treatment of COVID-19,Professor Shiyun Yan uses the“harmonizing”method and sticks to the basic principles of“protecting middle qi,pectoral qi and yin fluid”to consolidate the root,dispersing externally and clearing internally and using in combination drugs cold and warm in property.The specific treatment approaches include ventilating lung and expelling pathogens,clearing heat and removing the toxin,tonifying qi and nourishing yin,activating blood and resolving stasis,resolving dampness,and dredging collaterals,to prevent the patient’s condition from getting worse and save the dying.
文摘Epidemics spread quickly and are highly contagious.And there has been a profound understanding of etiology,pathogenesis,prevention,and treatment of these diseases in traditional Chinese medicine(TCM).Coronavirus disease 2019(COVID‑19)falls into the category of“epidemic dampness”,and the core pathogenesis is that latency of externally‑contracted dampness turbidity and epidemic toxin in pleurodiaphragmatic interspace provokes Shaoyang ministerial fire and causes concomitant attack of external and internal pathogens,resulting in wood fire tormenting metal and the upward rushing of dampness fire(toxin),ultimately leading to a syndrome of epidemic toxin blocking the lung.Throughout the treatment of COVID‑19,Professor Shiyun Yan uses the“harmonizing”method and sticks to the basic principles of“protecting middle qi,pectoral qi and yin fluid”to consolidate the root,dispersing externally and clearing internally and using in combination drugs cold and warm in property.The specific treatment approaches include ventilating lung and expelling pathogens,clearing heat and removing the toxin,tonifying qi and nourishing yin,activating blood and resolving stasis,resolving dampness,and dredging collaterals,to prevent the patient’s condition from getting worse and save the dying.
基金Project supported by the National Natural Science Foundation of China(Nos.12002057,11872127,11832002)the Scientific Research Project of Beijing Educational Committee(No.KM202111232023)the Qin Xin Talents Cultivation Program,Beijing Information Science&Technology University(Nos.QXTCP C202102,A201901)。
文摘In this study,the first-order shear deformation theory(FSDT)is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC).The vibration analyses of the FG-GPLRC truncated conical shell are presented.Considering the graphene platelets(GPLs)of the FG-GPLRC truncated conical shell with three different distribution patterns,the modified Halpin-Tsai model is used to calculate the effective Young’s modulus.Hamilton’s principle,the FSDT,and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell.The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell.Then,the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method.The effects of the weight fraction and distribution pattern of the GPLs,the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed.This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.
基金Project supported by the National Science Fund for Distinguished Young Scholars of China (No.12025204)the Shanghai Municipal Education Commission of China (No.2019-01-07-00-09-E00018)。
文摘A broadband adaptive vibration control strategy with high reliability and flexible versatility is proposed.The high vibration damping performance of nonlinear energy sink(NES)has attracted attention.However,targeted energy transfer may cause severe vibration of NES.Besides,it is difficult to realize pure nonlinear stiffness without the linear part.As a result,the reliability of NES is not high.The low reliability of NES has hindered its application in engineering.In addition,the performance of NES depends on its mass ratio of the primary system,and NES lacks versatility for different vibration systems.Therefore,this paper proposes the concept of NES cell.The advantages of the adaptive vibration control of NES are applied to cellular NES.By applying a large number of NES cells in parallel,the reliability of NES and its versatility to complex vibration structures are improved.An elastic beam is used as the primary vibration structure,and a limited NES is used as the cell.The relationship between the vibration suppression effect of NES cells and the number of NES cell is studied.In addition,the effect of the distribution of NES cells on the multi-mode resonance suppression of the beam is also studied.In summary,the mode of the primary structure can be efficiently controlled by a large number of lightweight NES cell.Therefore,the lightweight NES cell is flexible for vibration control of complex structures.In addition,it improves the reliability of NES applications.Therefore,the distributed application of NES cells proposed in this paper is a valuable vibration suppression strategy.
基金Project supported by the National Natural Science Foundation of China(No.11902097)the China Postdoctoral Science Foundation(No.2019M661266)。
文摘A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance.In this paper,a generalized vibration isolation system is established with nonlinear stiffness,nonlinear viscous damping,and Bouc-Wen(BW)hysteretic damping.An approximate analytical analysis is performed based on a harmonic balance method(HBM)and an alternating frequency/time(AFT)domain technique.To evaluate the damping effect,a generalized equivalent damping ratio is defined with the stiffness-varying characteristics.A comprehensive comparison of different kinds of damping is made through numerical simulations.It is found that the damping ratio of the linear damping is related to the stiffness-varying characteristics while the damping ratios of two kinds of nonlinear damping are related to the responding amplitudes.The linear damping,hysteretic damping,and nonlinear viscous damping are suitable for the small-amplitude,medium-amplitude,and large-amplitude conditions,respectively.The hysteretic damping has an extra advantage of broadband isolation.
基金supported by the National Natural Science Foundation of China(Grant No.41972323 and 51991364)Science and Technology Project of the 13th Five-Year Plan of Jilin Provincial Department of Education(Grant No.JJKH20190126KJ)the Science and Technology Developing Plan Project of Jilin Province(Grant No.20160520021JH).
文摘This paper is focused on the post-buckling behavior of the fixed laminated composite beams with effects of axial compression force and the shear deformation.The analytical solutions are established for the original control equations(that is not simplified)by applying the Maclaurin series expansion,Chebyshev polynomials,the harmonic balance method and the Newton’s method.The validity of the present method is verified via comparing the analytical approximate solutions with the numerical ones which are obtained by the shooting method.The present third analytical approximate solutions can give excellent agreement with the numerical solutions for a wide range of the deformation amplitudes.What’s more,the effect of shear deformation on the post-bucking configuration of the sandwich beam is also proposed.It can be found that the shear angle has a great influence on the post-buckling load of composite beams.Therefore,the model simplifying the shear formation term as small quantity is not accurate for the case of sandwich beam with soft core.
基金Project supported by the National Natural Science Foundation of China(Nos.11972381 and 11572354)the Fundamental Research Funds for the Central Universities(No.18lgzd08)。
文摘The subharmonic resonance and bifurcations of a clamped-clamped buckled beam under base harmonic excitations are investigated.The nonlinear partial integrodifferential equation of the motion of the buckled beam with both quadratic and cubic nonlinearities is given by using Hamilton’s principle.A set of second-order nonlinear ordinary differential equations are obtained by spatial discretization with the Galerkin method.A high-dimensional model of the buckled beam is derived,concerning nonlinear coupling.The incremental harmonic balance(IHB)method is used to achieve the periodic solutions of the high-dimensional model of the buckled beam to observe the nonlinear frequency response curve and the nonlinear amplitude response curve,and the Floquet theory is used to analyze the stability of the periodic solutions.Attention is focused on the subharmonic resonance caused by the internal resonance as the excitation frequency near twice of the first natural frequency of the buckled beam with/without the antisymmetric modes being excited.Bifurcations including the saddle-node,Hopf,perioddoubling,and symmetry-breaking bifurcations are observed.Furthermore,quasi-periodic motion is observed by using the fourth-order Runge-Kutta method,which results from the Hopf bifurcation of the response of the buckled beam with the anti-symmetric modes being excited.
基金Project supported by the State Key Program of National Natural Science Foundation of China(No.11232009)the National Natural Science Foundation of China(No.11572182)
文摘The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of different analytical approximate approaches.The forced vibration of snap-through mechanism is treated as a quadratic nonlinear oscillator.The Lindstedt-Poincar′e method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses.It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method.The analytical approximations are compared with the numerical integrations in terms of the frequency response curves and the phase portraits.Supported by the numerical results, the harmonic balance method predicts that the quadratic nonlinearity bends the frequency response curves to the left.If the excitation amplitude is a second-order small quantity of the bookkeeping parameter,the steady-state responses predicted by the second-order approximation of the LindstedtPoincar′e method and the multiple-scale method agree qualitatively with the numerical results.It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.
基金supported by the National Natural Science Foundation of China(No.11972112)the Fundamental Research Funds for the Central Universities of China(Nos.N2103024 and N2003014)the National Science and Technology Major Project of China(No.J2019-I-0008-0008)。
文摘Soft nonlinear support is a major engineering project,but there are few relevant studies.In this paper,a dynamic pipeline model with soft nonlinear supports at both ends is established.By considering the influence of the Coriolis force and centrifugal force,the dynamical coupling equation of fluid-structure interaction is derived with extended Hamilton’s principle.Then,the approximate analytical solutions are sought via the harmonic balance method.The amplitude-frequency response curves show that different effects can be determined by approximate analysis.It is demonstrated that the increase in the fluid velocity can increase the amplitude of the pipeline system.The frequency range of unstable response increases when the fluid pressure raises.The combination of the soft nonlinear clamp and the large geometrical deformation of the pipeline affects the nonlinear vibration characteristic of the system,and the external excitation force and damping have significant effects on the stability.
