Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non...Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.展开更多
The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-P...The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-Planck-Kolmogorov et/ualion approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under consideration are characterized by the dependence ofnonconservative fqrces on the first integrals of the corresponding conservative systems and arc catted generalized-energy-dependent f G.E.D.) systems. It is shown taht for each of the four classes of G.E.D. nonlinear stochastic systems there is a family of non-G.E.D. systems which are equivalent to the G.E.D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G.E.D. system is indicated and. as an example, the equivalent stochastic systems for the second order G.E. D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D. nonlinear stochastic systems may he found by searching the equivalent G.E.D. systems.展开更多
We studied the feedback maximization of reliability of multi-degree-of-freedom （MDOF） quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged Ito equat...We studied the feedback maximization of reliability of multi-degree-of-freedom （MDOF） quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged Ito equations are derived by using the stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Then, the dynamical programming equation and its boundary and final time conditions for the control problems of maximizing the reliability is established from the partially averaged equations by using the dynamical programming principle. The nonlinear stochastic optimal control for maximizing the reliability is determined from the dynamical programming equation and control constrains. The reliability function of optimally controlled systems is obtained by solving the final dynamical programming equation. Finally, the application of the proposed procedure and effectiveness of the control strategy are illustrated by using an example.展开更多
By virtue of the singular point theory for one-dimension diffusionprocess and the stochastic averaging approach of energy envelop, thebifurcation behavior of a homoclinic bifurcation system, which is inthe presence of...By virtue of the singular point theory for one-dimension diffusionprocess and the stochastic averaging approach of energy envelop, thebifurcation behavior of a homoclinic bifurcation system, which is inthe presence of parametric white noise and is concealed behind acodimension two bifurcation point, is investigated in this paper.展开更多
Applying the wavenumber frequency transfer function to describe the whole system including tht elastic cylindrical shell and the fluid loading, a general expression of the cross spectrum of the interior noise induced ...Applying the wavenumber frequency transfer function to describe the whole system including tht elastic cylindrical shell and the fluid loading, a general expression of the cross spectrum of the interior noise induced by the TBL (turbulent boundary layer) pressure fiuctuations is derived. There are two production mechanisms of the noise: one is direct transfer of the convective ridge of the pressure fluctuations through the shell, the other is the reradiation of resonance modes excited by the pressure fluctuations. At low frequencies the noise produced by the latter mechanism is dominant. Solving the frequency equation of the cylindrical shell with liquid loading, the two Stoneley-type poles in the complex K plane are presented. They are the major sources of the reradiation of shell at low frequencies. Finally, effects of the shell radius, shell thickness, absorption of material and the flow speeds on the noise reduction are computed by numerical iniegration.展开更多
A unified theory for calculating the noise radiation of an infinite elastic plate excited by the turbulent boundary layer pressure fluctuations is presented . Using the wave number frequency transfer function to desri...A unified theory for calculating the noise radiation of an infinite elastic plate excited by the turbulent boundary layer pressure fluctuations is presented . Using the wave number frequency transfer function to desribe the whole system , consisting of the plate and the liquid loading, a general expression of the cross spectrum was derived. It is an integral in the complex wave number plane and leads to a sum of the residues at the poles of two types. One pole introduced by the convective ridge of the pressure fluctuations yields a direct transfer component , which is an evanescent wave in liquid because the pole lies in the high wave number region . The other poles introduced by the transfer function of structure produce the radiation field components with the resonance modes of a liquid loaded plate. The pole positions and their residues can be computed approximately by use of the Resonance Scattering Theory . For the case of hydrodynamic noise, where the range of the frequency-thickness product of interest is relatively low , the symmetric zero-order mode dominates the noise radiation.展开更多
Finite hydrophone and hydrophone array are the wave vector filter and can re-duce the flow noise. In this paper the responses of the cylindrical area hydrophone and two-circular area hydrophone within viscoelastic cyl...Finite hydrophone and hydrophone array are the wave vector filter and can re-duce the flow noise. In this paper the responses of the cylindrical area hydrophone and two-circular area hydrophone within viscoelastic cylindrical shell to the TBL (turbulent boundary layer) pressure fluctuations are investigated. Applying the method based on the wavenumber frequency spectrum analysis, the expressions of 1) the noise power spectrum of a single hy-drophone; 2) the space correlation of two hydrophones; 3) the noise power spectrum of array are derived. The dependencies of the noise reduction on hydrophone shape, dimension, element amount and separation of hydrophones of array are calculated by numerical integration. The wide-band and narrow-band correlation for two hydrophones is also calculated. The numerical results show that hydrophone array can effectively reduce the interior noise.展开更多
We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-ba...We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.展开更多
The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed ap...The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged It? stochastic differential equations for the system are derived by using the stochastic averaging method. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of the first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of the first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. The effects of time delay in feedback control force on the conditional reliability function, conditional probability density and moments of the first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.展开更多
基金the National Natural Science Foundation of China(No.12072118)the Natural Science Funds for Distinguished Young Scholar of Fujian Province of China(No.2021J06024)the Project for Youth Innovation Fund of Xiamen of China(No.3502Z20206005)。
文摘Hysteresis widely exists in civil structures,and dissipates the mechanical energy of systems.Research on the random vibration of hysteretic systems,however,is still insufficient,particularly when the excitation is non-Gaussian.In this paper,the radial basis function(RBF)neural network(RBF-NN)method is adopted as a numerical method to investigate the random vibration of the Bouc-Wen hysteretic system under the Poisson white noise excitations.The solution to the reduced generalized Fokker-PlanckKolmogorov(GFPK)equation is expressed in terms of the RBF-NNs with the Gaussian activation functions,whose weights are determined by minimizing the loss function of the reduced GFPK equation residual and constraint associated with the normalization condition.A steel fiber reinforced ceramsite concrete(SFRCC)column loaded by the Poisson white noise is studied as an example to illustrate the solution process.The effects of several important parameters of both the system and the excitation on the stochastic response are evaluated,and the obtained results are compared with those obtained by the Monte Carlo simulations(MCSs).The numerical results show that the RBF-NN method can accurately predict the stationary response with a considerable high computational efficiency.
基金Project Supported by The National Natural Science Foundation of China
文摘The exact solutions for stationary responses of one class of the second order and three classes of higher order nonlinear systems to parametric and/or external while noise excitations are constructed by using Fokkcr-Planck-Kolmogorov et/ualion approach. The conditions for the existence and uniqueness and the behavior of the solutions are discussed. All the systems under consideration are characterized by the dependence ofnonconservative fqrces on the first integrals of the corresponding conservative systems and arc catted generalized-energy-dependent f G.E.D.) systems. It is shown taht for each of the four classes of G.E.D. nonlinear stochastic systems there is a family of non-G.E.D. systems which are equivalent to the G.E.D. system in the sense of having identical stationary solution. The way to find the equivalent stochastic systems for a given G.E.D. system is indicated and. as an example, the equivalent stochastic systems for the second order G.E. D. nonlinear stochastic system are given. It is pointed out and illustrated with example that the exact stationary solutions for many non-G.E.D. nonlinear stochastic systems may he found by searching the equivalent G.E.D. systems.
基金Project supported by the National Natural Science Foundation of China (No. 10772159)the Research Fund for the Doctoral Program of Higher Education of China (No. 20060335125)the Zhejiang Provincial Nature Science Foundation of China (No. Y7080070)
文摘We studied the feedback maximization of reliability of multi-degree-of-freedom （MDOF） quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. First, the partially averaged Ito equations are derived by using the stochastic averaging method for quasi integrable-Hamiltonian systems under combined harmonic and white noise excitations. Then, the dynamical programming equation and its boundary and final time conditions for the control problems of maximizing the reliability is established from the partially averaged equations by using the dynamical programming principle. The nonlinear stochastic optimal control for maximizing the reliability is determined from the dynamical programming equation and control constrains. The reliability function of optimally controlled systems is obtained by solving the final dynamical programming equation. Finally, the application of the proposed procedure and effectiveness of the control strategy are illustrated by using an example.
基金Supported by the National Science Foundation of China under Grant No.19602016
文摘By virtue of the singular point theory for one-dimension diffusionprocess and the stochastic averaging approach of energy envelop, thebifurcation behavior of a homoclinic bifurcation system, which is inthe presence of parametric white noise and is concealed behind acodimension two bifurcation point, is investigated in this paper.
文摘Applying the wavenumber frequency transfer function to describe the whole system including tht elastic cylindrical shell and the fluid loading, a general expression of the cross spectrum of the interior noise induced by the TBL (turbulent boundary layer) pressure fiuctuations is derived. There are two production mechanisms of the noise: one is direct transfer of the convective ridge of the pressure fluctuations through the shell, the other is the reradiation of resonance modes excited by the pressure fluctuations. At low frequencies the noise produced by the latter mechanism is dominant. Solving the frequency equation of the cylindrical shell with liquid loading, the two Stoneley-type poles in the complex K plane are presented. They are the major sources of the reradiation of shell at low frequencies. Finally, effects of the shell radius, shell thickness, absorption of material and the flow speeds on the noise reduction are computed by numerical iniegration.
文摘A unified theory for calculating the noise radiation of an infinite elastic plate excited by the turbulent boundary layer pressure fluctuations is presented . Using the wave number frequency transfer function to desribe the whole system , consisting of the plate and the liquid loading, a general expression of the cross spectrum was derived. It is an integral in the complex wave number plane and leads to a sum of the residues at the poles of two types. One pole introduced by the convective ridge of the pressure fluctuations yields a direct transfer component , which is an evanescent wave in liquid because the pole lies in the high wave number region . The other poles introduced by the transfer function of structure produce the radiation field components with the resonance modes of a liquid loaded plate. The pole positions and their residues can be computed approximately by use of the Resonance Scattering Theory . For the case of hydrodynamic noise, where the range of the frequency-thickness product of interest is relatively low , the symmetric zero-order mode dominates the noise radiation.
文摘Finite hydrophone and hydrophone array are the wave vector filter and can re-duce the flow noise. In this paper the responses of the cylindrical area hydrophone and two-circular area hydrophone within viscoelastic cylindrical shell to the TBL (turbulent boundary layer) pressure fluctuations are investigated. Applying the method based on the wavenumber frequency spectrum analysis, the expressions of 1) the noise power spectrum of a single hy-drophone; 2) the space correlation of two hydrophones; 3) the noise power spectrum of array are derived. The dependencies of the noise reduction on hydrophone shape, dimension, element amount and separation of hydrophones of array are calculated by numerical integration. The wide-band and narrow-band correlation for two hydrophones is also calculated. The numerical results show that hydrophone array can effectively reduce the interior noise.
基金Project supported by the National Natural Science Foundation of China(Nos.10772159 and 10802030)the Research Fund for Doctoral Program of Higher Education of China(No.20060335125)
文摘We studied the response of harmonically and stochastically excited strongly nonlinear oscillators with delayed feedback bang-bang control using the stochastic averaging method. First, the time-delayed feedback bang-bang control force is expressed approximately in terms of the system state variables without time delay. Then the averaged It6 stochastic differential equations for the system are derived using the stochastic averaging method. Finally, the response of the system is obtained by solving the Fokker-Plank-Kolmogorov （FPK） equation associated with the averaged lt6 equations. A Duffing oscillator with time-delayed feedback bang-bang control under combined harmonic and white noise excitations is taken as an example to illus- trate the proposed method. The analytical results are confirmed by digital simulation. We found that the time delay in feedback bang-bang control will deteriorate the control effectiveness and cause bifurcation of stochastic jump of Duffing oscillator.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10932009, 11072212 and 50905051)Key Discipline of the Ocean Mechatronic Equipments Technology Foundation
文摘The first-passage failure of Duffing oscillator with the delayed feedback control under the combined harmonic and white-noise excitations is investigated. First, the time-delayed feedback control force is expressed approximately in terms of the system state variables without time delay. Then, the averaged It? stochastic differential equations for the system are derived by using the stochastic averaging method. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of the first-passage time are established. Finally, the conditional reliability function, the conditional probability density and moments of the first-passage time are obtained by solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. The effects of time delay in feedback control force on the conditional reliability function, conditional probability density and moments of the first-passage time are analyzed. The validity of the proposed method is confirmed by digital simulation.
