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
In this article,the seismic performance of box-shaped steel piers embedded with energy-dissipating shells under a multi-directional seismic load is investigated.A finite element(FE)model was accurately established and...In this article,the seismic performance of box-shaped steel piers embedded with energy-dissipating shells under a multi-directional seismic load is investigated.A finite element(FE)model was accurately established and verified by the quasi-static test results.A parametric analysis of the hysteretic behaviour of a novel box-shaped steel pier under eccentric pressure was carried out on this basis.We discussed the influence of the eccentricity,axial compression ratio,thickness of embedded shell,ratio of slenderness,spacing of transverse stiffening ribs on the embedded shell,and width-to-thickness ratio of wallboard on the anti-seismic performance of a novel box-shaped steel bridge pier.The results revealed that the load carrying capacity and ductility coefficient of the specimen are substantially influenced by the eccentricity,variation in the axial compression ratio,and slenderness ratio.The specimen′s plastic energy dissipation capacity can be effectively improved by increasing the thickness of the embedded shell.The spacing of the transverse stiffening ribs only marginally affects seismic performance.In addition,the width-to-thickness ratio of the wallboard exerts a more considerable influence on the deformability of the square-section specimen.Finally,a formula for calculating the bearing capacity of the novel box-shaped steel piers under cyclic loading is proposed.展开更多
As a promising vibration control device, the vibro-impact nonlinear energy sink (VI-NES) gathered extensively attention in recent years. However, general optimization procedures have not been available forthe design o...As a promising vibration control device, the vibro-impact nonlinear energy sink (VI-NES) gathered extensively attention in recent years. However, general optimization procedures have not been available forthe design of VI-NES subjected to random excitations. To this end, this paper constitutes a research effortto address this gap. Specifically, the approximate analytical solution of the system stochastic responseis obtained in conjunction with non-smooth conversion and stochastic averaging methodology. Takingadvantages of this approximate solution, the variance of the system is defined and easily minimized tocalculate the optimal parameters for VI-NES. In addition, the results computed by this way fairly correlatewith direct numeric simulations.展开更多
Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determinin...Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructing the trial solution. The assumed solution consists of the analytically constructed trial solutions satisfying the sufficient conditions and an exponential polynomial of the state variables, and delivers a high accuracy of the solution because the analytically constructed trial solutions capture the main characteristics of the nonlinear system. We also make use of the concept from the data-science and propose a symbolic integration over a hypercube to replace the numerical integrations in a higher-dimensional space, which has been regarded as the insurmountable difficulty in the classical method of weighted residuals or stochastic averaging for high-dimensional dynamic systems. Three illustrative examples of MDOF nonlinear systems are analyzed in detail. The accuracy of the numerical results is validated by comparison with the Monte Carlo simulation(MCS) or the available exact solution. Furthermore, we also show the substantial gain in the computational efficiency of the proposed method compared with the MCS.展开更多
To enable rapid recovery of a steel bridge column after an earthquake,a novel tubular-section steel bridge column equipped with low-yield-point(LYP)steel tubular plates in the root replaceable pier is proposed.For the...To enable rapid recovery of a steel bridge column after an earthquake,a novel tubular-section steel bridge column equipped with low-yield-point(LYP)steel tubular plates in the root replaceable pier is proposed.For the purpose of discussing the seismic behavior of the novel steel bridge column,quasi-static tests and finite element simulation analyses of the specimens were carried out.The effects of parameters such as the axial compression ratio,eccentricity,and thickness and material strength of the tubular plate in the energy-dissipating zone are discussed.Experimental results from seven specimens that were subjected to four failure modes are presented.The damage to the quasi-static specimens is localized to the replaceable energy-dissipating pier.The seismic behavior of the novel steel bridge columns is significantly influenced by the axial compression ratio and eccentricity of specimens.Numerical results show that the high stress area of the specimens is mainly concentrated in the connection zone between the LYP steel tubular plate and the bottom steel plate,which is consistent with the position of the quasi-static specimen when it was prone to fracture.Finally,a calculation formula is proposed to facilitate the capacity prediction of this new steel tubular bridge column under repeated loading.展开更多
The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resona...The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.展开更多
Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction systems.Nevertheless,an effective approach to capture the non-smooth transition behavior of such sy...Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction systems.Nevertheless,an effective approach to capture the non-smooth transition behavior of such systems is still lacking.Accordingly,we propose a piecewise radial basis function neural network(RBFNN)strategy to solve the transient response of the randomly excited dry friction system.Within the established framework,the transient probability density function of the dry friction system is expressed in a piecewise form.Each segment of the solution is expressed by the sum of a series of Gaussian activation functions with time-dependent weights.These time dependent weights are solved by minimizing the loss function,which involves the residual of the Fokker-Planck-Kolmogorov equations and constraint conditions.To avoid the singularity of the initial condition being a Dirac delta function,a short-time Gaussian approximation strategy is presented to solve the initiating time-dependent weights.Based on some numerical results,the proposed scheme effectively performs.Moreover,a comparison with other existing methods reveals that the proposed scheme can completely capture the nonlinear characteristic of the dry friction system stochastic response more closely.Noteworthy,we can easily extend the proposed method to other types of non-smooth systems with piecewise response characteristics.Moreover,the semi-analytical solution provides a valuable reference for system optimization.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National Science Foundation of China under Grant No.51778248Natural Science Foundation of Fujian Province under Grant No.2018J01075+2 种基金Promotion Program for Young and Middle-aged Teacher in Science and Technology Research of Huaqiao University under Grant No.ZQN-PY312Research Trained Fund for Outstanding Young Researcher in Higher Education Institutions of Fujian ProvinceSubsidized Project for Postgraduates′Innovative Fund in Scientific Research of Huaqiao University under Grant No.18013086021。
文摘In this article,the seismic performance of box-shaped steel piers embedded with energy-dissipating shells under a multi-directional seismic load is investigated.A finite element(FE)model was accurately established and verified by the quasi-static test results.A parametric analysis of the hysteretic behaviour of a novel box-shaped steel pier under eccentric pressure was carried out on this basis.We discussed the influence of the eccentricity,axial compression ratio,thickness of embedded shell,ratio of slenderness,spacing of transverse stiffening ribs on the embedded shell,and width-to-thickness ratio of wallboard on the anti-seismic performance of a novel box-shaped steel bridge pier.The results revealed that the load carrying capacity and ductility coefficient of the specimen are substantially influenced by the eccentricity,variation in the axial compression ratio,and slenderness ratio.The specimen′s plastic energy dissipation capacity can be effectively improved by increasing the thickness of the embedded shell.The spacing of the transverse stiffening ribs only marginally affects seismic performance.In addition,the width-to-thickness ratio of the wallboard exerts a more considerable influence on the deformability of the square-section specimen.Finally,a formula for calculating the bearing capacity of the novel box-shaped steel piers under cyclic loading is proposed.
基金This work is supported by the National Natural Science Foundation of China(No.12072118)the National Natural Science Funds for Distinguished Young Scholar of the Fujian Province of China(No.2021J06024)the Project for Youth Innovation Fund of Xiamen(No.3502Z20206005).
文摘As a promising vibration control device, the vibro-impact nonlinear energy sink (VI-NES) gathered extensively attention in recent years. However, general optimization procedures have not been available forthe design of VI-NES subjected to random excitations. To this end, this paper constitutes a research effortto address this gap. Specifically, the approximate analytical solution of the system stochastic responseis obtained in conjunction with non-smooth conversion and stochastic averaging methodology. Takingadvantages of this approximate solution, the variance of the system is defined and easily minimized tocalculate the optimal parameters for VI-NES. In addition, the results computed by this way fairly correlatewith direct numeric simulations.
基金Project supported by the National Natural Science Foundation of China (Nos.11672111,11332008,11572215,and 11602089)the Program for New Century Excellent Talents in Fujian Province’s University+1 种基金the Natural Science Foundation of Fujian Province of China (No.2019J01049)the Scholarship for Overseas Studies from Fujian Province of China。
文摘Analytical and numerical studies of multi-degree-of-freedom(MDOF) nonlinear stochastic or deterministic dynamic systems have long been a technical challenge.This paper presents a highly-efficient method for determining the stationary probability density functions(PDFs) of MDOF nonlinear systems subjected to both additive and multiplicative Gaussian white noises. The proposed method takes advantages of the sufficient conditions of the reduced Fokker-Planck-Kolmogorov(FPK) equation when constructing the trial solution. The assumed solution consists of the analytically constructed trial solutions satisfying the sufficient conditions and an exponential polynomial of the state variables, and delivers a high accuracy of the solution because the analytically constructed trial solutions capture the main characteristics of the nonlinear system. We also make use of the concept from the data-science and propose a symbolic integration over a hypercube to replace the numerical integrations in a higher-dimensional space, which has been regarded as the insurmountable difficulty in the classical method of weighted residuals or stochastic averaging for high-dimensional dynamic systems. Three illustrative examples of MDOF nonlinear systems are analyzed in detail. The accuracy of the numerical results is validated by comparison with the Monte Carlo simulation(MCS) or the available exact solution. Furthermore, we also show the substantial gain in the computational efficiency of the proposed method compared with the MCS.
基金National Natural Science Foundation of China under Grant No.51778248Natural Science Foundation of Fujian Province under Grant No.2018J01075+1 种基金Education and Science Project for Young and Middle-aged Teacher of Fujian Province under Grant No.JAT200825Research Trained Fund for Outstanding Young Researcher in Higher Education Institutions of Fujian Province。
文摘To enable rapid recovery of a steel bridge column after an earthquake,a novel tubular-section steel bridge column equipped with low-yield-point(LYP)steel tubular plates in the root replaceable pier is proposed.For the purpose of discussing the seismic behavior of the novel steel bridge column,quasi-static tests and finite element simulation analyses of the specimens were carried out.The effects of parameters such as the axial compression ratio,eccentricity,and thickness and material strength of the tubular plate in the energy-dissipating zone are discussed.Experimental results from seven specimens that were subjected to four failure modes are presented.The damage to the quasi-static specimens is localized to the replaceable energy-dissipating pier.The seismic behavior of the novel steel bridge columns is significantly influenced by the axial compression ratio and eccentricity of specimens.Numerical results show that the high stress area of the specimens is mainly concentrated in the connection zone between the LYP steel tubular plate and the bottom steel plate,which is consistent with the position of the quasi-static specimen when it was prone to fracture.Finally,a calculation formula is proposed to facilitate the capacity prediction of this new steel tubular bridge column under repeated loading.
基金Project supported by the National Natural Science Foundation of China (Grant No. 12072118)the Natural Science Funds for Distinguished Young Scholar of the Fujian Province, China (Grant No. 2021J06024)the Project for Youth Innovation Fund of Xiamen, China (Grant No. 3502Z20206005)。
文摘The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.
基金supported by the National Natural Science Foundation of China(Grant No.12072118)the Natural Science Funds for Distinguished Young Scholar of the Fujian Province of China(Grant No.2021J06024)the Project for Youth Innovation Fund of Xiamen(Grant No.3502Z20206005)。
文摘Over the years,practical importance and interesting dynamical features have caused a growing interest in dry friction systems.Nevertheless,an effective approach to capture the non-smooth transition behavior of such systems is still lacking.Accordingly,we propose a piecewise radial basis function neural network(RBFNN)strategy to solve the transient response of the randomly excited dry friction system.Within the established framework,the transient probability density function of the dry friction system is expressed in a piecewise form.Each segment of the solution is expressed by the sum of a series of Gaussian activation functions with time-dependent weights.These time dependent weights are solved by minimizing the loss function,which involves the residual of the Fokker-Planck-Kolmogorov equations and constraint conditions.To avoid the singularity of the initial condition being a Dirac delta function,a short-time Gaussian approximation strategy is presented to solve the initiating time-dependent weights.Based on some numerical results,the proposed scheme effectively performs.Moreover,a comparison with other existing methods reveals that the proposed scheme can completely capture the nonlinear characteristic of the dry friction system stochastic response more closely.Noteworthy,we can easily extend the proposed method to other types of non-smooth systems with piecewise response characteristics.Moreover,the semi-analytical solution provides a valuable reference for system optimization.
