This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment sta...This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.展开更多
An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that con- stants can be o...An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that con- stants can be obtained from first three-order response moments was used to map a non-Gaussian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load, it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 11072107 and 91016022)the Specialized Research Fund for the Doctoral Program of Higher Education of China (GrantNo.20093218110003)
文摘This article examines a viscoelastic plate that is driven parametrically by a non-Guassian colored noise,which is simplified to an Ornstein-Uhlenbeck process based on the approximation method.To examine the moment stability property of the viscoelastic system,we use the stochastic averaging method,Girsanov theorem and Feynmann-Kac formula to derive the approximate analytic expansion of the moment Lyapunov exponent.Furthermore,the Monte Carlo simulation results for the original system are given to check the accuracy of the approximate analytic results.At the end of this paper,results are presented to show some quantitative pictures of the effects of the system parameters,noise parameters and viscoelastic parameters on the stability of the viscoelastic plate.
基金the National Natural Science Foundation of China (No. 50478017)
文摘An analytical moment-based method was proposed for calculating first passage probability of structures under non-Gaussian stochastic behaviour. In the method, the third-moment standardization that con- stants can be obtained from first three-order response moments was used to map a non-Gaussian structural response into a standard Gaussian process; then the mean up-crossing rates, the mean clump size and the initial passage probability of some critical barrier level by the original structural response were estimated. Finally, the formula for calculating first passage probability was established on the assumption that the corrected up-crossing rates are independent. By a nonlinear single-degree-of-freedom system excited by a stationary Gaussian load, it is demonstrated how the procedure can be used for the type of structures considered. Further, comparisons between the results from the present procedure and those from Monte-Carlo simulation are performed.
