An explicit time-domain approach for sensitivity analysis of non-stationary random vibration problems

Abstract This paper presents an explicit time-domain method for sensitivity analysis of structural responses under non-stationary random excitations. Based on time-domain explicit expressions of dynamic responses, a new and more concise time-domain explicit expression of response sensitivity is derived using the direct differentiation method (DDM). Then a more efficient algorithm for direct construction of the explicit expression of response sensitivity is developed based on the physical meanings of the coefficient matrices in the formulation. The adjoint variable method (AVM) is further used to establish the explicit expression of the sensitivity of an arbitrary response. Finally, based on the time-domain explicit expressions for both dynamic response and its sensitivity, an efficient time-domain approach is proposed to calculate the sensitivity of variance responses of a structure subjected to non-stationary random excitations. Numerical examples of different structural systems under non-stationary random excitations are presented to demonstrate the accuracy and efficiency of the proposed method.

[1]  Qimao Liu,et al.  Sensitivity and Hessian Matrix Analysis of Evolutionary PSD Functions for Nonstationary Random Seismic Responses , 2012 .

[2]  Jiahao Lin,et al.  Accurate and highly efficient algorithms for structural stationary/non-stationary random responses , 2001 .

[3]  Giuseppe Marano,et al.  Sensitivity analysis of optimum stochastic nonstationary response spectra under uncertain soil parameters , 2008 .

[4]  Pierfrancesco Cacciola,et al.  A modal approach for the evaluation of the response sensitivity of structural systems subjected to non-stationary random processes , 2005 .

[5]  C. Su,et al.  Random vibration analysis of structures by a time-domain explicit formulation method , 2014 .

[6]  Kiyoshi Kanai,et al.  Semi-empirical Formula for the Seismic Characteristics of the Ground , 1957 .

[7]  S. Caddemi,et al.  Gaussian and non-Gaussian stochastic sensitivity analysis of discrete structural system , 2000 .

[8]  T. T. Soong,et al.  Random Vibration of Mechanical and Structural Systems , 1992 .

[9]  Masanobu Shinozuka,et al.  Simulation of Nonstationary Random Process , 1967 .

[10]  David Kennedy,et al.  Sensitivity analysis and optimization of vehicle-bridge systems based on combined PEM-PIM strategy , 2011 .

[11]  Yu-Kweng Michael Lin,et al.  Probabilistic Structural Dynamics: Advanced Theory and Applications , 1967 .

[12]  Subrata Chakraborty,et al.  Sensitivity evaluation in seismic reliability analysis of structures , 2004 .

[13]  Rui Xu,et al.  Efficient MCS for random vibration of hysteretic systems by an explicit iteration approach , 2014 .

[14]  H. Tajimi,et al.  Statistical Method of Determining the Maximum Response of Building Structure During an Earthquake , 1960 .

[15]  K. Bathe.  Finite Element Procedures , 1995 .

[16]  Haitao Ma,et al.  Fast Equivalent Linearization Method for Nonlinear Structures under Nonstationary Random Excitations , 2016 .

[17]  Subrata Chakraborty,et al.  STOCHASTIC DYNAMIC SENSITIVITY OF UNCERTAIN STRUCTURES SUBJECTED TO RANDOM EARTHQUAKE LOADING , 2002 .

[18]  Gui-Rong Liu,et al.  Dynamic design of structures under random excitation , 1998 .