Dynamic response analysis of stochastic truss structures under non-stationary random excitation using the random factor method

Abstract The dynamic characteristics and responses of stochastic truss structures under non-stationary random excitation are investigated using a new method called the random factor method (RFM). Using the RFM, the structural physical parameters and geometry can be considered as random variables. Based on the assumption that the randomness on each element is the same for all elements, the structural stiffness and mass matrices can then respectively be described by the product of two parts corresponding to the random factor and the deterministic matrix. From the expressions of structural random response in the frequency domain, computational expressions for the mean value, standard deviation and variation coefficient of the mean square value of the non-stationary random displacement and stress response are developed by means of the random variable’s functional moment method and the algebra synthesis method. The influences of the randomness of the structural parameters on the dynamic characteristics, structural displacement and stress responses are demonstrated using a truss structure.

[1]  Michał Kleiber,et al.  Perturbation based stochastic finite element method for homogenization of two-phase elastic composites , 2000 .

[2]  Manolis Papadrakakis,et al.  Parallel solution methods for stochastic finite element analysis using Monte Carlo simulation , 1999 .

[3]  Ted Belytschko,et al.  Transient probabilistic systems , 1988 .

[4]  Jian-Jun Chen.  Analysis of engineering structures response to random wind excitation , 1994 .

[5]  Mihailo D. Trifunac,et al.  A note on the nonstationarity of seismic response of structures , 2000 .

[6]  Wei Gao,et al.  Optimal placement of active bars in active vibration control for piezoelectric intelligent truss structures with random parameters , 2003 .

[7]  M. Junk,et al.  Quasi-Monte Carlo algorithms for diffusion equations in high dimensions , 2005, Math. Comput. Simul..

[8]  J. Tinsley Oden,et al.  Research directions in computational mechanics , 2003 .

[9]  David Moens,et al.  A survey of non-probabilistic uncertainty treatment in finite element analysis , 2005 .

[10]  N. C. Nigam,et al.  Applications of Random Vibrations , 1994 .

[11]  W. Thomson.  Theory of vibration with applications , 1965 .

[12]  H. Saunders,et al.  Random vibration of structures , 1986 .

[13]  S. Maire,et al.  Quasi-Monte Carlo quadratures for multivariate smooth functions , 2006 .

[14]  Yi Ping.  Stationary random responses of structures with stochastic parameters , 2001 .

[15]  Hector A. Jensen,et al.  Response of Systems with Uncertain Parameters to Stochastic Excitation , 1992 .

[16]  Zhao Lei,et al.  Neumann dynamic stochastic finite element method of vibration for structures with stochastic parameters to random excitation , 2000 .

[17]  Izuru Takewaki,et al.  Critical Envelope Function for Nonstationary Random Earthquake Input , 2004 .

[18]  Yong Sun,et al.  Non-stationary random seismic responses of non-uniform beams , 1995 .

[19]  George Stefanou,et al.  Stochastic finite element analysis of shells with combined random material and geometric properties , 2004 .

[20]  Marcin Kamiński,et al.  Monte-Carlo simulation of effective conductivity for fiber composites , 1999 .

[21]  Yabin Zhou,et al.  Dynamic response analysis of closed-loop control system for random intelligent truss structure under random forces , 2004 .

[22]  Marcin Kamiński,et al.  Stochastic finite element modeling of transient heat transfer in layered composites , 1999 .

[23]  Jon C. Helton,et al.  A comparison of uncertainty and sensitivity analysis results obtained with random and Latin hypercube sampling , 2005, Reliab. Eng. Syst. Saf..

[24]  N.G.R. Iyengar,et al.  Natural frequencies of composite plates with random material properties using higher-order shear deformation theory , 2001 .

[25]  Christian Bucher,et al.  Sensitivity of expected exceedance rate of SDOF-system response to statistical uncertainties of loading and system parameters , 1987 .

[26]  Antonina Pirrotta,et al.  Stochastic dynamics of linear elastic trusses in presence of structural uncertainties (virtual distortion approach) , 2004 .

[27]  Mingtao Cui,et al.  Dynamic response analysis of linear stochastic truss structures under stationary random excitation , 2005 .

[28]  Kyu Nam Cho.  Mass perturbation influence method for dynamic analysis of offshore structures , 2002 .