A new method for random vibration analysis of stochastic truss structures

A new method called the random factor method (RFM) for the natural frequency, mode shape and random vibration analysis of stochastic truss structures is presented in this paper. Using the RFM, the structural physical parameters and geometry can be considered as random variables. The structural stiffness and mass matrices can then, respectively, be described by the product of two parts corresponding to the random factors and the deterministic matrix. The structural natural frequencies, mode shapes and random response can be expressed as the function of the random factors. By means of the random variable's functional moment method and the algebra synthesis method, computational expressions for the mean value, standard deviation and variation coefficient of the dynamic characteristics, mean square value of the stationary random displacement and stress response are developed. The influences of the randomness of the structural parameters on the dynamic characteristics, structural displacement and stress responses are demonstrated using a truss structure and Monte-Carlo simulations illustrate the efficiency of the proposed method.