THE PROBABILITY DENSITY EVOLUTION METHOD FOR COMPOUND RANDOM VIBRATION ANALYSIS OF STOCHASTIC STRUCTURES

A probability density evolution method for compound random vibration analysis of stochastic structures is proposed. The augmented state vector is introduced to construct a state equation with random initial conditions. The probability density evolution equation (PDEE) for the response of compound random vibrations is deduced. With the precise integration method and the Lax-Wendroff difference scheme, the PDEE is solved numerically. An example is studied where the probability densities of the response of an 8-story floor shear frame structure are evaluated, verifying the high computational efficiency, stable convergence and high accuracy of the present method. The investigations demonstrate that the probability density curves tend to be complex with time, which means that the widely applied second moment method for reliability evaluation based on normal distribution assumption may have great deviation. In addition, compared with the response when only the randomness of the structural parameter is taken into account and only the randomness of the input is considered, the probability density curves of the response of compound vibration have lower peak and wider distribution, and the fluctuation of the response of compound vibration is enlarged in contrast to that of response of vibration with single randomness source.