Stochastic Structure Dynamic Analysis And Optimization Design Based On Dynamic Reliability

Stochastic structure dynamic analysis and optimization design based on dynamic reliability have wide engineering background and are of important theoretical significance and research worthiness. This paper developed the theory of stochastic structure dynamic analysis, and studied the dynamic reliability of stochastic structure and structure optimization design based on the dynamic reliability. The main research works can be described as follows.1. Stochastic dynamic characteristic analysis of stochastic structure.Considering the randomness of physics parameters and geometric dimensions, to the uniform stochastic structure all the elements of which have the same randomness, the analytic model of the stochastic structural frequencies are built from the Rayleigh formula with the Random Factor Method. And then putting the random frequencies into the dynamic characteristic equation, the connection between the randomness of frequencies and that of mode shapes is gained. And the randomness of canonical mode shapes is analyzed from its educing process.Furthermore, to the inhomogeneous stochastic structure all the elements of which have not the same randomness, the stiff matrix and mass matrix are outspreaded to several matrixes separately. Taking them into the Rayleigh formula, the obvious functional expression of stochastic structural frequency about every structural random parameter can be gotten. The computational expression of the sensitivity of stochastic structural every rank frequency to every physical parameter and geometrical parameter of different element are educed from the expression of stochastic structural frequency. The upper and lower limits of mode shapes are calculated from the 3σrule, and then the mean value and the variance of the mode shapes can be computed. Finally, the influence of the randomness of structural physical and geometric dimensions parameters on the structural frequencies and mode shapes is analyzed by several examples with the method of this paper and the Monte Carlo method, validating the feasibility of this method presented in this paper.2. Dynamic response analysis of stochastic structure with random excitation.Based on the analysis of stochastic structural frequencies and mode shapes above, from the expressions of structural random vibration of the frequency domain, the computational expressions of the mean value and variance of the mean square value of the structural displacement and stress response under the stationary random excitation...