Dynamic Analysis and Design of Uncertain Systems Against Random Excitation Using probabilistic Method

In this paper, a method to obtain the sensitivity of eigenvalues and the random responses of the structure with uncertain parameters is proposed. The concept of the proposed method is that the perturbed equation of each uncertain substructure is obtained using the finite element method, and the perturbed equation of the overall structure is obtained using the mode synthesis method. By this way, the reduced order perturbed equation of the uncertain system can be obtained. And the response of the uncertain system is obtained using probability method. As a numerical example, a simple piping system is considered as an example structure. The damping and spring constants of the support are considered as the uncertain parameters. Then the variations of the eigenvalues, the correlation function and the power spectral density function of the responses are calculated. As a result, the proposed method is considered to be useful technique to analyze the sensitivities of eigenvalues and random response against random excitation in terms of the accuracy and the calculation time.