Effect of Ritz Vectors on Random Seismic Response of Cantilever Beam

Abstract

To understand the effect of Ritz vectors on the random seismic response of non-uniform cantilever beam, the following works are performed: Firstly, the equation of random seismic response of non-uniform cantilever beam based on Hamilton theory is presented. The solution is derived using the combined classical Ritz and pseudo-excitation method. Secondly, by considering the principle of virtual displacement, the pertinent function can be obtained from the characteristics of pseudo-excitation method. The mode of analysis is transformed from structural stationary random to structural harmonic response. Finally, the results of the analysis of the cantilever beam samples of different Ritz vectors are presented. The functional extremum corresponding to increasing Ritz vectors is compared. It can be concluded based on the result findings that the Ritz vectors, which satisfy both the geometrical and the natural boundary conditions, do not necessarily lead to accurate results. It is, therefore, recommended that the extreme value of the function for the whole system should be considered as an evaluation criterion for the Ritz vectors.