The Local Effect Of The Random Excitation

Finite element method is commonly used in dynamic analysis of structures. The magnitude of dynamic internal force and dynamic displacement and their change laws can be obtained by solving dynamic equations with these methods, but the effects of structural inertia force induced by continuous masses on the internal forces of elements, i.e. the effects of local dynamic responses, are neglected. However, theories and practices prove that while density of the material is high, external damping is very large, whiplash happens or solid-liquid couples with structural system, local dynamic responses have great effects on the internal forces of elements. The errors will be caused if the local dynamic responses of structures are not considered in these cases.In this paper, aiming at the developmental conditions of the local dynamic responses at present, further discussions on local dynamic responses of structures under random excitation are proceeded based on achievements at home or abroad. Firstly, the calculational formulas of response deviations are deduced when power spectral density function are white noise and filtered white noise by using mathematical integral formulas, the calculational formulas of local dynamic responses of beam element, plate element, and shell element under random excitation are deduced. And then calculational models for local dynamic responses are established. Secondly, the corresponding computer program of local dynamic responses is compiled based on the deduced calculational formulas. Finally, using the compiled computer program, the local responses of structures under random excitation are calculated and analyzed. Some significative conclusions are acquired.The numerical results show that the local dynamic responses have great effects on some members, and have more effects on life forecast , thus local dynamic responses have dominating effects on the design, which are neglected before. This paper indicates that the local dynamic responses should be considered in dynamic analysis of structures.This research is one of fund items which are imbursed by national natural science fund and Shandong province natural science fund.