Variational Principles and Explicit Finite-Element Formulations for the Dynamic Analysis of Partial-Interaction Composite Beams

Abstract

In this paper, we conduct a systematic dynamic investigation of partial-interaction composite beams under various sophisticated loading conditions that have seldom been presented in the literature. For the purpose of easy implementation of the present theory and the convenience of interested readers, we utilize the dynamic variational principles under the same framework of the (extended) Hamilton’s principle to develop finite-element (FE) formulations for the dynamic responses of composite beams with Timoshenko’s beam theory. The forced vibrations of composite beams are focused with a transverse point load, a moving mass, or a moving mass-spring-damper system, respectively, some of which are important in the consideration of the vehicle–bridge (structure) interaction. The explicit expressions of the local FE expressions are also given in the appendixes. The developed dynamic FE theoretical framework is validated against numerical results in the literature with excellent agreement. We believe that the present work provides a solid theoretical foundation for the future research of vehicle/load–composite beam interactions that have seldom been studied.