Nonlinear transverse vibrations of a jointed structure with two slightly curved beams connected by complex elastic joints

Abstract

The research of jointed structures has attracted extensive attention and most of the current research focuses on the dynamic modeling and analysis of straight-beam jointed structures, while sometimes the jointed structures are composed of curved beams in engineering practice. Therefore, this paper aims to propose a novel nonlinear dynamic modeling method regarding a jointed structure with two slightly curved beams (SCBs) connected by complex elastic joints. Firstly, the nonlinear dynamic analytic model of a single SCB is established as one part of the jointed structure. Secondly, the idea of the global mode method is used to establish the entire nonlinear dynamic analytic model of a two-SCB jointed structure and obtain its natural frequencies and mode shapes. The dynamic characteristics of the complex elastic joints are subsequently introduced into the entire nonlinear dynamic analytic model of the jointed structure by applying the equilibrium conditions and boundary conditions. Thirdly, a procedure to calculate the forced vibration responses of the two-SCB jointed structure is proposed by successively using the Galerkin truncation method, harmonic balance method and pseudo arc-length method. Finally, the proposed nonlinear dynamic modeling method is validated by carrying out case studies and the results calculated by the proposed method are in good agreement with the results of finite element analysis, which demonstrates the accuracy of the proposed nonlinear dynamic modeling method. Furthermore, the effects of stiffness at the complex elastic joints, external excitation amplitude, and initial curvature on the nonlinear dynamic characteristics of the jointed structure are also analyzed by the comparative case studies.