Dynamic Behavior Analysis of an Axially Loaded Beam Supported by a Nonlinear Spring-Mass System

Abstract

Dynamic analysis of an Euler–Bernoulli beam with nonlinear supports is receiving greater research interest in recent years. Current studies usually consider the boundary and internal nonlinear supports separately, and the system rotational restraint is usually ignored. However, there is little study considering the simultaneous existence of axial load, lumped mass and internal supports for such nonlinear problem. Motivated by this limitation, the dynamic behavior of an axially loaded beam supported by a nonlinear spring-mass system is solved and investigated in this paper. Modal functions of an axially loaded Euler–Bernoulli beam with linear elastic supports are taken as trail functions in Galerkin discretization of the nonlinear governing differential equation. Stable steady-state response of such axially loaded beam supported by a nonlinear spring-mass system is solved via Galerkin truncation method, which is also validated by finite difference method. Results show that parameters of nonlinear spring-mass system and boundary condition have a significant influence on system dynamic behavior. Moreover, appropriate nonlinear parameters can switch the system behavior between the single-periodic state and quasi-periodic state effectively.