Thermo-mechanical nonlinear vibration analysis of a spring-mass-beam system

Abstract

Thermo-mechanical vibrations of a simply supported spring-mass-beam system are investigated analytically in this paper. Taking into account the thermal effects, the nonlinear equations of motion and internal/ external boundary conditions are derived through Hamilton’s principle and constitutive relations. Under quasi-static assumptions, the equations governing the longitudinal motion are transformed into functions of transverse displacements, which results in three integro-partial differential equations with coupling terms. These are solved using the direct multiple-scale method, leading to closed-form solutions for the mode functions, nonlinear natural frequencies and frequency–response curves of the system. The influence of system parameters on the linear and nonlinear natural frequencies, mode functions, and frequency–response curves is studied through numerical parametric analysis. It is shown that the vibration characteristics depend on the mid-plane stretching, intra-span spring, point mass, and temperature change.