Nonlinear vibrations of a bi-material beam under thermal and mechanical loadings

Abstract

Nonlinear vibration of a two layers (bi-material) beam under thermal and mechanical loadings is studied in the paper. The model of the beam is based on the extended Timoshenko beam theory taking into account geometric nonlinearities. The derived nonlinear partial differential equations are reduced to ordinary differential equations for the first three vibration modes. The reduced model is compared with results based on modal experimental analysis and the finite element method and a very good agreement was found. The complete bifurcation analysis is carried out for the reduced 3 DOF system for the clamped–clamped boundary conditions. The obtained resonance curves demonstrated the hardening phenomenon with instability zones in a case of large vibrations. The elevated temperature leaded to buckling, stronger modes interaction, an increase of instability zones occurring on the resonance curves and to chaotic oscillations coexisting with the periodic response.