Nonlinear vibrations of a bi-material beam under thermal andmechanical loadings

Nonlinear vibration of a two layers (bi-material) beam under thermal and mechanical loadingsis studied in the paper. The model of the beam is based on the extended Timoshenko beamtheory taking into account geometric nonlinearities. The derived nonlinear partial differentialequations 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 thefinite element method and a very good agreement was found. The complete bifurcation analysisis carried out for the reduced 3 DOF system for the clamped-clamped boundary conditions.The obtained resonance curves demonstrated the hardening phenomenon with instability zonesin a case of large vibrations. The elevated temperature leaded to buckling, stronger modesinteraction, an increase of instability zones occurring on the resonance curves and to chaoticoscillations coexisting with the periodic response

Automated summary

The paper investigates the nonlinear vibration of a two-layer beam under thermal and mechanical loadings. The model is based on the extended Timoshenko beam theory considering geometric nonlinearities. The obtained resonance curves show a hardening phenomenon and instability zones under large vibrations. Elevated temperature leads to buckling, increased interaction of stronger modes, more instability zones, and coexisting chaotic oscillations with periodic response.