Free vibration analysis of pre/post buckled rotating functionally graded beams subjected to uniform temperature rise

In this paper, a comprehensive examination is presented to study the free vibration treatment of pre- and post-buckled rotating functionally graded beams. The framework of the Euler-Bernoulli beam model alongside the von-Karman strain-displacement relationship is employed to access the weak form of the nonlinear governing equations. The thermo-mechanical properties of the constituent materials are considered to be temperature-dependent. The nonlinear finite element method is accompanied by some proposed algorithms to release the pre/post-buckling natural frequencies. The outcomes for the pre/post-buckling fundamental natural frequencies reveal that rotating simply-clamped beams treat qualitatively different in comparison with the other boundary condition types including the clamped-simply one although stationary simply-clamped and clamped-simply beams treat similarly.

Automated summary

This paper presents a comprehensive examination of the free vibration treatment of pre- and post-buckled rotating functionally graded beams, utilizing the nonlinear finite element method and temperature-dependent thermo-mechanical properties. The outcomes reveal that rotating simply-clamped beams treat qualitatively differently from other boundary condition types.