Nonlinear Vibration of Temperature-Dependent FGM Beams with Symmetric and Asymmetric Boundary Conditions via the Generalized Differential Quadrature Method

Functionally graded (FG) materials can deliver greater mechanical performance compared to pure isotropic and composite materials. Temperature has a significant effect on structural performance, as it can substantially reduce the stiffness parameter and induce thermal stresses in fully restrained structures. This study investigates the nonlinear free vibration of functionally graded beams under a thermal environment. First, the nonlinear formulation of a Timoshenko beam using von Kármán nonlinear strain theory is derived. Then, the effect of temperature is applied. Finally, using the generalized quadrature method, which is a mesh-free method, the nonlinear vibration of the FG beam with different boundary conditions is analyzed. To the best of the authors’ knowledge, this study distinctively contributes to the existing literature by providing a rigorous integration of the GDQM with strongly nonlinear thermal vibration of FG beams, highlighting the lack of purely mesh-free treatments incorporating such coupled physics. The results show that increasing the temperature can lead to an instability phenomenon. Specifically, temperature increments cause a thermally induced mode change, profoundly altering the dynamic response. The conducted parametric study indicates that increasing the gradient index n enhances the nonlinear vibration behavior of FG beams.