Buckling and Vibration of Fully Clamped Functionally Graded Material Microplates With Partial Cracks Under Thermal Effects Using the Symplectic Method

The free vibration and buckling of partially cracked isotropic and functionally graded material rectangular microplates in a thermal environment are investigated. Thermal effects are introduced into the control equations as thermal bending moments and in‐plane forces, while the linear spring model represents cracks. Furthermore, analytical solutions in series form are obtained for the free vibration and buckling of fully clamped microplates using the symplectic superposition method. The obtained analytical solutions are uniformly applicable to solving the dynamic problems of isotropic and functionally graded material microplates. Using this solution, the effects of different parameters on the natural frequency and critical buckling temperature of the plate are systematically analyzed through specific numerical examples. The results indicate that cracks significantly reduce the natural frequency and critical buckling temperature of the plate, whereas the internal material length scale parameter increases the natural frequency and enhances the plate's resistance to thermal buckling. The accuracy of the analytical solutions obtained in this work is verified against existing results in the literature. Furthermore, convergence analysis demonstrates that the symplectic superposition solutions converge rapidly.