Hermite radial basis collocation method for vibration of functionally graded plates with in-plane material inhomogeneity

• A HRBCM is proposed for the eigenvalue analysis of thin plate vibration.
• Vibration analysis of FGM plates with in-plane material inhomogeneity is studied.
• Effects on the natural frequencies and mode shapes are numerically investigated.

A meshfree Hermite-type collocation method with radial basis functions is presented to investigate the free vibration of thin FGM plates with in-plane material inhomogeneity. For the eigenvalue analysis of thin plate vibration, conventional radial basis collocation method (RBCM) leads to an over-determined system for the eigenproblems, while Hermite radial basis collocation method (HRBCM) introducing more degrees of freedom can result in a determined system. Convergence and comparison studies with analytical solutions demonstrate the effectiveness and accuracy of the proposed method. Effects on the natural frequencies and mode shapes originated from the material inhomogeneity are numerically investigated.