Free vibration analysis of two-dimensional functionally graded coated and undercoated substrate structures

In this paper, the free vibration behaviors of the functionally graded (FG) coated and undercoated substrate structures are studied by a meshfree boundary–domain integral equation method. Based on the two-dimensional elasticity theory, the boundary–domain integral equations for each single layer of these coating–substrate structures are derived initially by using elastostatic fundamental solutions. Employ the radial integration method to transform the domain integrals into boundary integrals and achieve a meshfree scheme. By applying the multi-region boundary element method, obtain the generalized eigenvalue system of the whole structure, which involves system matrices with boundary integrals only and the complete solutions for natural frequency and vibration modes are rigidly resolved. A comparative study of FG versus homogeneous coating is conducted. The influences of material composition, material gradient, coating thickness ratio, substrate structure aspect ratio and the boundary conditions on the natural frequencies of the FG coated and undercoated substrate structure are evaluated and discussed.