Free vibration analysis of FGM non-coplanar plate assemblies with arbitrary boundary conditions through a novel analytic method

A novel analytic model is proposed for free vibration analysis of FGM non-coplanar plate assemblies with arbitrary boundary conditions. To establish the governing equation, the titled structures are firstly decomposed to several independent rectangular plates. The first-order shear deformation theory (FSDT) and the superposition method are employed, and both out-of-plane and in-plane displacements and forces are simultaneously expressed as some unknowns. Then, continuity conditions at coupling edges are utilized to assemble all plates, and displacements at other edges are restrained by artificial springs. By virtue of the orthonormal properties of trigonometric functions, continuity and boundary conditions become a series of algebraic equations, which are integrated to form the final governing equation. To evaluate the accuracy and application, natural frequencies of four different models are compared, and present results agree well with ones of the literature, finite element method and modal testing. Furthermore, influences of material parameters, elastic boundary conditions and discontinuity conditions are carried out. The results reveal that major differences between FGM and homogenous L-shaped plates are natural frequencies and mode shapes keep unchanged. The increase of coupling angle can efficiently increase natural frequencies as the coplanar plate becomes non-coplanar L-shaped one, and natural frequencies slightly change as the nonzero coupling angle further increases. Three discontinuity conditions including the coupling angle, coupling location and thickness can obviously affect natural frequencies of L-shaped plates.