Free in-plane vibration of irregular laminated plate with curved edges based on boundary-type Chebyshev–Ritz method

The free in-plane vibration characteristics of laminated plate with arbitrarily geometrical shape and generally restrained edges, including curved and inclined edges, are investigated based on the boundary-type Chebyshev–Ritz method (BCRM). By adopting the divergence theorem, the double integral encountered in solving the energy equation of irregular laminates is converted to the integral on the boundary edge, which effectively reduces the computational complexity of the involved domain. The Chebyshev polynomials are utilized as test functions and the primitives of domain integrand functions are deduced according to the properties of Chebyshev polynomials. General boundary conditions on straight or even curved edges are achieved by introducing normal and tangential springs and assigning reasonable stiffness values. Natural frequencies and modes of laminated composite plates with straight edges (triangle, square, trapezoid, and hexagon), laminated composite plates with curved edge (ellipse), and irregular laminated composite plates are obtained. The method validation is carried out by comparison of the obtained solutions with literature and finite element results. The effects of variations in layering mode, number of layers, boundary conditions, and geometry on the eigenpairs of composite plate are extensively discussed.