Free vibration of thick generally laminated quadrilateral plates having arbitrarily located point supports

Free vibration of generally laminated plates having arbitrarily located point supports is studied via the Rayleigh-Ritz method. Chebychev polynomials are chosen as the trial functions and essential boundary conditions along the edges are imposed by means of appropriate large artificial springs, This allows for the edges of the plate to be free, simply supported, or clamped. An elastically restrained point is represented by the appropriate spring constant value and by allowing this spring constant to become large, a point support is represented. The first-order shear deformation theory is utilized in the development of the equations of motion, along with the linear stress/strain relationship. Verification of the method is carried out through comparison with published results for point-supported plates. After the method is verified, a brief study of generally laminated plates having point supports is carried out. The method developed is simple and efficient, making it perfectly suited to applications that require multiple calculations, such as optimization, and can be applied to analyze joined-wings and truss-braced wings.