RAYLEIGH-RITZ ANALYSIS OF ELASTICALLY CONSTRAINED THIN LAMINATED PLATES ON WINKLER INHOMOGENEOUS FOUNDATIONS

Anisotropic layered composite plates laying on Winkler foundations are analyzed in this paper. Different boundary conditions are examined: i deal constraints as well as elastic ones are taken into account. For a ny given structure, i.e. for any lamination sequence, a method is deve loped to determine the relevant eigenproperties such as the first fund amental frequencies and the associated eigenmodes. The main objectives of the paper include: (i) identification of a lamination sequence so as to extremize the eigenvalues of the system; (ii) determination of t he effects of elastic foundations, homogeneous as well as inhomogeneou s, on the properties of the system; (iii) incorporating in the formula tion constraints of elastic nature, for their relevance in view of pra ctical applications; (iv) investigating the effectiveness of the Rayle igh-Ritz method in limit cases such as high gradients and stiffnesses. The Rayleigh-Ritz method is used herein as analysis method: polynomia l functions defined over the entire domain of definition of the struct ure are derived which satisfy the geometric boundary conditions and ma y locally violate the natural ones. The solution is then expanded as a finite sum of such functions which thus constitute a basis of finite dimension. Numerical examples are worked out to demonstrate the monoto nic convergence of the Rayleigh-Ritz based solution to the ideally con strained one when the stiffness of the boundaries grows large.