Rayleigh-Ritz analysis of elastically constrained thin laminated plates on Winkler inhomogeneous foundations Original Research Article

Anisotropic layered composite plates laying on Winkler foundations are analyzed in this paper. Different boundary conditions are examined: ideal constraints as well as elastic ones are taken into account. For any given structure, i.e. for any lamination sequence, a method is developed to determine the relevant eigenproperties such as the first fundamental 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 the effects of elastic foundations, homogeneous as well as inhomogeneous, on the properties of the system; (iii) incorporating in the formulation constraints of elastic nature, for their relevance in view of practical applications; (iv) investigating the effectiveness of the Rayleigh-Ritz method in limit cases such as high gradients and stiffnesses. The Rayleigh-Ritz method is used herein as analysis method: polynomial functions defined over the entire domain of definition of the structure are derived which satisfy the geometric boundary conditions and may 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 monotonic convergence of the Rayleigh-Ritz based solution to the ideally constrained one when the stiffness of the boundaries grows large.