VIBRATION AND BUCKLING OF ANISOTROPIC PLATE ASSEMBLIES WITH WINKLER FOUNDATIONS

Numerous papers have presented alternative stiffness matrices for an individual plate of any prismatic assembly of plates that is either vibrating or buckling. The associated displacements vary sinusoidally with the longitudinal co-ordinate and time, and in the most powerful theories the spatial phase differences caused by anisotropy or in-plane shear are allowed for. Some of the plate stiffness matrices are approximate finite strip ones, but others are exact and are given either by entirely explicit expressions or by a mixture of explicit expressions and numerical procedures. It is shown that very minor adaptations will usually be sufficient to enable any of these alternative stiffness matrices to include Winkler foundations. Detail is given of the adaptations needed in the case of the most general entirely explicit, exact, member stiffness expressions known to the authors. Out-of-plane and in-plane Winkler stiffnesses are included, but with the latter restricted to be the same for all directions in the plane. These adaptations required only a handful of lines of the associated computer program to be changed. Numerical stiffnesses are presented for three problems which adequately cover the alternative (parameter-dependent) forms which the explicit expressions can take. These numerical stiffnesses can be used as a benchmark check for other theories, because they have been independently verified by increasing the number of narrow strips used to approximate the plate until convergence to the values presented was demonstrated. Finally, appropriate general cautions are given which apply whenever any existing plate stiffness matrices are adapted to include Winkler foundations. © 1990.