Dynamic response of Mindlin plates resting on arbitrarily orthotropic Pasternak foundation and partially in contact with fluid

摘要

In this study, a method of analysis is presented for investigating the dynamic response behavior of moderately thick plates (Mindlin plates) resting on arbitrarily orthotropic two parameter foundation and partially in contact with a quiescent fluid on its other side. A mixed-type finite element formulation is derived for the Mindlin plate-arbitrarily orthotropic Pasternak foundation interaction by applying the Gateaux differential. A four nodded isoparametric C° class element is adopted and at each node eight degrees of freedom are assigned. The rotary inertia effect is taken into account through the consistent mass matrix formulation. For calculation of the fluid-structure interaction effects, the boundary element method is adopted. The fluid is assumed to be ideal, i.e., inviscid, incompressible, and its motion is irrotational. The infinite frequency limit condition is applied on the fluid's free surface using a modified fundamental solution implicitly satisfying the appropriate free surface boundary condition. It is assumed that the plate-elastic orthotropic foundation system vibrates in its in vacuo eigenmodes when it is in contact with fluid, and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure. The fluid-structure interaction forces are calculated in terms of the generalized hydrodynamic added mass coefficients (due to the inertial effect of fluid). To assess the influence of the arbitrarily orthotropic Pasternak foundation and fluid on the dynamic response behavior of moderately thick plates, the natural frequencies and associated mode shapes are presented for rectangular and circular plates with various boundary conditions.