Nonlinear geometric fluid-structure interaction model of multilayered sandwich plates in contact with unbounded or bounded fluid flow

Abstract

Based on the Kirchhoff-Love theory and von Kármán's geometric nonlinearity, the nonlinear vibration analysis of multilayered sandwich plates under ideal flow is presented. Rectangular plates are considered to be laminated of orthotropic composite layers as upper and lower face sheets as well as a central lightweight core made of functionally graded (FG), anisogrid lattice or metal foam materials. Three coupled equations of motion are reformulated into one decoupled governing equation in terms of transverse deflection (w) using the method of inverse differential operator. For the first time, an impermeability condition is developed that considers the moderately large deflection of the contact surface in order to correct the pressure distribution of fluid flow. Based on the potential flow theory, closed-form expressions of hydrodynamic pressure are obtained for different fluid boundary conditions including infinite depth of fluid, flow bounded by a rigid wall and flow between two identical elastic plates. Then, the Galerkin and multiple-scale perturbation methods are used to obtain closed-form solution of nonlinear natural frequency in terms of maximum vibration amplitude. Finally, case studies are presented to investigate the effects of geometric ratios, boundary condition, material distribution, layup, characteristics of flow and geometric nonlinearity on the response quantities. Findings indicate that the large deformation term in the developed impermeability condition has significant effect on the pressure distribution and its effect is more pronounced for thicker plates with larger mode number in the flow direction. Therefore, the novel nonlinear fluid-structure interaction model should be considered to study flow-induced dynamic behavior of sandwich plates with different boundary conditions. In addition, the snap-through behavior is seen in the nonlinear frequency-upstream speed curves and the incipient points of dynamic instability can vary remarkably with the fluid boundary conditions.