High-order free vibration of sandwich panels with a flexible core

Abstract

Free vibration analysis of sandwich panels with a flexible core based on the high-order sandwich panel theory approach is presented. The mathematical formulation uses the Hamilton principle and includes derivation of the governing equations along with the appropriate boundary conditions. The formulation embodies a rigorous approach for the free vibration analysis of sandwich plates with a general construction, having high-order effects owing to the non-linear patterns of the in-plane and the vertical displacements of the core through its height. As such, it improves on the available classical and high-order theories. The formulation uses the classical thin plate theory for the face sheets and a three-dimensional elasticity theory or equivalent one for the core. The analyses are valid for any type of loading scheme, localized as well as distributed, and distinguish between loads applied at the upper or the lower face. It can also deal with any type of boundary conditions that may be different at the upper and the lower face sheets at the same edge. The effects of the rotary inertia of the various constituents of the sandwich construction are included. Two types of computational models are considered. The first model uses the vertical shear stresses in the core in addition to the displacements of the upper and the lower face sheets as its unknowns. The second model assumes a polynomial description of the displacement fields in the core that is based on the displacement fields of the first model. In this case the unknowns are the coefficients of these polynomials in addition to the displacements of the various face sheets. The two computational models have been validated numerically through a very good comparison with the well known classical and high-order plate theories. The numerical study consists of free vibration eigenmodes of two typical simply-supported panels, including higher modes that cannot be detected by other high-order computational models, and a parametric study that compares the results of the various computational models and the first-order shear deformable results.