Lowest Twelve Frequencies of Sandwich Plates Using Third-Order Shear-Normal Deformation Theory

Abstract

We delineate effects of 1) face-to-core stiffness ratio (FCSR) and mass density ratio (FCDR) in square laminates and sandwich plates and 2) the fiber and transverse direction elastic modulus ratio in cross-ply laminates on the first 12 distinct frequencies found by analytically solving the three-dimensional linear elasticity theory equations and using an equivalent single-layer third-order shear and normal deformation plate theory (TSNDT). Whereas the elasticity equations for simply supported plates are solved by using Srivinas and Rao’s approach, the TSNDT equations are numerically solved by using weighted Jacobi polynomials and the Ritz method. We note that previous studies have generally compared only the fundamental frequency. For square laminates with a side-length/plate-thickness ratio of 100 (10), the maximum error in the TSNDT predicted first 12 frequencies is less than 0.4% (7%). For a FCSR less than 20, the maximum difference in predictions from the two approaches for the first six distinct frequencies is 5.4%. However, the FCDR has little effect on the difference between frequencies from the two methods. The frequencies and mode shapes presented herein should help us better understand the dynamic behavior of laminated and sandwich plates and provide benchmark results for others to assess their theories.