Flexural loss factors of sandwich and laminated composite beams using linear and nonlinear dynamic analysis

The purpose of the article presented here is to analyze the flexural loss factors of beams with sandwich or constrained layer damping arrangements and laminated composite beams using a C 1 continuous, three-noded beam element. The formulation is general in the sense that it includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects, and is applicable for both flexural and torsional studies. The geometric nonlinearity based on von Karman’s assumptions is incorporated in the formulation while retaining the linear behavior for the material. The finite element employed here is based on a sandwich beam theory, which satisfies the interface stress and displacement continuity and has zero shear stress on the top and bottom surfaces of the beam. The transverse shear deformation in the form of trigonometric sine function is introduced in the formulation to define the transverse shear strain. The governing equations of motion for the dynamic analysis are obtained using Lagrange’s equation of motion. The solution for nonlinear equations is sought by using an algorithmdirect iteration technique suitably modified for eigenvalue problems, based on the QR algorithm. A detailed numerical study is carried out to highlight the influences of amplitude of vibration, shear modulus and thickness of the core of the sandwich beam, aspect ratios, boundary conditions, and lay-up in the case of laminates on the system loss factors. q 1999 Elsevier Science Ltd. All rights reserved.