Torsional vibration and damping analysis of sandwich beams

The objective of the paper presented here is to investigate the torsional vibration and damping analysis of beams with sandwich or constrained layer damping arrangements using finite element procedure. Finite element 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, is employed. The element is capable of simulating free as well as constrained torsion. The transverse shear deformation in the form of trigonometric sine function is incorporated to define the transverse shear strain. The inertia effects due to in-plane, rotary and torsional motion have been included in the formulation. The governing equations of motion for the dynamic analysis are obtained using Lagrange's equation of motion. The solutions are evaluated by QR algorithm. Numerical results are presented for both free-free and cantilever beams. A detailed parametric study is carried out to highlight the influence of shear modulus of the core or constrained layer in beams, thickness ratio, and boundary condition on the torsional resonance frequencies and its associated system loss factors.