New benchmark free vibration solutions of passive constrained layer damping beams by the symplectic method

In this paper, new analytic solutions for the free vibration analysis of passive constrained layer damping (PCLD) beams, which are widely used in engineering to suppress vibrations and noise, are shown based on the symplectic method. The Hamiltonian-based governing equations and the new boundary condition expressions of PCLD beams are established by the original vector and its dual vector obtained by variation of the quasi Lagrangian function. The explicit solutions are obtained in the symplectic space in a direct, rigorous way without any trail functions under various boundary conditions. To verify the accuracy of the present method, the frequency parameters and loss factors of PCLD beams are compared with the results available in the literature. Comprehensive results under various boundary conditions are also tabulated for further benchmark use.