Review: Complex modes based numerical analysis of viscoelastic sandwich plates vibrations

In this paper, a numerical method for linear and nonlinear vibrations analysis of viscoelastic sandwich beams and plates is developed with finite element based solution. This method couples the harmonic balance technique to complex mode Galerkin's procedure. This results in a scalar nonlinear complex amplitude-frequency relationship involving numerical computation of three coefficients. A general formulation taking into account the frequency dependence of the viscoelastic behaviour allowing to intoduce any viscoelastic law is given. Complex eigenmodes are numerically computed in a general procedure and used as Galerkin's basis. The free and steady-state vibrations analyses of viscoelastic sandwich beams and plates are investigated for constant and frequency dependent viscoelastic laws and for various boundary conditions. The equivalent frequencies and loss factors as well as forced harmonic response and phase curves are performed. The obtained results show the efficiency of the present approach to large amplitudes vibrations of viscoelastic sandwich structures with nonlinear frequency dependence.