Nonlinear harmonic vibrations of laminate plates with VE layers using refined zig-zag theory. Part 2 – Numerical solution

Abstract

The paper is devoted to the numerical analysis of the harmonic vibrations of laminate plates with viscoelastic layers in the von Kàrmàn geometrically non-linear regime. The amplitude equation derived in the prequel paper Part 1 – theoretical background is discretized using the 8-noded bi-quadratic plate finite elements. The response curves are obtained using the continuation method to solve the discretised amplitude equation treated as the equation with the frequency of vibrations as a parameter. The proposed method of solution is verified by comparing the results with those from available literature. Furthermore, several numerical analyses are performed, including testing of FE mesh density, plate aspect ratio, various VE materials, support conditions and layers layout as well as the possibility of simplification of the complex-valued zig-zag function used in the description of plate kinematics. Several results of practical importance are found and discussed in the conclusions.