Transverse Vibration of Plate with at least Two Sequent Free Edges — Part II: Nonlinear Analysis of Cantilever Plate

The nonlinear vibration of isotropic cantilever plate with viscoelastic laminate is investigated in this article. Based on Von-Karman’s nonlinear geometry and using the methods of multiple scales and finite difference, nonlinear equations of motion are to be analyzed and solved. The solvability condition of nonlinear equations is obtained by eliminating secular terms and finally, nonlinear natural frequencies and mode-shapes are obtained. Knowing that the linear vibration of this type of plate does not have exact solution, the results of Ritz method used in previous part regarded to these authors, is employed. Here nonlinearity is due to geometry of the plate and its internal viscoelastic damping.

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nonlinear-vibration-viscoelastic- plate