Nonlinear vibration analysis of isotropic cantilever plate with viscoelastic laminate. (English) Zbl 1204.74022
Summary: The nonlinear vibration of an isotropic cantilever plate with viscoelastic laminate is investigated in this article. Based on the Von Karman’s nonlinear geometry and using the methods of multiple scales and finite difference, the dimensionless nonlinear equations of motion are 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, Ritz method is employed to obtain semi-analytical nonlinear mode-shapes of transverse vibration of this plate. Airy stress function and Galerkin method are employed to reduce nonlinear PDEs into an ODE of duffing type. Stability of plate and chaotic behavior are investigated by Runge-Kutta method. Poincare section diagrams are in good agreement with results of Lyapunov criteria.
MSC:
| 74H45 | Vibrations in dynamical problems in solid mechanics |
| 74K20 | Plates |
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74D05 | Linear constitutive equations for materials with memory |
References:
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