Vibration analysis of thin shallow shells using spectral element method (original) (raw)
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Nonlinear Vibration of the Laminated Shallow Shells with Complex Planform
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Investigation method of free nonlinear vibration of laminated plates and shallow shells with an arbitrary plan form and different boundary conditions is proposed. The offered method is based on combined application of R-functions theory and variational methods. The passing to nonlinear system of the ordinary differential equations (NSODE) is connected with solving the sequence of the boundary problems in the domain of an arbitrary shape: linear vibration problem; sequence of problems of elasticity theory simulated by partial differential equations with special right part and corresponding boundary conditions. The variation method by Ritz together with R-functions theory is applied to solve foregoing boundary value problems. The final passing to NSODE is carried out by Galerkin procedure. The coefficients of the obtained NSODE are presented in explicit form and expressed through the double integrals of known functions for the cases of single-mode and multi-mode approximation. The following investigation of the obtained nonlinear ordinary differential equation or system is fulfilled by Rung-Kutt method. The proposed method is illustrated on specific examples and compared with another approaches.
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