Root / Conference Proceedings / 6th EUROMECH Nonlinear Dynamics Conference (ENOC 2008) / NONLINEAR VIBRATION OF THE LAMINATED SHALLOW SHELLS WITH COMPLEX PLANFORM
NONLINEAR VIBRATION OF THE LAMINATED SHALLOW SHELLS WITH COMPLEX PLANFORM
Galina Timchenko, Tatyana Shmatko
Investigation method of free nonlinear vibration of lami-nated 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 or-dinary differential equations (NSODE) is connected with solv-ing 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 fi-nal passing to NSODE is carried out by Galerkin procedure. The coefficients of the obtained NSODE are presented in ex-plicit 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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