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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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