ABSTRACT
I.D. Breslavsky National Technical University “KhPI”, Kharkov, Ukraine
K.V. Avramov & E.A. Strelnikova Podgorny Institute for Problems of Engineering Mechanical NAS of Ukraine, Kharkov, Ukraine
ABSTRACT: Shallow shells with complex geometry and partly clamped boundaries are studied. The method of shell free nonlinear oscillations analysis is suggested based on the Donnell-Mushtari-Vlasov equations with respect to displacements and the energetic approach. Geometrical nonlinear deformations of shells are treated. R-function method is applied to satisfy the panel boundary conditions. The Rayleigh-Ritz method is used to obtain the linear vibrations eigenmodes. The nonlinear vibrations of panel with complex base are expanded as a series of these obtained eigenmodes. As a result, the finite degree-of-freedom dynamical system is derived. The methods of nonlinear dynamics (harmonic balance method, nonlinear modes) are used to study the free nonlinear vibrations. The hydraulic turbine blade interaction with fluid is treated. The frequency responses of free vibrations are presented.
