Papers by Keyword: Free Oscillations

Abstract: Specified calculation of steady-state oscillations of circular transtropy plates of medium thickness was performed. The calculation considers transverse displacement deformation and transverse compression effect. Compared to other plate models, such clarifications highly increase calculation accuracy of their stress-strain state. While considering the influence of tangential loads and inertia forces, they do not change equations structure nor increase their order. Obtained equations deal with specification via certain parameters, which depend on characteristics of plate anisotropy and geometry. The calculation order of the equations remains the same, stresses and forces stay similar as in other plate models. At the same time, their accuracy highly increases and becomes close to the results of elasticity theory spatial problem. In case of hinged round plate, the solutions for the free oscillation frequencies are found. Obtained numeric results are compared with corresponding results of classic theory of Kirchhoff’s thin plates. On the basis of these comparisons, the conclusions about significant influence of transverse displacement and compression effects on the magnitude of oscillation frequencies in the direction of their significant decrease are made. This effect is especially noticeable at low transverse physical characteristics of the plate. This conclusion coincides with corresponding results, which were obtained in the monograph of V.T. Grinchenko for a thick plate in a spatial setting.

Abstract: Considered small oscillations geometrically nonlinear shallow shell of revolution relative to the initial deformed state. Orthotropic material model is considered. Research methodology based on the finite element method is developed.

Abstract: Considered small oscillations geometrically nonlinear shallow shell of revolution relative to the initial deformed state. Isotropic material model is considered. Problem is solved by mixed finite element method. Results of solution of test task are represented.

Abstract: An analytical technique, namely the method of multiple scales, is applied to solve the differential equations of free oscillations with even nonlinearities in a mass-spring system. Unlike other perturbation methods, the method of multiple scales is effective in determining the transient response as well as determining the approximation to the frequency of the nonlinear system. In this paper, the periodic solutions of the even nonlinear differential equations have been obtained by using the method of multiple scales. Compared with the numerical examples, the approximate solutions are in good agreement with exact solutions. The numerical and analytical solutions have clearly shown that there exists the so-called drift phenomenon in the free oscillations of systems with even nonlinearities without any external excitation.