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Abstract

The paper presents dynamic responses of annular plate composed of three layers. The middle layer of the plate has electrorheological properties expressed by the Bingham body model. The plate is loaded in the plane of facings with time-dependent forces. The electrorheological effect is observed in the area of supercritical plate behaviour. The influence of both material properties and geometrical dimensions of the core on plate behaviour is examined. The problem is solved analytically and numerically using the orthogonalization method and the finite difference method. Comparison of the results obtained using the finite difference and the finite element methods for a plate in critical state is shown. The numerical calculations are carried out for axisymmetric and asymmetric plate modes. The presented diagrams show the plate reaction to the changes in values of plate parameters and indicate that the supercritical control of plate work is possible.
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Abstract

Three-layered, annular plate with viscoelastic core is subjected to loads acting in the plane of the plate facings. One formulates the dynamic, stability problem concerning the action of time-dependent compressive stress on a plate with imperfection. This problem has been solved. One created the basic system of differential equations in which the approximation finite difference method was used for calculations. The essential analysis of the problem was concentrated on evaluation of the influence of the plate imperfection rate and the rate of plate loading growth on the results of calculation of critical parameters at the moment of loss of plate stability. It determines the analysed problem of sensitivity of the plate to imperfection and loading. In the evaluation of the dynamics of this problem, the dynamic factor defined as the quotient of the critical, dynamic load to the static one was used. The idea of dynamic factor and the type of the accepted criterion of the loss of plate stability were taken from the Volmir's work. The observations were confirmed by comparable results of calculations of plate models built in finite element method using the ABAQUS system. The analysis of the stress state in an exemplary plate model calculated in FEM demonstrated the importance of the strength condition in total evaluation of the plate work. One achieved satisfactory correctness of results in both methods.
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