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Identification of Properties of Inhomogeneous Plate in the Framework of the Timoshenko Model

Authors: Bogachev I. V., Vatulyan A. O., Dudarev V. V., Lapina P. A., Nedin R. D.

We consider an inverse problem on identification of properties of an inhomogeneous circular plate for the Timoshenko model. The identification procedure is based on the analysis of acoustical response at some point of the plate in the given set of frequencies. The vibrations are caused by a uniformly distributed load applied to the upper face of the plate. We have derived the oscillation equations for a symmetric circular plate and formulated the boundary conditions in the dimensionless form.

Mathematical Modeling of Interaction Between Layer of Viscous Liquid and Elastic Walls of Channel, Which Was Installed on Vibration Foundation

Authors: Ageev R. V., Bykova T. V., Kondratova Y. N.

The article solves the problem of mathematical modeling dynamic processes in hydrosupport with elastic stator. The dynamic problem of hydroelasticity is found and amplitude and phase frequency characteristics of hydrosupport was built.

A Certain Approach to Solving of Some One-Dimensional Contact Problems

Authors: Nyashin Y. I.

The paper deals with the problems of the unbonded contact of beams, strings, circular membranes and plates. A new approach to solving of such problems is suggested. This approach includes the rigorous problem statement, the elementary proof of the uniqueness of solution and the analytical solution construction method. The method is based on the iterative correction of the contact region. A number of examples of this method application are given.