ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

# plate

## The Geometrical Irregular Plates under the Influence of the Quick Changed on the Time Coordinate Forces and Temperature Effects

On the basis of incoherent thermoelasticity, the dynamic behaviour of geometrically irregular plates under the influence of quick changed, on the time coordinate, forces and temperature effects on surfaces is considered. An approach allowing to obtain the analytical solution of the thermoelasticity dynamic problem for the plate under inhomogeneous boundary conditions at all four edges is suggested.

## Modified Spline Collocation Method in the Problems of Thin Rectangular Viscoelastic Plate Vibration

Numerical method for evaluation of critical frequencies during steadystate bending vibrations of viscoelastic plate is presented. The solution is based on applying modified spline collocation method for lowering the problem’s dimension and numerical solving of the obtained problem via discrete orthogonalization method. The application of this approach with different boundary conditions is examined in detail.

## Spline-Collocation Method and its Modification in the Problems of Static Bending of Thin Orthotropic Rectangular Plate

A numerical method for determining the stress-strain state (SSS) of a bended thin rectangular plate with non-classical boundary conditions is presented. Numerical results for three different materials can be used to estimate the influence of the material anisotropy and boundary conditions on its SSS.

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

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

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.

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

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.