The dynamics of a rectangular orthotropic plate in a membrane

Аuthors

Tushavin N. A.

CALLISTO VISION, Moscow, Russia

e-mail: natushavin@mai.education

Abstract

This paper examines the dynamic behavior of a thin rectangular orthotropic plate in a membrane state under the influence of an arbitrary nonstationary temperature field. A linear thermoelastic formulation of the problem for a plate of constant thickness with rigid pinching and hinged support along the contour is considered. The orthotropy of the elastic characteristics of the material and the anisotropy of thermal expansion are taken into account. It is shown that, unlike a hinged support, rigid fastening completely prevents flat movements of the boundary, as a result of which temperature deformations are constrained, and uniform heating can cause internal membrane stresses. A system of differential equations of motion in the plane of the plate for the displacement components of the middle surface is obtained. The corresponding initial and boundary conditions are formulated. For a rectangular area, an analytical approach based on the decomposition of the desired functions in trigonometric series is proposed, which makes it possible to reduce the initial boundary value problem to a system of ordinary differential equations in time. It is shown that the nature of the dynamic response significantly depends on the spatial heterogeneity of the temperature field, the rate of its change over time, and the relationship between the elastic and temperature parameters of the orthotropic material. The obtained ratios can be used in the calculation of heat-loaded structural elements made of composite and anisotropic materials.

Keywords:

orthotropic plate; thermoelasticity; membrane state; plate dynamics; temperature field; hinge bearing; rigid pinching; anisotropy; eigenfunctions

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