FREE VIBRATIONS OF A THREE-LAYER PLATE EXCITED BY A HEAT FLUX

The eff ect of a heat fl ux of constant intensity on a circular three-layer plate, thermally insulated along the contour and lower surface, is considered. A solution of the problem of thermal conductivity of the plate with thicknessaveraged thermophysical parameters of materials is presented. The nonstationary temperature fi eld is nonuniform over the thickness of the plate. It is shown that on instantaneous drop, the heat fl ux can cause sagging and free vibrations of the three-layer plate. The kinematics of the plate package obeys the broken line hypothesis. After applying a load, the normal in thin load-bearing layers does not change its length and remains perpendicular to the middle surface of the layer. In a relatively thick fi ller, the deformed normal retains its length and straightness, but is rotated by a small additional angle, i.e., the shift is taken into account. The formulation of the corresponding initial boundary-value problem is given. The equations of motion were obtained using the variational method with account for the transverse forces of inertia. The boundary pivot conditions are accepted on the contour of the plate. Radial movements in the layers are expressed through three sought functions: plate sagging, shear, and radial movement of the middle plane of the fi ller. It is shown that these sought functions satisfy the inhomogeneous system of three diff erential equations. To solve the system, the method of series expansion in the constructed fundamental system of eigenorthonormal functions was used. A transcendental equation is written out to obtain the corresponding eigenvalues. A numerical parametric analysis of the solution was carried out depending on the geometric and thermophysical characteristics of the layer materials and the time of exposure to the heat fl ux
The eff ect of a heat fl ux of constant intensity on a circular three-layer plate, thermally insulated along the contour and lower surface, is considered. A solution of the problem of thermal conductivity of the plate with thicknessaveraged thermophysical parameters of materials is presented. The nonstationary temperature fi eld is nonuniform over the thickness of the plate. It is shown that on instantaneous drop, the heat fl ux can cause sagging and free vibrations of the three-layer plate. The kinematics of the plate package obeys the broken line hypothesis. After applying a load, the normal in thin load-bearing layers does not change its length and remains perpendicular to the middle surface of the layer. In a relatively thick fi ller, the deformed normal retains its length and straightness, but is rotated by a small additional angle, i.e., the shift is taken into account. The formulation of the corresponding initial boundary-value problem is given. The equations of motion were obtained using the variational method with account for the transverse forces of inertia. The boundary pivot conditions are accepted on the contour of the plate. Radial movements in the layers are expressed through three sought functions: plate sagging, shear, and radial movement of the middle plane of the fi ller. It is shown that these sought functions satisfy the inhomogeneous system of three diff erential equations. To solve the system, the method of series expansion in the constructed fundamental system of eigenorthonormal functions was used. A transcendental equation is written out to obtain the corresponding eigenvalues. A numerical parametric analysis of the solution was carried out depending on the geometric and thermophysical characteristics of the layer materials and the time of exposure to the heat fl ux
Author:  É. I. Starovoitov, Yu. M. Pleskachevskii, D. V. Leonenko, D. V. Tarlakovskii
Keywords:  nonstationary temperature fi eld, three-layer circular plate, free vibrations
Page:  1432