Abstract:
The effect of thermal shock on forced vibrations of a circular three-layer plate excited by a resonant load is investigated. The plate is asymmetrical in thickness, thermally insulated on the lower surface and contour. The distribution of the non-stationary temperature over the thickness of the plate is calculated using an approximate formula obtained as a result of solving the problem of thermal conductivity by averaging the thermophysical properties of materials of a three-layer package. In accordance with the Neumann hypothesis, forced oscillations from a resonant load are superimposed on free oscillations caused by heat stroke (instantaneous drop in heat flow). The hypothesis of a broken line is used as a kinematic one: for high-strength thin bearing layers, the Kirchhoff hypothesis; for an incompressible thicker filler, the Timoshenko hypothesis about the straightness and incompressibility of a deformed normal that rotates by some additional angle (relative shift). The formulation of the initial boundary value problem includes differential equations of transverse vibrations of the plate in partial derivatives obtained by the variational method, homogeneous initial conditions and boundary conditions of the spherical support of the contour. The desired functions are plate deflection, relative shear, and radial displacement of the median plane of the filler. The analytical solution of the initial boundary value problem is constructed by decomposing the desired displacements into a series according to a system of proper orthonormal functions. The corresponding calculation formulas and the results of numerical parametric analysis of the dependence of the solution on the intensity and time of exposure to the heat flux, the magnitude of the power load are presented.
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