Oscillations of a Three-Layer Plate Caused by a Thermal Shock and Pulse Load

• Published in: Journal of engineering physics and thermophysics Vol. 98; no. 3; pp. 779 - 787
• Main Authors: Starovoitov, É. I., Pleskachevskii, Yu. M., Leonenko, D. V.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2025; Springer Nature B.V
• Subjects: Boundary conditions; Boundary value problems; Classical Mechanics; Complex Systems; Contours; Eigenvectors; Engineering; Engineering Thermodynamics; Equations of motion; Exact solutions; Fillers; Forced vibration; Formulas (mathematics); Free vibration; Heat; Heat and Mass Transfer; Heat Conduction and Heat Transfer in Technological Processes; Heat flux; Heat transfer; Hypotheses; Incompressibility; Industrial Chemistry/Chemical Engineering; Initial conditions; Kinematics; Parametric analysis; Partial differential equations; Temperature distribution; Thermal conductivity; Thermal shock; Thermodynamics; Thermophysical properties; Thickness; Thin films; circular three-layer plate; forced oscillations; heat flux; pulse load
• ISSN: 1062-0125; 1573-871X
• DOI: 10.1007/s10891-025-03158-3

The effect of thermal shock on forced oscillations caused by a pulse load on a circular three-layer plate is investigated. The plate is asymmetrical in thickness, its lower surface and contour are thermally insulated. The distribution of nonstationary temperature over the plate thickness is calculated using an approximate formula obtained by solving the heat conductivity problem with averaging the thermophysical properties of the materials of the three-layer package. Using Neumann′s hypothesis, forced oscillations from a pulse load are superimposed on free oscillations caused by a thermal shock (an instantaneous drop in a heat flux). The hypothesis of a broken line is used as a kinematic one: the Kirchhoff hypothesis for high-strength thin load-bearing layers; the Timoshenko hypothesis on the rectilinearity and incompressibility of the deformed normal, which rotates by a certain additional angle (shear), for a thicker filler incompressible in thickness. The formulation of the initial-boundary value problem includes partial differential equations of motion obtained by the Lagrange variational method, homogeneous initial conditions, and boundary conditions of the hinged contour of the plate. The sought functions are the defection of the plate, shear in the filler, and the radial displacement of the median plane of the filler. For the analytical solution of the initial-boundary value problem on the oscillations of a three-layer plate under the action of a pulse surface load in a nonstationary temperature field, a system of orthonormal eigenfunctions is constructed. The sought solution is written in series. Calculation formulas for displacements are given. A numerical parametric analysis of the plate deflection depending on the intensity and time of exposure to the heat flux is carried out.