Natural Oscillations of Circular Sandwich Plates in the Temperature Field

Abstract

The effect of a homogeneous temperature field on the frequencies of natural oscillations of a circular sandwich plate is investigated. The hypothesis of a broken line is used as a kinematic one: for identical high-strength thin load-bearing layers, the Kirchhoff hypothesis; for a light incompressible thicker filler, the Timoshenko hypothesis on the straightness and incompressibility of a deformed normal. The differential equations of the transverse vibrations of the plate are obtained by the variational method. The desired functions are plate deflection and displacement in the filler. The analytical solution of the initial boundary value problem is constructed by decomposing into a series according to a system of proper orthonormal functions with hinged support or sealing of the plate contour. Calculation formulas for displacements are given. A numerical parametric analysis is carried out for the dependence of the oscillation frequencies of the plate on the materials of the bearing layers and temperature.

Keywords

• circular sandwich plate
• natural oscillations
• frequencies
• temperature