FORCED OSCILLATIONS OF A RECTANGULAR TWO-LAYER PIECEWISE HOMOGENEOUS PLATE OF CONSTANT THICKNESS

Abstract

This article examines the forced vibrations of a rectangular, two-layer, piecewise homogeneous plate of constant thickness subjected to an external harmonic disturbance. The plate consists of two layers with different physical and mechanical properties, such as elastic modulus, density, and Poisson's ratio, with each layer assumed to be homogeneous within its own region. Based on the classical theory of thin plates and the equations of elastic dynamics, a mathematical model of forced vibrations is derived. The influence of interlayer interaction and boundary conditions corresponding to different types of plate edge fastening are taken into account. A distributed harmonic load, causing steady-state vibrations, is considered as the external disturbance. To solve the problem, the method of separation of variables and expansion of the desired functions into series in terms of natural vibration modes are used. Analytical expressions are obtained for the deflection amplitudes and the stress-strain state of the plate depending on the frequency of the external disturbance. An analysis of resonance phenomena and the influence of layer parameters on the dynamic behavior of the structure is conducted. The results of the study can be used in the design and calculation of multilayer structural elements in mechanical engineering, construction, and aerospace engineering, where consideration of dynamic loads and the layered structure of materials is required.