Vibrations of a rectangular three-layer plate

In this paper, a three-layer rectangular plate is considered. The averaged differential equation of plate vibrations is derived. Approximate formulas for calculating eigenvalues and eigenforms (vibration frequences and vibrations modes) were obtained based on the two-dimensional theory of thin plates. The analytical and numerical results are compared. Numerical calculations were performed using the finite element method using the ANSYS software package and the MAXIMA package.