Free vibrations of a five-layer circular plate at different fixations of the contour

A mathematical model for the study of the natural vibrations of a five-layer circular plate asymmetric in thickness with pinched or hinged contours is developed. Transcendental equations depending on boundary conditions are written out to find the eigenvalues. The formula linking the eigennumbers and frequencies of oscillations is given. A numerical study of the influence of the thickness of the inner non-substantial layer and the elastic characteristics of the layer materials on the eigen-numbers and frequencies is carried out. It is shown that an increase in the elastic moduli of the materials or in the thickness of the supporting layer leads to an increase in the natural frequencies.