Plates Vibration

This chapter is devoted to plates’ vibrations covering the following topics: Technical theory of bending, small vibrations of elastic plates; application of the refined theory of bending in plate vibrations; anisotropic plates; flexible plates; methods of solving equations of vibrations of plates; free vibrations of rectangular plates; forced vibrations of plates; vibration of plates on elastic foundation; forced vibrations of a rectangular plate on an elastic foundation, problems and solutions are provided. As an example of the application of the Spectral Method of Boundary Elements (SMBE) to dynamic problems, the oscillations of a plate of an arbitrary form, which lies on the elastic Winklerian base, under the action of a load q(x, y, t) is presented. This chapter presents solutions to plate vibration problems which were developed by Korenev and Tseitlin (Plates vibrations, Stroyisdat, pp. 213–249, 1982), Petrosian (About one elastic foundation model. In: Structural mechanics and calculation, Vol. 5, pp. 7–11, n.d.), and Petrosian (Analysis of structures on elastic foundation. Incorporating the spectral method of boundary elements, p. 556, 2022).