Construction of the solutions of the equations of vibration of the classical theory of plates with parameters periodic on one coordinate

Abstract

The system of classical equations of transverse vibrations of plates that are inhomogeneous on one coordinate and have exponential dependence of the solution on the other coordinate and time are presented in the canonical Hamiltonian form with suitably chosen canonical variables. For periodically varying parameters we use the general properties of periodic Hamiltonian systems to study the structure of the solutions of boundary-value problems for stationary vibrations of plates.