Equations of vibration of a two-dimensionally layered plate strictly based on the decision of various boundary-value problems

Abstract

In this paper, the theory of oscillation of laminated plates of building structures is developed, which is rigorously grounded in the formulation of various boundary-value oscillation problems. When studying the oscillation of plates, the exact three-dimensional problem is replaced by a simpler, two-dimensional problem for the points of the middle plane of the plate, which imposes restrictions on the external conditions. These limitations boil down to the fact that external forces can not be high-frequency. Since the general equations of plate oscillation, the resulting wound contain derivatives of any order in terms of coordinates x, y and time t, are structured and therefore not suitable for solving applied problems and performing engineering calculations. For this, it is necessary to formulate approximate boundary-value oscillation problems.