КОЛЕБАНИЯ ЗАЩЕМЛЕННОЙ ПРЯМОУГОЛЬНОЙ ПЛАСТИНЫ ПРИ РАСТЯЖЕНИИ – СЖАТИИ ЕЕ ПЛОСКОСТИ

Abstract

The dependence of the natural oscillation frequency of a pinched rectangular plate on the magnitude of uniformly distributed compressive (or tensile) forces applied to all its faces is investigated. The problem is solved using two hyperbolo-trigonometric series satisfying all the conditions of the boundary value problem. A resolving infinite homogeneous system of linear algebraic equations is obtained with respect to a single sequence of coefficients of a series, which contains the natural frequency and intensity of the longitudinal load as parameters. The natural frequency was calculated for a number of values of the longitudinal load up to its critical value. At the same time, an iterative method of finding nontrivial solutions of the system was used in combination with the frequency sampling method (the “shooting” method). It is established that with increasing compressive load, the natural frequency of the square plate decreases according to the parabolic law. Numerical results are compared with the results of other authors.