Нестационарные колебания мембран и пластин в форме прямоугольного равнобедренного треугольника

Abstract

Nonstationary deforming of mechanical objects (membranes and plates) having the shape of a rectangular isosceles triangle is considered. To solve the problem, we use the approach proposed by J. V. Strutt (Lord Rayleigh) in the monograph “The Theory of Sound” and used by S. P. Timoshenko in the problem of static deformation of a triangular plate. This approach consists in supplementing the triangular plate with the second one (identical to the original plate) to compose a full square and solving the problem for a square membrane/plate, to which, in addition to the disturbing force, an additional load of the opposite sign is applied. Thus, solving the problem is reduced to the study of vibrations of a square membrane fixed along the contour or of a hinged square isotropic plate of medium thickness (Timoshenko type). Examples of calculations for a triangular membrane and a mediumthickness plate are presented, which demonstrate the effectiveness of the proposed approach in solving problems of nonstationary deformation.