Flexural vibrations of prestressed isotropic plates

Abstract

We propose a method of solving problems of forced vibrations of prestressed plates based on the perturbation method and making it possible to solve problems for both low and high frequencies. We describe a method of determining the ground natural frequency.I Table. Bibliography: 5 titles.The first and third of the present authors [1], in solving problems on the flexural vibrations of circular plates by the perturbation method, took the perturbation to be the reduced frequencywhere p is the density, w is the frequency of the vibrations, and h, D, and R are respectively the thickness, the cylindrical stiffness, and the radius of the bar.In the present article, in the framework of the theory of flexible plates of small deflection, we study the stress-strain state of a rigidly clamped bar under the action of transverse vibrating forces. In doing this, taking account of [2], we introduce the perturbation e connected with f/2 by the equality i.e.,