Transverse Forced Vibrations of the Plates, the Dissipative Properties of Which are Described Memory Functions

Abstract

Abstract The fundamentals of theoretical methods for engineering calculations of bending vibrations of thin plates, the material of which has hereditary properties, are presented. The manifestation of the hereditary properties of the material of the plate under consideration at a given stress-strain state can be judged by the relaxation core of the material. The dependence of the creep and relaxation kernels on the time difference corresponds to the fact that the “memory” of the material about the force effect produced at a given moment is determined by the elapsed time interval. In particular, this means that if the force action on the elastic-viscous body is cyclic, then the deformation of the body will also be cyclic with some phase shift. A technique for solving forced vibrations of plates under the influence of harmonic loads is proposed. An exact solution to the problem of forced vibrations of a supported rectangular plate, whose dissipative properties are described by memory functions, is constructed.