Plates are widely used as flat structural elements in various spheres of construction and engineering. Development of industrial and residential building techniques furthers development of the construction science. Therefore, the design and the refined theory of plate vibrations is one of signifi cant issues considered within the framework of the applied theory of elasticity, which is of practical interest to the researchers. The authors provide a summary of frequency equations that describe self-excited oscillations of a transversally isotropic plate resting on the strain foundation bed, if one edge of the plate is flexibly fixed and the other three edges are hinged. Oscillations are described by partial differential equations of the fourth order. The problem is resolved through the employment of an approximate method of decompositions. As a result, the frequency equation is derived to identify self-excited lateral oscillations of the plate. The equations derived by the authors for the purpose of identifi cation of the frequencies of self-excited transverse vibrations of a plate are fit for practical use, and they may be applied in calculations to identify the dependence of the selfexcited frequency of the plate on its geometry.

Приведено решение уравнения собственных колебаний трансверсально-изотропной пластины, лежащей на деформируемом основании, один край которой упруго закреплен, а три других шарнирно оперты. Колебания пластины описаны уравнением в частных производных четвертого порядка. В ходе решения задачи приближенным методом декомпозиций выведено частотное уравнение для определения собственных поперечных колебаний пластины.