СВОБОДНЫЕ КОЛЕБАНИЯ ОРТОТРОПНЫХ ПЛАСТИН
Journal Title: Science Review - Year 2018, Vol 2, Issue 3
Abstract
The solution of the problem of natural oscillations of a rectangular orthotropic plate is considered using the numerical-analytic method of boundary elements. The transition from a two-dimensional problem to a one-dimensional problem is carried out using the Kantorovich-Vlasov variational method. To select the function of the transverse deflection distribution, it is recommended to use the dynamic method, since it is sufficient to change only the values of the natural frequencies of the beam oscillation with the corresponding boundary conditions. 64 analytical expressions of fundamental functions for all possible roots of the characteristic equation corresponding to the differential equation of the problem are obtained. Thus, the problem is solved for any conditions for fixing the plate. A transcendental frequency equation is obtained, the roots of which give the full spectrum of natural frequencies of oscillations of the orthotropic plate. It is noted that the proposed approach ensures the stability of numerical operations and high accuracy of results.
Authors and Affiliations
Н. Г. Сурьянинов, А. Ю. Бажанова, Т. С. Маковкина
Keywords
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