Аннотації
04.06.2020
Для аналізу нестаціонарних коливань пружних масивів використовуються два граничноелементні підходи. Перший пов'язаний з переходом в частотну область, а другий реалізує процедуру інтегрування за часом. Проведено порівняння методів при вирішенні задачі про імпульсне навантаження пружного середовища з двома циліндричними порожнинами.
Для анализа нестационарных колебаний упругих массивов используются два граничноэлементных подхода. Первый из них связан с переходом в частотную область, а второй реализует процедуру интегрирования по времени. Проведено сравнение методов при решении задачи об импульсном нагружении упругой среды с двумя цилиндрическими полостями.
Two boundary element approaches are used to solve the problem on non-stationary vibrations of elastic solids. The first approach is based on the transition to the frequency domain by means of a Fourier series expansion. The second approach is associated with the direct solution of a system of time-dependent boundary integral equations, with a piecewise constant approximation of the dependence of the unknowns on time. In both cases, a collocation scheme is used to algebraize the integral equations, and the difficulties associated with the calculation of singular integrals are overcome by replacing the kernels with the initial segment of the Maclaurin series. After such a replacement, the kernels take the form of a sum, the first term of which is the corresponding fundamental solution of the statics problem while other terms are regular. Since integration of static kernels is not difficult the problem of calculating the diagonal coefficients of the SLAE turns out to be solved. The developed techniques are compared in the process of dynamics analysis solving of elastic media with two cylindrical cavities. The boundary of one of the cavities is subjected to a radial impulse load, which varies according to the parabolic law. Both approaches have shown the similar effectiveness and qualitative consistency.
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