Boundary element approaches to the problem of 2-d non-stationary elastic vibrations
Дата
2020
Автори
Vorona, Yu. V.
Kozak, A. A.
Заголовок журналу
Журнал ISSN
Назва тому
Видавець
КНУБА
Анотація
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.
Опис
Ключові слова
кафедра будівельної механіки, time-dependent boundary integral equations, frequency domain, Hankel functions, Maclaurin series, impulse loading, гранично-часові інтегральні рівняння, частотна область, функції Ганкеля, ряд Маклорена, імпульсне навантаження, гранично-временные интегральные уравнения, частотная область, функции Ганкеля, ряд Маклорена, импульсное нагружение
Бібліографічний опис
Vorona Yu. V. Boundary element approaches to the problem of 2-d non-stationary elastic vibrations / Yu. V. Vorona, A. A. Kozak // Опір матеріалів і теорія споруд : зб. наук. праць / Київ. нац. ун-т буд-ва і архіт. ; гол. ред. П. П. Лізунов. - Київ : КНУБА, 2020. - С. 321 - 327. - Бібліогр. : 4 назви.