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Известия РАН. Механика твердого тела, 2023, № 5, стр. 138-146

ФУНДАМЕНТАЛЬНЫЕ РЕШЕНИЯ УРАВНЕНИЙ ТЕОРИИ КОЛЕБАНИЙ ДЛЯ АНИЗОТРОПНЫХ УПРУГИХ СРЕД

А. В. Ильяшенко a, *

a Московский государственный строительный университет
Москва, Россия

* E-mail: avi_56@mail.ru

Поступила в редакцию 20.12.2022
После доработки 09.01.2023
Принята к публикации 12.01.2023

Аннотация

Осуществляется построение фундаментальных решений в R3 для уравнений гармонических колебаний в теории упругости анизотропных упругих сред. Решения строятся в виде рядов по мультиполям. Доказываются теоремы о сходимости рядов в топологии компактной сходимости в ${{R}^{{\text{3}}}}{{\backslash }}0$. Обсуждаются проблемы построения некоторых сингулярных решений теории колебаний анизотропного тела. Фундаментальное решение уравнений колебаний для изотропной среды получено в замкнутом виде.

Ключевые слова: фундаментальные решения, анизотропия, изотропия, теория колебаний

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