Пространственная дисперсия акустических волн в функционально-градиентных стержнях

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Аннотация

Гармонические акустические волны в полубесконечном функционально-градиентном (ФГ) одномерном стержне с продольной произвольной неоднородностью анализируются комбинированным методом, основанным на модифицированном формализме Коши и методе экспоненциальных матриц. Построены замкнутые дисперсионные уравнения для гармонических волн, из решения которых получены неявные дисперсионные соотношения для акустических волн в ФГ стержнях. Для продольной неоднородности полиномиального типа соответствующие дисперсионные соотношения строятся в явном виде.

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А. И. Каракозова

Национальный исследовательский Московский Государственный Строительный Университет

Автор, ответственный за переписку.
Email: karioca@mail.ru
Россия, Москва

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2. Рис. 1. 1D ФГ-стержень; n показывает направление нормали волны и x показывает направление координатной оси вдоль направления распространения волны.

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3. Рис. 2. Вариации величин и удельных энергий с расстоянием для линейного бинома при гармоническом по времени возбуждении 2 Гц и возрастающей фазовой скорости; (а) величины; (b) удельные энергии.

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4. Рис. 3. Изменения модулей и удельных энергий с расстоянием для линейного бинома при гармоническом по времени возбуждении 2 Гц и убывающей фазовой скорости; (а) величины; (b) удельные энергии.

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