Двусторонняя аналитическая оценка первой частоты плоской фермы

Двусторонняя аналитическая оценка первой частоты плоской фермы

Автор: Воробьев Олег

Журнал: Строительство уникальных зданий и сооружений @unistroy

Статья в выпуске: 7 (92), 2020 года.

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Объект исследования - статически детерминированная консольная ферма. Трасса состоит из прямоугольных панелей с направленными вниз диагональными балками. Ферма имеет две опоры, одна из которых неподвижно-шарнирная, а другая роликовая. Массы располагаются в узлах верхней и нижней поясов. Силы в стержнях и реакции на опорах определяются методом совместной изоляции. Вертикальное смещение узлов выводится из метода Максвелла-Мора с предпосылкой линейной упругости. Зависимость вертикального смещения, оценок Дункерли и Рэлея частоты первичной фермы от количества панелей выводится из индуктивного анализа набора конкретных ферм с увеличивающимся количеством панелей. Рекуррентные уравнения, отвечающие определенным коэффициентам, выводятся с использованием специальных функций системы компьютерной алгебры Maple. Полученные решения являются полиномиальными с количеством панелей в качестве переменных. Коэффициент Рэлея рассчитывается с предположением, что первая мода вибрации равна прогибу фермы под действием равномерно распределенной нагрузки. Построены графики зависимости полученных оценок от масс узлов, количества панелей, жесткости и размеров фермы.

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Ферма, аналитическое решение, частота, метод Дункерли, фактор Рэлея, клен, символьная индукция

Короткий адрес: https://sciup.org/143172555

IDR: 143172555   |   DOI: 10.18720/CUBS.92.4

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