Моделирование нелокальных пористых функционально-градиентных нанобалок под действием движущихся нагрузок

Исследован динамический отклик пористых функционально-градиентных наноматериалов на движущиеся нагрузки. Анализ проводился с использованием двух подходов: метода Ритца с использованием преимуществ, достигаемых за счет внедрения полиномов Чебышева в форме косинуса, и метода дифференциальных квадратур с последующим обратным преобразованием Лапласа. Оба подхода применяют модель нанотонкой балки с учетом улучшенной модели более высокого порядка и нелокальной теории градиента деформации с двумя характерными шкалами длины, называемыми шкалами нелокальности и градиента деформации. Степенные зависимости ориентируются на составных конструкциях пористых материалов с различными факторами: объем пор, равномерное или неравномерное распределение пор. Принят переменный модуль масштаба для дальнейшего повышения точности за счет учета масштабных эффектов для градуированных нанотонких балок. В первой части работы рассмотрено уравнение движения, которое решено путем применения техники Ритца с полиномами Чебышева. Во второй части выполнен анализ уравнения для нанобалок, где применен метод дифференциальных квадратур для их дальнейшей дискретизации, а обратное преобразование Лапласа использовано для получения динамических прогибов. Результаты исследования позволяют объяснить влияние скорости движущейся нагрузки, нелокальных факторов градиента деформации, пористости, числа и распределения пор, а также упругой среды на динамический прогиб функционально-градуированных нанобалок.

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