弹性地基上自由边矩形薄板几个问题的注记
Remarks of Some Problems for Rectangular Thin Plates with Free Edges on Elastic Foundations
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摘要: 对于弹性地基上自由边矩形薄板的弯曲、稳定和振动问题,本文选择了一个挠曲函数,它能精确满足自由边全部边界条件以及自由角点的条件.应用能量变分原理,给出了确定挠曲函数中待定参数的方程,以及稳定性方程和频率方程,给出了求最小临界力和最小固有频率的一般公式.Abstract: For the bending,stability and vibrations of rectangular thin plates with free edges on elastic foundations,in this paper we give a flexural function which exactly satisfies not only all the boundary conditions on free edges but also the conditions at free corner points.Applying energy variation principle,we give equations defining parameters in flexural function,stability equation,frequency equation,and general formulae of minimum critical force and minimum eigenfrequency as well.
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Key words:
- bending /
- flexural function /
- stability /
- vibration /
- critical force /
- frequency
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[1] Власов В.З.и Н.Н.Леонтъев,Балкц,Плцмы ц Оболочкц на Упруюм Основанцц,Гос.ИЗ.,М.(1960). [2] Кононенко Е.С.,О цриближенном расчете прямоуголъных длнт аа упругом основании,Исслебованця по Теорцц Сооруженцй,Сборнцк Смамей,9,11(1960). [3] 张福范,《弹性薄板》(第二版),科学出版社(1984) 237-249. [4] 成祥生,弹性地基上自由边矩形板的弯曲、稳定和振动,应用数学和力学,9,6(1988),529-533. -
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