文克尔地基上阶梯式单向矩形薄板的振动

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Vibrations of One-Way Rectangular Stepped Thin Plates on Winkler’s Foundation

1.
Division 508. Department of Flight Vehicle Design and Applied Mechanics, Peking University ofAeronautics and Astronauties, Beijing 100083, P. R. China;
2.
North China Electric Power University, Beijing 102206, P. R. China

摘要: 用奇异函数建立文克尔地基上阶梯式单向矩形薄板自由振动和强迫振动的微分方程并求得其通解,用W算子给出主振型函数的表达式及常见支承条件下板的频率方程,用广义函数讨论板在不同形式载荷作用下的强迫振动响应.
- 文克尔地基 /
- 阶梯式单向矩形薄板 /
- 自由振动 /
- 强迫振动响应
Abstract: Differential equations of free forced vibrations of one-way rectangular stepped thin plated on Winkler's foundation are established by using singular functions,their general solutions are solved:exprssion of vibration mode function and frequency equations on usual supports are derived from Woperator:forced responses of such plates under different-type loads are discussed with generalized functions.
- Winkler’s foundation /
- one-way rcctangular stepped thin plate /
- free vibration /
- forced response

[1]	曹志远,《板壳振动理论》,中国铁道出版社,北京(1989).13-36.(in Chinese).
[2]	王燮山,《奇异函数及其在力学中的应用》,科学出版社,北京(1993).3-75.230-233.(in Chinese).
[3]	S.Timoshenko.et al.Vibration Problems in Engineering.4th.Ed.U.S.A.John Wiley& Sons Inc.(1974).363-433.

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