Vibrations of Stepped One-Way Thin Rectangular Plates Subjected to in-Plane Tensile/Compressive Force in y-Direction on Winkler’s Foundation

Zhang Yingshi

Volume 21 Issue 7

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Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(7): 708-714

Zhang Yingshi. Vibrations of Stepped One-Way Thin Rectangular Plates Subjected to in-Plane Tensile/Compressive Force in y-Direction on Winkler’s Foundation[J]. Applied Mathematics and Mechanics, 2000, 21(7): 708-714.

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Vibrations of Stepped One-Way Thin Rectangular Plates Subjected to in-Plane Tensile/Compressive Force in y-Direction on Winkler’s Foundation

Zhang Yingshi

Division 508, Department of Flight Vehicle Design and Applied Mechanics, Beijing University of Aeronautics and Astronautics, Beijing 100083, P R China

Received Date: 1998-10-20
Rev Recd Date: 2000-03-25
Publish Date: 2000-07-15

Abstract

Abstract

Differential equations of free/forced vibrations of n-step one-way thin rectangular plates subjected to in-plane tensile/compressive force in y-direction on Winkler's foundation are established by using singular functions,their general solutions solved for,expression of vibration mode function and frequency equation on usual supports derived with Woperator.Influence functions for various cases deduced here may also be used to resolve problems of static buckling or stability for beams and plates in relevant circumstances.
- rectangular plate,
- free vibration,
- forced vibration,
- response,
- Winkler’s foundation,
- subjected to in-plane tensile/compressive force,
- stepped

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References

[1]	Ercoli L, Laura P A A. Analytical and experimental investigation on vibrating, continuous rectangular plates of non-uniform thickness[J]. Journal of Sound and Vibration,1987,112(3):447～454.
[2]	张英世,王燮山. 文克尔地基上阶梯式单向矩形薄板的振动[J]. 应用数学和力学,1998,19(2):157～164.
[3]	张英世,蒋持平. 阶梯式矩形板的振动[J]. 应用力学学报,1998,15(4):109～115.
[4]	张英世. 文克尔地基上阶梯式矩形薄板的振动[J]. 应用数学和力学,1999,20(5):535～542.
[5]	张英世,顾煜炯. 中面单向受拉(压)的阶梯式矩形薄板的振动[J]. 上海力学,1999,20(4):437～442.
[6]	曹志远. 板壳振动理论[M]. 北京:中国铁道出版社,1989,16-33,182～183.

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