DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD

Applied Mathematics and Mechanics (English Edition) ›› 2000, Vol. 21 ›› Issue (6): 691-698.

DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD

陈荣毅¹, 沈小璞², 沈鹏程³

1. Structural Engineering Department, Tongji University, Shanghai 200092, P R China;
2. Structural Engineering Department, Anhui Industry College of Architecture, Hefei 230022, P R China;
3. Civil Engineering Department, Hefei University of Technology, Hefei 230009, P R China

收稿日期:1999-01-18 修回日期:1999-12-24 出版日期:2000-06-18 发布日期:2000-06-18
基金资助:
the Natural Science Foundations of Anhui Education Committee of China(97JL171)

DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD

Chen Rongyi¹, Shen Xiaopu², Shen Pengcheng³

1. Structural Engineering Department, Tongji University, Shanghai 200092, P R China;
2. Structural Engineering Department, Anhui Industry College of Architecture, Hefei 230022, P R China;
3. Civil Engineering Department, Hefei University of Technology, Hefei 230009, P R China

Received:1999-01-18 Revised:1999-12-24 Online:2000-06-18 Published:2000-06-18
Supported by:
the Natural Science Foundations of Anhui Education Committee of China(97JL171)

摘要/Abstract

摘要： Application of spline element and state space method for analysis of dynamic response of elastic rectangular plates is presented. The spline element method is used for space domain and the state space method in control theory of system is used for time domain. A state variable recursive scheme is developed, then the dynamic response of structure can be calculated directly. Several numerical examples are given. The results which are presented to demonstrate the accuracy and efficiency of the present method are quite satisfactory.

关键词: spline element, state space method, dynamic response, recursive scheme, spline state variable method

Abstract: Application of spline element and state space method for analysis of dynamic response of elastic rectangular plates is presented. The spline element method is used for space domain and the state space method in control theory of system is used for time domain. A state variable recursive scheme is developed, then the dynamic response of structure can be calculated directly. Several numerical examples are given. The results which are presented to demonstrate the accuracy and efficiency of the present method are quite satisfactory.

Key words: spline element, state space method, dynamic response, recursive scheme, spline state variable method

中图分类号:

TU311.3

陈荣毅;沈小璞;沈鹏程. DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(6): 691-698.

Chen Rongyi;Shen Xiaopu;Shen Pengcheng. DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(6): 691-698.

参考文献

[1] Clough R W. Dynamics of Structures[M]. New York: McGraw-Hill Book Co,1975.
[2] Newmak N M. A method of computation for structural dynamics[J]. ASCE J Engineering Mechanics Division,1959,85(3):67～94.
[3] Bathe K J, Wilson E L. Numerical Methods in Finite Element Analsis[M]. New Jersey: Prentice-Hall, Inc,1976.
[4] Liu Wenqing,Xu Cida.An unconditional stable calculation scheme for the dynamic response of structures by the method of spline collocation[J].Acta Mechanica Sinica,1988,20(4):353~361.(in Chinese).
[5] Shen Pengcheng, Huang Dade. Dynamics analysis of stiffened plates and shells using spline Gauss callocation method[J]. Int J Computers & Structures,1990,36(4):625～629.
[6] Peng Jianshe,Zhang Jinyu.A semi-analytical approach based on Gurtin variational principle for dynamic response of one dimensional problems[J].Acta Mechanica Sinica,1992,26(6):708~716.(in Chinese).
[7] Zhong Wanxie.A precise time computational method[J].Computational Structural Mechanics and Applications,1995,12(1):1~6.(in Chinese).
[8] Shen Pengcheng.Multivariable Spline Finite Element Method[M].Beijing:Science Press,1997.(in Chinese).
[9] Qin Rong.Computational Structural Dynamics[M].Nanning:Guangxi Educational University Press,1997.(in Chinese).
[10] Chang Chunxin.Fundamentals of Modern Control Theory[M].Beijing:Machine Industry Press,1988.(in Chinese).
[11] Timoshenko S P, Krieger S W. Theory of Plates and Shells[M]. 2nd ed. New York: McGraw-Hill,1959.
[12] Shi Chungtze.On spline f inite element method[J].Math Numer Sinica,1979,1(1):50~72.(in Chinese).
[13] Mizusawa T, Kajita T, Naruok M. Vibration of skew plates using spline functions[J]. J Sound and Vibration,1979,62(2):301～308.
[14] Shen Xiaopu,Xiao Zhuo.State space iteration method f or analysis of dynamic time history response of tall building structures[J].J Building Structures,1998,19(5):8~16.(in Chinese).
[15] Shen Pengcheng, He Peixiang. Vibration analysis for plates using multivariable spline element method[J]. Int J Solid & Structures,1992,29(24):3289～3295.
[16] Hou Yu,He Fubao.The state space method f or the free vibration problem of annular plates with variable thickness[J].Computational Structural Mechanics and Applications,1988,5(1):29~38.(in Chinese).
[17] Wang Xiuxi.Computational Mechanics and Applications in Engineering[M].Hefei:University of Science and Technology of China Press,1992.(in Chinese).

DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD

DYNAMIC RESPONSE OF ELASTIC RECTANGULAR PLATES BY SPLINE STATE VARIABLE METHOD

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