Dynamic Response of Elastic RectangularPlates by Spline State Variable Method

Chen Rongyi; Shen Xiaopu; Shen Pengcheng

Volume 21 Issue 6

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 2000 > 21(6): 625-632

Chen Rongyi, Shen Xiaopu, Shen Pengcheng. Dynamic Response of Elastic RectangularPlates by Spline State Variable Method[J]. Applied Mathematics and Mechanics, 2000, 21(6): 625-632.

Citation:

Chen Rongyi, Shen Xiaopu, Shen Pengcheng. Dynamic Response of Elastic RectangularPlates by Spline State Variable Method[J]. Applied Mathematics and Mechanics, 2000, 21(6): 625-632.

Citation:

Chen Rongyi, Shen Xiaopu, Shen Pengcheng. Dynamic Response of Elastic RectangularPlates by Spline State Variable Method[J]. Applied Mathematics and Mechanics, 2000, 21(6): 625-632.

PDF( 2145 KB)

Dynamic Response of Elastic RectangularPlates by Spline State Variable Method

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 Date: 1999-01-01
Rev Recd Date: 1999-12-24
Publish Date: 2000-06-15

Abstract

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.
- spline element,
- state space method,
- dynamic response,
- recursive scheme,
- spline state variable method

FullText(HTML)

References(17)

References

[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]	林文菁,徐次达.样条配点法分析结构动力响应的无条件稳定计算格式[J].力学学报,1988,20(4):353~361.
[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]	彭建设,张敬宇.由 Gurtin 变分原理求解一维动力响应的半解析法[J].力学学报,1998,26(6):708.
[7]	钟万勰.暂态历程的精细计算方法[J].计算结构力学及其应用,1995,12(1):1~6.
[8]	沈鹏程.多变量样条有限元法[M].北京:科学出版社,1997.
[9]	秦荣.计算结构动力学[M].南宁:广西师范大学出版社,1997.
[10]	常春馨.现代控制理论基础[M].北京:机械工业出版社,1988.
[11]	Timoshenko S P,Krieger S W.Theory of Plates and Shells[M].2nd ed.New York:McGraw-Hill,1959.
[12]	石钟慈.样条有限元[J].计算数学,1979,1(1):50~72.
[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]	沈小璞,肖卓.高层建筑结构动力时程响应分析的状态空间迭代法[J].建筑结构学报,1998,19(5):8~16.
[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]	侯宇,何福保.变厚度环形板自由振动问题的状态空间法[J].计算结构力学及其应用,1988,5(1):29~38.
[17]	王秀喜.工程中的计算力学及其应用[M].合肥:中国科技大学出版社,1992.

Relative Articles

[1]	LUO Gang, ZHANG Yulong, PAN Shaokang, JIA Hanghang, LIU Chang. Response Parameter Analysis of Submerged Floating Tunnels Under Underwater Shock[J]. Applied Mathematics and Mechanics, 2020, 41(5): 467-479. doi: 10.21656/1000-0887.400249
[2]	LIANG Xiqiang, GAO Qiang, YAO Weian. An Efficient Algorithm Based on Dynamic System Properties and Group Theory for Transient Responses of 1D Periodic Structures[J]. Applied Mathematics and Mechanics, 2018, 39(2): 170-182. doi: 10.21656/1000-0887.380129
[3]	KOU Lei, XU Jianguo, WANG Bo. Dynamic Response Analysis of Viscoelastic Multilayered Foundation in the Cartesian Coordinate System[J]. Applied Mathematics and Mechanics, 2018, 39(5): 529-537. doi: 10.21656/1000-0887.380155
[4]	LIU Xue-mei, DENG Zi-chen, HU Wei-peng. Structure-Preserving Algorithm for Fluid-Solid Coupling Dynamic Responses of Saturated Poroelastic Rods[J]. Applied Mathematics and Mechanics, 2016, 37(10): 1050-1059. doi: 10.21656/1000-0887.370106
[5]	LIU Xue-mei, DENG Zi-chen, HU Wei-peng. A Multi-Symplectic Method for Dynamic Responses of Incompressible Saturated Poroelastic Rods[J]. Applied Mathematics and Mechanics, 2015, 36(3): 242-251. doi: 10.3879/j.issn.1000-0887.2015.03.002
[6]	DONG Man-sheng, LI Man, LIN Zhi, TANG Fei, JIANG Shu-ping. Dynamic Response of the Submerged Floating Tunnel Under Random Seismic Excitation[J]. Applied Mathematics and Mechanics, 2014, 35(12): 1320-1329. doi: 10.3879/j.issn.1000-0887.2014.12.004
[7]	WANG Xiao-gang, HUANG Yi. 3-D Dynamic Response of Transversely Isotropic Saturated Soils[J]. Applied Mathematics and Mechanics, 2005, 26(11): 1278-1286.
[8]	LI Ying-hui, GAO Qing, YIN Xue-gang. Nonlinear Dynamic Response and Active Vibration Control of the Viscoelastic Cable With Small Sag[J]. Applied Mathematics and Mechanics, 2003, 24(5): 529-536.
[9]	DAI Jun, CHEN Jian-jun, LI Yong-gong, ZHAO Zhu-qing, MA Hong-bo. Dynamic Response Optimization Design for Engineering Structures Based on Reliability[J]. Applied Mathematics and Mechanics, 2003, 24(1): 39-46.
[10]	LI Ying-hui, GAO Qing, JIAN Kai-lin, YIN Xue-gang. Dynamic Responses of Viscoelatic Axially Moving Belt[J]. Applied Mathematics and Mechanics, 2003, 24(11): 1191-1196.
[11]	YAN Bo, ZHANG Ru-qing. Penalty Finite Element Method for Nonlinear Dynamic Response of Viscous Fluid-Saturated Biphasic Porous Media[J]. Applied Mathematics and Mechanics, 2000, 21(12): 1247-1254.
[12]	Zhang Lianwen, Xia Renwei, Zeng Guangwu. Computation of Frequencies and Damping Ratios for Adaptive Structures[J]. Applied Mathematics and Mechanics, 1999, 20(6): 647-653.
[13]	Jin Bo. Using Fredholm Integral Equation of the Second Kind to Solve the Vertical Vibration of Elastic Plate on an Elastic Half Space[J]. Applied Mathematics and Mechanics, 1998, 19(2): 145-150.
[14]	Ding Rui, Zhu Zhengyou, Cheng Changjun. Boundary Element Method for Solving Dynamical Response of Viscoelastic Thin Plate(Ⅱ)——Theoretical Analysis[J]. Applied Mathematics and Mechanics, 1998, 19(2): 95-103.
[15]	Ding Rui, Zhu Zhengyou, Cheng Changjun. Boundary Element Method for Solving Dynamical Response of Viscoelastic Thin Plate (Ⅰ)[J]. Applied Mathematics and Mechanics, 1997, 18(3): 211-216.
[16]	Peng Jianshe, Zhang Jingyu, Yang Jie. Formulation of a Semi-Analytical Approach Based on Gurtin Variational Principle for Dynamic Response of General Thin Plates[J]. Applied Mathematics and Mechanics, 1997, 18(11): 987-991.
[17]	Yin Bangxin. Analysis of Dynamic Responce of an impacted Elastic Plate[J]. Applied Mathematics and Mechanics, 1996, 17(7): 639-644.
[18]	Ji Zhen-yi, Yeh Kai-yuan. The General Solution for Dynamic Response of Nonhomogeneous Beam with Variable Cross Section[J]. Applied Mathematics and Mechanics, 1994, 15(5): 381-388.
[19]	Yeh Kai-yuan, Tong Xiao-hua, Ji Zhen-yi. General Analytic Solution of Dynamic Response of Beams with Nonhomogeneity and Variable Cross Section[J]. Applied Mathematics and Mechanics, 1992, 13(9): 753-764.
[20]	Fu Yi-ming, Liu Xiao-hu. Nonlinear Dynamic Response and Dynamic Buckling of Shallow Spherical Shells with Circular Hole[J]. Applied Mathematics and Mechanics, 1992, 13(2): 145-156.