An Equation of Motion for a Thick Viscoelastic Plate

Yang Zheng-wen; Yang Ting-qing

Volume 13 Issue 5

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(5): 459-467

Yang Zheng-wen, Yang Ting-qing. An Equation of Motion for a Thick Viscoelastic Plate[J]. Applied Mathematics and Mechanics, 1992, 13(5): 459-467.

Citation:

Yang Zheng-wen, Yang Ting-qing. An Equation of Motion for a Thick Viscoelastic Plate[J]. Applied Mathematics and Mechanics, 1992, 13(5): 459-467.

Citation:

Yang Zheng-wen, Yang Ting-qing. An Equation of Motion for a Thick Viscoelastic Plate[J]. Applied Mathematics and Mechanics, 1992, 13(5): 459-467.

PDF( 512 KB)

An Equation of Motion for a Thick Viscoelastic Plate

Huazhong University of Science and Technology, Wuhan

Received Date: 1991-05-11
Publish Date: 1992-05-15

Abstract

Abstract

In this paper an equation of motion is presented for a general thick viscoelastic plate, including the effects of shear deformation, extrusion deformation and rotatory inertia.This equation is the generalization of equations of motion for the corresponding thick elastic plate, and it can be degenerated into several types of equations for various special cases.
- viscoelastic,
- thick plate,
- equation of motion

FullText(HTML)

References(16)

References

[1]	Reissner,E.,The effect of transverse shear deformation on the bending of elastic plates,J.Appl.Mech.,12 (1945),69-77.
[2]	Mindlin,R.D.,Influence ofrotatory inertia and shear on flexural motions of isotropic elastic plates,J.Appl.Mech.,18 (1951),31-38.
[3]	胡海昌,各向同性夹层板反对称小挠度的若干问题,力学学报,(6)(1963),53-60
[4]	曹志远、杨异田,《厚板动力学理论及其应用》,科学出版社(1983).
[5]	Radovskii,B.S.,Application of the calculation scheme for a layered viscoelastic medium to the estimation of the stressed state of highways and airport pavements with moving loads,Soviet Appl.Mech.,15,10 (1979),940-946.
[6]	Hewitt,J.S.and J.Mazumdar,Vibration of viscoelastic plates under transverse load by the method of constant deflection contours,J.Sound Vib.,33,3 (1974),319-333.
[7]	Robertson,S.R.,Solving the problem of forced motion of viscoelastic plates by Valanis' method with an application to a circular plate,J.Sound Vib.,14,3 (1971),263-278.
[8]	杨挺青等,粘弹性基支薄板的准静态弯曲,华中工学院学报,15(1987),1-6
[9]	Mase,G.E.,Behavior of viscoelastic plates inbending,J.Engng Mech.Div.ASCE,86,EM3 (1960),25-39.
[10]	Pan,H,H.,Vibration of viscoelastic plates,J.de Mecanique,5,3 (1966),355-374.
[11]	Nagaya,K.,Dynamics of viscoelastic plate with curved boundaries of arbitrary shape,J.Appl.Mech.,45 (1978),629-635.
[12]	Pister,K.S.,Viscoelastic plate on a viscoelastic foundation,J.Engng.Mech.Div.ASCE,87,EM1(1961),43-54.
[13]	Srinivas,S.and A.K.Rao,Flexure of thick rectangular viscoelastic plates,J.Engng Mech.Div.ASCE,98,EM3,(1972),771-776.
[14]	Kobayashi,H.and K.Sonoda,Thick circular plates on linear viscoelastic foundations,Proc.31rd Japan National Congress for Appl.Mech.,Tokyo,Theo.& Appl.Mech.,81,Nov.(1981),153-164.
[15]	Gurtin,M.E.and E.Sternberg,On the linear theory of viscoelasticity,Arch.Rational Mech.Anal.,11 (1962),291-356.
[16]	Власов Б.Ф.,Об уравнениях теории изгиба пластинок,Изэ.АН СССР.ОТН,12(1957),57-60

Relative Articles

[1]	Rebhi A. Damseh, Ben Bella A. Shannak. Visco-Elastic Fluid Flow Past an Infinite Vertical Porous Plate in the Presence of First Order Chemical Reaction[J]. Applied Mathematics and Mechanics, 2010, 31(8): 909-916. doi: 10.3879/j.issn.1000-0887.2010.08.003
[2]	LI Dan, HU Geng-kai. Effective Viscoelastic Behavior of Particulate Polymer Composites at Finite Concentration[J]. Applied Mathematics and Mechanics, 2007, 28(3): 270-280.
[3]	ZHANG Neng-hui, WANG Jian-jun, CHENG Chang-jun. Complex-Mode Galerkin Approach in Transverse Vibration of an Axially Accelerating Viscoelastic String[J]. Applied Mathematics and Mechanics, 2007, 28(1): 1-8.
[4]	BAO Lin, HU Jin-song, YU Yong-liang, CHENG Peng, XU Bo-qing, TONG Bing-gang. Viscoelastic Constitutive Model Related to Deformation of Insect Wing Under Loading in Flapping Motion[J]. Applied Mathematics and Mechanics, 2006, 27(6): 655-662.
[5]	ZHAO Wei-jia, CHEN Li-qun, Jean W Zu. Finite Difference Method for Simulatting Transverse Vibrations of an Axially Moving Viscoelatic String[J]. Applied Mathematics and Mechanics, 2006, 27(1): 21-27.
[6]	ZHENG Yu-fang, FU Yi-ming. Effect of Damage on Nonlinear Dynamic Properties of Viscoelastic Rectangular Plates[J]. Applied Mathematics and Mechanics, 2005, 26(3): 293-299.
[7]	GUO Shao-hua. Eigen Theory of Viscoelastic Dynamics Based on theKelvin-Voigt Model[J]. Applied Mathematics and Mechanics, 2004, 25(7): 723-728.
[8]	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.
[9]	YANG Hai-tian, GAO Qiang, GUO Xing-lin, WU Rui-feng. A New Algorithm of Time Stepping in Dynamic Viscoelastic Problems[J]. Applied Mathematics and Mechanics, 2001, 22(6): 579-586.
[10]	YAO Da-kang, YAN Yu-bing, LIU Zhao-rong. The Effects of Blood Viscoelasticity on the Pulse Wave in Arteries[J]. Applied Mathematics and Mechanics, 2000, 21(9): 954-960.
[11]	Ding Rui, Zhu Zhengyou, Cheng Changjun. Some Dynamical Properties of a Viscoelastic Cylindrical Shell[J]. Applied Mathematics and Mechanics, 1999, 20(3): 221-228.
[12]	Yin Yihui, Chen Gang, Chen Yuze. A Solving Method for a System of Partial Differential Equations With an Application to the Bending Problem of a Thick Plate[J]. Applied Mathematics and Mechanics, 1999, 20(11): 1168-1174.
[13]	Yang Haitian, Wu Ruifeng, Zhang Qun. Identification of Qusi-Static Displacement for Constitutive Models of Viscoelasticity[J]. Applied Mathematics and Mechanics, 1998, 19(3): 217-221.
[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]	Xu Xu, He Fubao. Three Dimensional Elasticity Solution for Vibration Problem of Thick Plate[J]. Applied Mathematics and Mechanics, 1998, 19(7): 577-585.
[16]	Xiao Wanshen, Zeng Qingyuan, Liu Qingtan. Three-Dimensional Analysis on Plates[J]. Applied Mathematics and Mechanics, 1997, 18(9): 833-844.
[17]	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.
[18]	Guo Zhong-san. Fluid Mechanics of Microvascular Vasomotion and the Effects of Blood Viscoelasticity[J]. Applied Mathematics and Mechanics, 1992, 13(2): 157-163.
[19]	Ji Zhen-yi. An Exact Element Method for the Bending of Nonhomogeneous Reissner’s Plate[J]. Applied Mathematics and Mechanics, 1991, 12(11): 997-1005.
[20]	Wang Ke-rang. Thick Rectangular Plates with Free Edges on Elastic Foundations[J]. Applied Mathematics and Mechanics, 1990, 11(9): 817-826.