GENERAL DYNAMIC EQUATION AND DYNAMICAL CHARACTERISTICS OF VISCOELASTIC TIMOSHENKO BEAMS

Applied Mathematics and Mechanics (English Edition) ›› 1990, Vol. 11 ›› Issue (2): 177-184.

GENERAL DYNAMIC EQUATION AND DYNAMICAL CHARACTERISTICS OF VISCOELASTIC TIMOSHENKO BEAMS

肖灿章, 计伊周, 常保平

Research Division of Engineering Mechanics, Shanxi Institute of Mechanical Engineering, Xi'an

收稿日期:1988-10-12 出版日期:1990-02-18 发布日期:1990-02-18

GENERAL DYNAMIC EQUATION AND DYNAMICAL CHARACTERISTICS OF VISCOELASTIC TIMOSHENKO BEAMS

Xiao Can-zhang, Ji Yi-zhou, Chang Bao-ping

Research Division of Engineering Mechanics, Shanxi Institute of Mechanical Engineering, Xi'an

Received:1988-10-12 Online:1990-02-18 Published:1990-02-18

摘要/Abstract

摘要： In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method.To measure the complex moduli and three parameters of standard linear solid, the forced vibration technique of beam is successfully used for PCL and PMMA specimens.The dynamical characteristics of viscoelastic Timoshenko beams, especially the damping properties, are derived from a considerable number of numerical computations.The analyses show that the viscosity of materials has great influence on dynamical characteristics of structures, especially on damping, and the standard linear solid model is the better one for describing the dynamic behavior of high viscous materials.

关键词: sharp criterion, invariant manifold, harmonic potential, combined powertype nonlinearities

Abstract: In this paper, a governing differential equation of viscoelastic Timoshenko beam including both extension and shear viscosity is developed in the time domain by direct method.To measure the complex moduli and three parameters of standard linear solid, the forced vibration technique of beam is successfully used for PCL and PMMA specimens.The dynamical characteristics of viscoelastic Timoshenko beams, especially the damping properties, are derived from a considerable number of numerical computations.The analyses show that the viscosity of materials has great influence on dynamical characteristics of structures, especially on damping, and the standard linear solid model is the better one for describing the dynamic behavior of high viscous materials.

Key words: sharp criterion, invariant manifold, harmonic potential, combined powertype nonlinearities

肖灿章;计伊周;常保平. GENERAL DYNAMIC EQUATION AND DYNAMICAL CHARACTERISTICS OF VISCOELASTIC TIMOSHENKO BEAMS[J]. Applied Mathematics and Mechanics (English Edition), 1990, 11(2): 177-184.

Xiao Can-zhang;Ji Yi-zhou;Chang Bao-ping. GENERAL DYNAMIC EQUATION AND DYNAMICAL CHARACTERISTICS OF VISCOELASTIC TIMOSHENKO BEAMS[J]. Applied Mathematics and Mechanics (English Edition), 1990, 11(2): 177-184.

参考文献

[1] Pan,H.H.,Vibration of a viscoelastic Timoshenkobeam,J.of Engineering Mechanic Div.,92,2(1966),213-234.
[2] Huang,T.C.and C.C.Huang,Free vibrations of viscoelastic Timoshenko beams,J.of Applied Mechanics,38.2(1971),515-521.
[3] Paipeties,S.A.,P.S.Theocaris and C.A.Stassnakis,Complex moduli derived form the vibrations of a Timoshenko beam.Acoustica,44,1(1980),27-34.
[4] Ji Yi-zhou,Wang Zhong-ming,Liu Xie-hui and Liu Xian-da.,Free vibrations of viscoelastic Timoshenko beams,Mechanics and Practice,5(1987),16-19.(in Chinese).
[5] Lee,C.H.,Forced lateral vibration of a uniform cantilever beam with internal and external damping,J.of Applied Mechanics,27.3(1960),551-556.
[6] Tobe,Toshimi and Keijin Sato,Lateral vibrations of cantilever beams considering the effects of rotatory inertia shear flexibility and viscosity.Bulletin of the JSME,16,94(1973),696-704.
[7] Sun Jia-ju and Jin Kai-hua.,Dynamic response of viscoelastic beam,Applied Mathematics and Mechanics,2,2(1981).255-264.
[8] Newman,M.K.,Viscous damping in flexural vibration of bars,J.of Applied Mechanics,26,3(1959),367-376.
[9] Baker,W.E.,W.E.Woolan and D.Young,Air and internal damping of thin cantilever beams,Int.J.Mech.Sci.,9,4(1967),743-766.
[10] Wu Rui-feng,Xi Xiao-feng and Hua Yu,The dynamical analysis of viscoelastic beams,Earthquake Engineering and Engineering Vibration,3,2(1983),16-30.(in Chinese).
[11] Chang Bao-ping.,Xiao Can-zhang and Ji Yi-zhou,Dynamical characteristics of viscoelastic beam on viscoelastic foundation,J.Shanxi Inst.of Mech.Engrg.,4,4(1988),97-106.(in Chinese).
[12] Chang Bao-ping,The vibration beam technique for measuring the complex modulus and viscoelastic parameters of viscoelastic material,M.A.Degree Thesis,Shanxi Inst.of Mech.Engrg.(1988).(in Chinese).
[13] Yu Jia-yu and Zhang Cong,The frequency response of viscoelastic model materials,J.of Civil Engrg.,20,1(1987),28-36.(in Chinese)

GENERAL DYNAMIC EQUATION AND DYNAMICAL CHARACTERISTICS OF VISCOELASTIC TIMOSHENKO BEAMS

GENERAL DYNAMIC EQUATION AND DYNAMICAL CHARACTERISTICS OF VISCOELASTIC TIMOSHENKO BEAMS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价

[1]	徐润章徐闯. Nonlinear Schr¨odinger equation with combined power-type nonlinearities and harmonic potential[J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(4): 521-528.
[2]	杨柳. THE INVARIANT MANIFOLD METHOD AND THE CONTROLLABILITY OF NONLINEAR CONTROL SYSTEM[J]. Applied Mathematics and Mechanics (English Edition), 2000, 21(11): 1320-1330.
[3]	赵国景;魏建国. INVARIANT SUB-MANIFOLDS AND MODES OF NONLINEAR AUTONOMOUS SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 1998, 19(7): 687-693.
[4]	刘杰. INVARIANT MANIFOLDS AND THEIR STABILITY IN A THREE-DIMENSIONAL MEASURE-PRESERVING MAPPING SYSTEMS[J]. Applied Mathematics and Mechanics (English Edition), 1995, 16(10): 943-950.