粘弹性Timoshenko梁的动力学普遍方程及其动态特性分析
General Dynamic Equation and Dynamical Characteristics of Viscoelastic Timoshenko Beams
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摘要: 本文用直接力法在时域内推导了粘弹性Timoshenko梁的控制微分方程,它同时计及了材料的拉伸粘性和剪切粘性.为了测定标准线性固体的复模量和三参数,对有机玻璃(PMMA)和尼龙6(PCL)试件成功地应用了强迫振动梁技术.通过大量数值计算,对粘弹性Timoshenko梁的动力特性,特别是阻尼特性进行了分析.结果表明,材料粘性对结构的动力特性,尤其是对阻尼有较大影响。对于高粘性材料,其动力学性质用标准线性固体模型来描写是合适的.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.
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[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] 计伊周、王忠民、刘协会、刘宪达,粘弹性Timoshenko梁的自由振动,力学与实践,(1987),16-19. [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] 孙家驹、金开骤,粘弹性梁的动力响应,应用数学和力学,2,2(1981),235-241. [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] 邬瑞锋、奚肖风、华玉,粘弹性梁的动力分析,地震工程与工程振动,3,2(1983),16-30. [11] 常保平、肖灿章、计伊周,粘弹性基础土的粘弹性梁的动力特性,哄西机械学院学报,4,4(1988),97-106. [12] 常保平,用振动梁方法测量粘弹性材料的复模量和粘弹性参数,常保平硕士学位论文第四节,陕西机械学院(1988). [13] 余家钮,张聪,粘弹性模型材料的频率响应,土木工程学报,20,1(1987),28-36.
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