弹性地基上简支梁在热载荷作用下的自由振动
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摘要
基于Hamilton原理,得到了弹性地基粱在均匀升温作用下的非线性自由振动控制方程。运用Kantorovich平均法将非线性偏微分方程转化成一组常微分方程,考虑不可移简支边界条件,采用打靶法得到了一阶屈曲位形下的前三阶振型的数值结果。结果表明:随地基弹性系数增加,热屈曲临界温度增加;在小振幅的情形下,振型对屈曲构型的影响很小。
Based on the Hamilton principle,the control equations of the nonlinear free vibration on elastic foundation beam under the uniform temperature rise are obtained in this paper and the nonlinear partial differential equations are converted into a set of ordinary ones by using Kantorovich averaging procedure.Considering immovable simply supported boundary conditions,the numerical results of the first to third vibration modes under the first post-buckling mode are obtained by employing the shooting method.The result shows that the critical temperature of thermal buckling will increase with the increase of the foundation's elastic coefficient value and the affect of vibration modes to the first buckling configuration is negligible in the small amplitude.
Based on the Hamilton principle,the control equations of the nonlinear free vibration on elastic foundation beam under the uniform temperature rise are obtained in this paper and the nonlinear partial differential equations are converted into a set of ordinary ones by using Kantorovich averaging procedure.Considering immovable simply supported boundary conditions,the numerical results of the first to third vibration modes under the first post-buckling mode are obtained by employing the shooting method.The result shows that the critical temperature of thermal buckling will increase with the increase of the foundation's elastic coefficient value and the affect of vibration modes to the first buckling configuration is negligible in the small amplitude.
引文
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[5]彭震,杨志安.Winkler地基梁在温度场中受简谐激励的3次超谐共振分析[J].地震工程与工程振动,2006,26(5):239-242.
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[10]Li S R,Batra R C.Thermal Buckling and Postbuckling of Euler-Bernoulli Beams Supported on Nonlinear elastic Foundations[J].AIAAJOURNAL,2007,45(3):712-720.
[2]Rosa MA.Free vibrations of Timoshenko beam on two-parameter elastic foundation[J].Computeres and Structures,1995,57(1):151-156.
[3]彭震,杨志安.Winkler地基梁在温度场中受简谐激励的主共振分析[J].地震工程与工程振动,2006,26(3):91-93.
[4]彭震,杨志安.Winkler地基梁在温度场中受简谐激励的1/3次亚谐共振分析[J].地震工程与工程振动,2006,26(4):132-135.
[5]彭震,杨志安.Winkler地基梁在温度场中受简谐激励的3次超谐共振分析[J].地震工程与工程振动,2006,26(5):239-242.
[6]康希良,王步云,赖远明.桥梁与基础共同工作时的弹塑性地震反映分析[J].甘肃科学学报,1999,11(2):23-29.
[7]李慧,赵世伟,杜永峰,等.用边界元法求解分层弹性地基上的中厚板[J].甘肃科学学报,2004,16(1):105-108.
[8]李世荣,程昌钧.加热弹性杆的热过屈曲分析[J].应用数学和力学,2000,21(2):119-125.
[9]Li Shirong.Nonlinear Free Vibration of Thermally Buckled Beam with Both Ends lmmovable and Simply Supported[J].Journal of Gansu Uni-versity of Technology,2001,Vol.E-5.(1):111-114.
[10]Li S R,Batra R C.Thermal Buckling and Postbuckling of Euler-Bernoulli Beams Supported on Nonlinear elastic Foundations[J].AIAAJOURNAL,2007,45(3):712-720.
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