弹性地基无限长梁动力问题的一般解
General Solution for Dynamical Problem of Infinite Beam on an Elastic Foundation
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摘要: 本文从Euler-Bernoulli梁出发,对弹性地基采用Winkler假定,建立了问题的数学模型.然后对空间变量和时间变量分别进行Fourier变换和Laplace变换,利用逆变换褶积积分,得到了弹性地基无限长梁一般动力问题的解析解.最后对自由振动,脉冲激励和运动载荷情况分别进行了讨论.Abstract: Based on the theory of Eider-Bernoulli beam and Winkler assumption for elastic foundation, a mathematical model is presented. By using Fourier transformation for space variable, Laplace transformation for time variable and convolution theorem for their inverse transformations, a general solution for dynamical problem of infinite beam on an elastic foundation is obtained. Finally, the cases of free vibration,impulsive response and moving load are also discussed.
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[1] Timoshenko,S.P.,Statical and dynamical stress in rails,Proc.Intern.Congr.Appl.Mech.,Zurich(1926),407-418. [2] Kenney,J.T.,Steady-state vibrations of beam on elastic foundation for moving load,J.Appl.Mech.,21,4(1954),359-364. [3] Saito,H.and T.Murakami,Vibrations of an infinite beam on an elastic foundation withconsideration of mass of a foundation,Japanese Soc.of Mech.Eng.,12(1969),200-205. [4] Fryba,L.,Infinite Beam on an elastic foundation subjected to a moving load,AplikaceMatematiky,2,2(1957),105-132. [5] I.N.史奈登,《富利叶变换》,科学出版社,北京(1958). [6] Fryba,L.,Vibration of Solids and Structures under Moving Loads,Academia Publishing House of the Czechoslovak(1971). -
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