Dynamic Analysis to Infinite Beam under a Moving Line Load with Uniform Velocity
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摘要: 基于线性叠加原理,本文首先证明了广义Duhamel积分,把运动线源荷载作用下梁的动力问题转化为求解位置固定的线源荷载作用下梁的动力响应即线源脉冲响应函数。然后,利用Laplace变换和Fourier变换求解梁的动力方程,获得了线源脉冲响应函数,继而得到了运动线源荷载下梁的动力解答。对动力响应的进一步分析表明,其最大值总是发生在线源的中心并随荷载运动而运。动最后,定义了运动动力系数。Abstract: Based on the principle of linear superposition,this paper proves generalized Duhamel's integral which reverses moving dynamical load problem to fixed dynamical load problem.Laplace transform and Fourier transform are used to solve patial differential equation of infinite beam.The generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem.Deep analyses indicate that the extreme value of dynamic response always lies in the center of the line load and travels with moving load at the same speed.Additionally,the authors also present definition of moving dynamic coefficient which reflects moving effect.
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Key words:
- generlaized Duhamel’s integral /
- integral transform /
- infinite beam /
- dynamic response /
- moving effect /
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