Analytical solutions for Euler‐Bernoulli Beam on Pasternak foundation subjected to arbitrary dynamic loads
Analytical solutions for Euler‐Bernoulli Beam on Pasternak foundation subjected to arbitrary dynamic loads
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DOI：
10.1002/nag.2672
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发表时间：
2017
影响因子：
4
通讯作者：
H. Yu;C. Cai;Y. Yuan;M. Jia
中科院分区：
文献类型：
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作者：
H. Yu;C. Cai;Y. Yuan;M. Jia
本文以解析解的形式给出了Pasternak地基上无限长梁在任意动荷载作用下的动力响应。梁的响应包括挠度、速度、加速度、弯矩和剪力。Pasternak基础的机械阻力使用两个参数建模，即，一个考虑由于土壤中的压缩应变引起的土壤阻力，另一个考虑由于剪切应变引起的阻力。由于Winkler模型只考虑了土的抗压强度，相比之下，Pasternak模型更能真实地反映土弹簧之间的剪切相互作用。通过积分变换将梁的控制方程简化为代数方程，从而可以方便地在频域中得到梁的动力响应的解析解。利用逆拉普拉斯变换和逆傅立叶变换结合卷积定理将解转换到时域。讨论了简谐线荷载、移动线荷载和移动荷载等特殊情况下的解，并通过算例分析了地基剪切模量对梁响应的影响。所提出的解决方案可以成为从业人员的有效工具。版权所有© 2017约翰威利父子有限公司
In this paper, the dynamic response of an infinite beam resting on a Pasternak foundation and subjected to arbitrary dynamic loads is developed in the form of analytical solution. The beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The mechanical resistance of the Pasternak foundation is modeled using two parameters, that is, one accounts for soil resistance due to compressive strains in the soil and the other accounts for the resistance due to shear strains. Because the Winkler model only represents the compressive resistance of soil, comparatively, the Pasternak model is more realistic to consider shear interactions between the soil springs. The governing equation of the beam is simplified into an algebraic equation by employing integration transforms, so that the analytical solution for the dynamic response of the beam can be obtained conveniently in the frequency domain. Both inverse Laplace and inverse Fourier transforms combined with convolution theorem are applied to convert the solution into the time domain. The solutions for several special cases, such as harmonic line loads, moving line loads, and travelling loads are also discussed and numerical examples are conducted to investigate the influence of the shear modulus of foundation on the beam responses. The proposed solutions can be an effective tool for practitioners. Copyright © 2017 John Wiley & Sons, Ltd.