Timoshenko梁理论
拉普拉斯变换
梁(结构)
振动
拉普拉斯逆变换
转动惯量
卷积定理
数学分析
结构工程
积分变换
傅里叶变换
频域
数学
卷积(计算机科学)
物理
计算机科学
工程类
傅里叶分析
声学
人工神经网络
机器学习
分数阶傅立叶变换
作者
Haitao Yu,Xizhuo Chen,Pan Li
标识
DOI:10.1142/s0219455422500456
摘要
An analytical solution is derived for dynamic response of a modified Timoshenko beam with an infinite length resting on visco-Pasternak foundation subjected to arbitrary excitations. The modified Timoshenko beam model is employed to further consider the rotary inertia caused by the shear deformation of a beam, which is usually neglected by the traditional Timoshenko beam model. By using Fourier and Laplace transforms, the governing equations of motion are transformed from partial differential forms into algebraic forms in the Laplace domain. The analytical solution is then converted into the time domain by applying inverse transforms and convolution theorem. Some widely used loading cases, including moving line loads for nondestructive testing, travelling loads for seismic wave passage, and impulsive load for impact vibration, are also discussed in this paper. The proposed generic solutions are verified by comparing their degraded results to the known solutions in other literature. Several examples are performed to further investigate the differences of the beam responses obtained from the modified and the traditional Timoshenko beam models. Results show that the modified Timoshenko beam simulates the beam responses more accurately than the traditional model, especially under the dynamic loads with a high frequency. The analytical solutions proposed in this paper can be conveniently used for design and applied as an effective tool for practitioners.
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