This research studies the vibration analysis of Euler–Bernoulli and Timoshenko beams utilizing the differential quadrature method (DQM) which has wide applications in the field of basic vibration of different components, for example, pillars, plates, round and hollow shells, and tanks. The free vibration of uniform and nonuniform beams laying on elastic Pasternak foundation will be studied under three sets of boundary conditions, that is, mixing between being simply upheld and fixed while utilizing the DQM. The natural frequencies and deflection values were produced through the examination of both beam types. Results show great concurrence with solutions from previous research studies. The impact of the nonuniform cross-section area on the vibration was contemplated. A comparison between the results from both beams is obtained. The focus of this work is on studying the deflection difference between both beam theories at different beam dimensions as well as showing the shape of rotation of the cross section while applying a nodal point load equation to simulate the moving load. The results were discussed and a general contemplation about the theories was developed.

中文翻译：

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移动荷载作用下弹性基础上的锥形Timoshenko梁和Euler–Bernoulli梁的分析

这项研究使用微分求积法（DQM）研究了Euler–Bernoulli和Timoshenko梁的振动分析，该方法在不同组件的基本振动领域中具有广泛的应用，例如，支柱，板，圆形和空心壳体以及储罐。将在三组边界条件下研究均布在弹性Pasternak地基上的均匀和不均匀梁的自由振动，即在使用DQM时简单保持和固定之间的混合。通过检查两种光束类型产生了固有频率和挠度值。结果表明与先前研究的解决方案非常一致。考虑了不均匀的横截面面积对振动的影响。获得了两个光束的结果之间的比较。这项工作的重点是研究两个梁理论在不同梁尺寸下的挠度差异，以及在应用节点载荷方程来模拟运动载荷的同时显示横截面的旋转形状。对结果进行了讨论，并对理论进行了一般性的思考。