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Boundary characteristic orthogonal polynomials method in the vibration analysis of multi-span plates acting upon a moving mass

机译:多跨板在运动质量作用下的振动分析中的边界特征正交多项式方法

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摘要

The Boundary Characteristic Orthogonal Polynomials (BCOP) method is used in this study in order to analyze multi-span plates traversed by a moving inertia load traveling on an arbitrary path with constant velocity. The plate is assumed to be free from any support at the longitudinal edges and the spans are made by simply supported constraints at width, i.e. SFSF. The plate's mode shapes are generated by the BCOP method while the boundary condition is satisfied over all computational modes. A free vibration analysis is done in order to find natural frequency. The governing differential equations of motion are derived by Hamilton's principle and the solution in the time domain is found by using the Matrix Exponential method after modeling the problem in state space. All of the convective inertia terms are included in the acceleration derivatives and the responses are presented both for the load moving on the plate's surface ignoring/including the mass inertia effect. A comprehensive parametric study on the plate's mid-spans is carried out for the single, two- and three-span plates, investigating Dynamic Amplification Factor (DAF) versus non-dimensional velocity (V). The effect of mass and aspect ratio along with the location of reference point of calculation on the dynamic behavior of a multi-span plate is investigated and many graphs are generated as spectra. One can easily find the critical velocity as well as the peak deflection for each case study by introducing a corrective factor. The solution under moving mass excitation is obtained by the factor if the same response for moving load is known.
机译:本研究中使用边界特征正交多项式(BCOP)方法来分析由惯性载荷在任意路径上以恒定速度行进的多跨板。假定该板在纵向边缘没有任何支撑,并且跨度是由宽度上的简单支撑约束即SFSF制成的。通过BCOP方法生成板的模式形状,同时在所有计算模式上都满足边界条件。为了找到固有频率,进行了自由振动分析。根据汉密尔顿原理导出运动的控制微分方程,并在对状态空间中的问题进行建模后,使用矩阵指数方法找到时域中的解。所有对流惯性项都包括在加速度导数中,并且在忽略/包括质量惯性效应的情况下,都给出了在板表面上移动的载荷的响应。针对单跨度,两跨度和三跨度板块,对板块中跨进行了全面的参数研究,研究了动态放大系数(DAF)与无量纲速度(V)的关系。研究了质量和长宽比以及计算参考点的位置对多跨板动力学行为的影响,并生成了许多图形作为光谱。通过引入校正因子,可以轻松找到每种案例研究的临界速度和峰偏斜。如果已知相同的运动载荷响应,则通过该因子获得运动质量激励下的解。

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