Exact solutions for free vibrations of axially inhomogeneous Timoshenko beams with variable cross section
Exact solutions for free vibrations of axially inhomogeneous Timoshenko beams with variable cross section
复制标题
变截面轴向非均匀Timoshenko梁自由振动的精确解
DOI：
10.1007/s00707-016-1658-6
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发表时间：
2016
期刊：
影响因子：
2.7
通讯作者：
Chen Weiqiu
中科院分区：
文献类型：
--
作者：
Yuan Jianghong;Pao Yih-Hsing;Chen Weiqiu
提出了一种新的方法，简化了沿梁轴沿着具有几何非均匀性和材料非均匀性的梁自由振动的控制方程。对于广泛的一类梁，这种方法使我们能够减少耦合的变系数的控制微分方程的Sturm-Liouville型的一对非耦合的二阶微分方程的旋转角，由于弯曲。简化后的方程包含两个重要参数，一个是描述梁的平移惯性和弯曲刚度沿着轴线的变化，另一个是反映转动惯性和剪切变形的综合影响。首次从简化方程组导出了一系列精确的解析解，并给出了几个算例作为基准。
A novel method is proposed to simplify the governing equations for the free vibration of Timoshenko beams with both geometrical nonuniformity and material inhomogeneity along the beam axis. For a wide class of Timoshenko beams, this method enables us to reduce the coupled governing differential equations with variable coefficients to a pair of uncoupled second-order differential equations of Sturm–Liouville type with respect to the rotation angle due to bending. The reduced equations contain two important parameters, one describing the variations of translational inertia and bending rigidity along the beam axis, and the other reflecting the comprehensive effect of rotatory inertia and shear deformation. A series of exact analytical solutions are derived from the reduced equations for the first time, and several examples are also provided as benchmarks.