A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches
A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches
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DOI：
10.1016/j.jsv.2008.02.005
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发表时间：
2008-08
影响因子：
4.7
通讯作者：
P. Malekzadeh;A. Setoodeh;E. Barmshouri
中科院分区：
文献类型：
--
作者：
P. Malekzadeh;A. Setoodeh;E. Barmshouri
本文介绍了一种基于二维弹性理论的任意层合厚圆深拱自由振动问题的精确而有效的求解方法。为了准确地描述应变沿厚度方向的变化，采用分层理论来近似径向位移分量。应用汉密尔顿原理，得到了径向运动方程的离散形式和相应的边界条件。然后使用微分求积法（DQM）离散所得到的控制方程。在进行收敛性研究后，得到了具有不同边界条件的叠层拱的新结果。此外，不同的值的拱参数，如张角，厚度与长度和正交各向异性比被认为是。在所有情况下，使用有限元软件'ABAQUS'，也与第一和高阶剪切变形理论在文献中获得的结果进行比较。密切的协议，特别是与ABAQUS的，实现。
An accurate and efficient solution procedure based on the two-dimensional elasticity theory for free vibration of arbitrary laminated thick circular deep arches with some combinations of classical boundary conditions is introduced. In order to accurately represent the variation of strain across the thickness, the layerwise theory is used to approximate the displacement components in the radial direction. Employing Hamilton's principle, the discretized form of the equations of motion and the related boundary conditions in the radial direction are obtained. The resulting governing equations are then discretized using the differential quadrature method (DQM). After performing the convergence studies, new results for laminated arches with different set of boundary conditions are developed. Additionally, different values of the arch parameters such as opening angle, thickness-to-length and orthotropy ratios are considered. In all cases, comparisons with the results obtained using the finite element software ‘ABAQUS’ and also with those of the first- and higher-order shear deformation theories available in the literature are performed. Close agreements, especially with those of ABAQUS, are achieved.