| 正交各向异性和各向同性方板自由振动的三维无网格解 |
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| 引用本文： | 项松,陈英涛.正交各向异性和各向同性方板自由振动的三维无网格解[J].工程力学,2013,30(8):18-22. |
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| 作者姓名： | 项松 陈英涛 |
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| 作者单位： | 1.沈阳航空航天大学通用航空重点实验室，沈阳 100136； |
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| 摘 要： | 推导了正交各向异性和各向同性弹性体自由振动的三维控制微分方程，利用基于逆复合二次径向基函数的无网格配点法对三维控制微分方程和边界条件进行离散，通过数值算例选取了逆复合二次径向基函数的形状参数，结果表明:形状参数(是x方向的节点数)时计算结果收敛最快。计算了不同边界条件的正交各向异性和各向同性板的固有频率，该文中的结果与文献中的结果具有较好的一致性。
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| 关 键 词： | 正交各向异性 各向同性 自由振动 无网格 径向基函数 |
| 收稿时间： | 2013-08-20 |
THREE-DIMENSIONAL MESHLESS SOLUTIONS FOR THE FREE VIBRATION OF ORTHOTROPIC AND ISOTROPIC SQUARE PLATES |
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| Affiliation: | 1.Liaoning Key Laboratory of General Aviation, Shenyang Aerospace University, Shenyang 110136, China;2.Liaoning General Aviation Academy, Shenyang 110136, China;3.Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China |
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| Abstract: | Three-dimensional governing differential equations are derived based on the linear elasticity theory and the equations are discretized using the meshless collocation method based on the inverse multiquadrics radial basis function. Through the numerical examples, the convergence characteristics and the choice of shape parameter are studied. It is found that the natural frequencies computed with shape parameter . (Nxis the number of node at the xside) converge most rapidly. The natural frequencies of orthotropic and isotropic plates under different boundary conditions are calculated by the proposed method. The proposed results are in good agreement with the available published results. |
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