| 王砚,王忠民,阮苗.无网格法在点弹性支承矩形薄板横向振动中的应用[J].计算力学学报,2010,27(2):238~243 |
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| 无网格法在点弹性支承矩形薄板横向振动中的应用 |
| Application of meshless method in the transverse vibration of rectangular thin plate with elastic point supports |
| 投稿时间：2008-02-24 |
| DOI：10.7511/jslx20102011 |
| 中文关键词: 无网格法 矩形薄板 点弹性支承 横向振动 |
| 英文关键词:element-free method rectangular thin plate elastic point supports transverse vibration |
| 基金项目:国家自然科学基金(10872163);机械设计及理论国家重点学科培育学科资助项目. |
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| 中文摘要: |
| 基于薄板理论和弹性动力学Hamilton原理的推广,采用无网格伽辽金法,建立了具有有限多个点弹性支承的弹性矩形薄板横向振动的无量纲量运动微分方程,给出了其特征方程。通过求解特征方程,得出了四边简支板的无量纲固有频率随点弹性支承的刚性系数和支承位置的变化曲线,分析了点弹性支承的刚性系数和支承位置对矩形薄板横向振动特性的影响。数值计算结果表明,无网格法求解点弹性支承板横向振动问题是切实可行的。 |
| 英文摘要: |
| Based on the thin plate theory and the extended Hamilton’s principle for the elastic dynamics system, the dimensionless equations of motion of rectangular plate with finite elastic point supports are established by the element-free Galerkin method. The eigenvalue equations are presented. By solving the eigenvalue equations, the curves of dimensionless natural frequency of thin plate with four edges simply supported versus the rigid constant and locations of elastic point support are obtained. The effects of rigid constant and locations of elastic point supports on the transverse vibration characteristics of the thin plate are analyzed. The number results show that the element-free Galerkin method is valid and feasible in solving the transverse vibration with elastic point supports. |
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