标题: | 利用Ritz法分析具有V型缺口之矩形薄板振动 Vibrations of Rectangular Thin Plates with a V-notch via the Ritz method |
作者: | 廖慎谦 Shen-Chien Liao 黄炯宪 Chiung-Shiann Huang 土木工程学系 |
关键字: | 矩形板;V型缺口;Ritz法;应力奇异性;rectangular plate;V-notch;Ritz method;stress singularity |
公开日期: | 2006 |
摘要: | 应力奇异点之问题常发生于工程力学的分析计算中。本论文以薄板理论为基础,利用Ritz法分析具有V型缺口之矩形板振动,在分析过程中使用两组允许函数序列,分别为:(1)多项式函数,其本身可构成一组完备之序列;(2)角函数,满足V型缺口两自由边缘之边界条件,并可精确地描述缺口尖端之应力奇异特性。本论文之研究案例包含完全自由与悬臂矩形板,先以完整的收敛性分析验证角函数能够有效地加速自然振动频率之收敛速度,并探讨不同几何及位置之V型缺口对矩形板振动行为之影响。本论文为首次研究具有V型缺口之矩形板振动,此研究结果可提供后人研究参考与比较。 This thesis presents a novel method for accurately determining the natural frequencies of rectangular plates with an edge V-notch. Based on the well-known Ritz method, two sets of admissible functions are used simultaneously: (1) algebraic polynomials, which form a complete set of functions; (2) corner functions, which are the general solutions of bi-harmonic equation, duplicate the boundary conditions along the edges of the notch, and describe the stress singularities at the sharp vertex of the V-notch exactly. The rectangular plates under consideration are either completely free or cantilevered. The effects of corner functions on the convergence of solutions are demonstrated through comprehensive convergence studies. Accurate numerical results and nodal patterns are tabulated for V-notched plates having various notch angle, depths and locations. These are the first known frequency and nodal pattern results of V-notched rectangular plates in the published literature. |
URI: | http://140.113.39.130/cdrfb3/record/nctu/#GT009316525 http://hdl.handle.net/11536/78645 |
显示于类别: | Thesis |
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