Vibrations of Rectangular Thin Plates with a V-notch via the Ritz method

• Main Authors: Shen-Chien Liao, 廖慎謙
• Other Authors: Chiung-Shiann Huang
• Format: Others
• Language: en_US
• Published: 2007
• Online Access: http://ndltd.ncl.edu.tw/handle/94804436931796543586

碩士 === 國立交通大學 === 土木工程系所 === 95 === 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.