Coupling Analysis of Vibration and Fatigue Crack Growth for Rectangular Plates with Central Crack or Cracks at Opposite Edges

• Main Authors: Hung-Chih Chuang, 莊鴻志
• Other Authors: Yan-Shin Shih
• Format: Others
• Language: en_US
• Published: 2002
• Online Access: http://ndltd.ncl.edu.tw/handle/84229175147075476460

碩士 === 中原大學 === 機械工程研究所 === 90 === ABSTRACT The coupling analysis of vibration and fatigue crack growth for rectangular plate with central crack or cracks at opposite edges is presented. The equations of motion for generally isotropic plates based on von Karman’s theory are considered in vibration analysis, and the modified Forman’s equation is employed to fatigue crack growth. The governing equations are reduced to Mathieu equation that is nonlinear equation by assuming mode shapes and Galerkin’s procedure. The relationships of amplitude, fatigue crack growth, natural frequency and loading cycles on cyclic vibration are determined by Rung-Kutta procedure and the modified Forman’s equation for crack propagation. The nonlinear natural frequency for Mathieu equation is obtained by Rung-Kutta scheme with corrected frequency ratio. The incremental harmonic balance method is applied to determine the region of dynamic instability. The results for square and rectangular cracked plates are provided in this study. The interactive of vibration and fatigue crack growth in loading cycles for cracked plates are determined and discussed. Since the coupling analysis of vibration and fatigue crack growth is lacking in the literature, this study provided an analytical procedure for the cracked plate is the major contributions. Keyword: central crack, crack at opposite edges, vibration, nonlinear natural frequency, dynamic instability, fatigue crack growth