NONLINEAR VIBRATION FOR MODERATE THICKNESS RECTANGULAR CRACKED PLATES INCLUDING COUPLED EFFECT OF ELASTIC FOUNDATION

• Published in: Applied mathematics and mechanics Vol. 26; no. 8; pp. 963 - 972
• Main Author: XIAO Yong-gang（肖勇刚） FU Yi-ming（傅衣铭） ZHA Xu-dong（查旭东）
• Format: Journal Article
• Language: English
• Published: Department of Engineering Mechanics, Hunan University, Changsha 410082, P. R. China 01.08.2005; College of Bridge and Structure Engineering, Changsha University of Science and Technology, Changsha 410076, P. R. China%Department of Engineering Mechanics, Hunan University, Changsha 410082, P. R. China%College of Bridge and Structure Engineering, Changsha University of Science and Technology, Changsha 410076, P. R. China
• Subjects: 中等厚度矩形指标; 弹性基础; 非线性振动; elastic foundation; crack; nonlinear vibration; moderate thickness rectangular plate
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/bf02466408

Based on Reissner plate theory and Hamilton variational principle, the nonlinear equations of motion were derived for the moderate thickness rectangular plates with transverse surface penetrating crack on the two-parameter foundation. Under the condition of free boundary, a set of trial functions satisfying all boundary conditions and crack＇s continuous conditions were proposed. By employing the Galerkin method and the harmonic balance method, the nonlinear vibration equations were solved and the nonlinear vibration behaviors of the plate were analyzed. In numerical computation, the effects of the different location and depth of crack, the different structural parameters of plates and the different physical parameters of foundation on the nonlinear amplitude frequency response curves of the plate were discussed.