Dynamic analysis of modal shifting and mode jumping in thermally buckled plates

被引:34
作者
Chen, H [1 ]
Virgin, LN [1 ]
机构
[1] Duke Univ, Pratt Sch Engn, Dept Mech Engn, Durham, NC 27708 USA
关键词
D O I
10.1016/j.jsv.2003.10.054
中图分类号
O42 [声学];
学科分类号
070206 ; 082403 ;
摘要
Both analytical and finite element investigations are performed for the various static and dynamic aspects of the mode jumping phenomenon of a simply-supported rectangular plate heated deeply into the postbuckling regime. For the analytical method, the von Karman plate equation is reduced to a system of nonlinear ODEs by expressing the transverse deflection as a series of linear buckling modes. The ODEs, combined with the non-linear algebraic constraint equations obtained from in-plane boundary conditions, are then solved numerically under the parametric variation of the temperature. The results are checked by the finite element method, where a hybrid static-dynamic scheme is implemented. The contribution of each assumed (buckling) mode component is studied systematically. Characterized by the strong geometrical non-linearity, the secondary bifurcation point of the thermally loaded plate with fixed in-plane boundary conditions occurs far beyond the primary buckling point, and the jump behavior cannot be predicted correctly without sufficient assumed modes. Stationary bifurcation analysis indicates that while the postbuckling deflection before mode jumping is composed of pure symmetric modes, additional pure antisymmetric modes will appear after the occurrence of the snapping and they play the role of destabilizing the equilibrium. Furthermore, by monitoring natural frequencies and modal shapes, we find that a mode shifting phenomenon (the exchanging of vibration modes) exists in the primary post-buckling regime. Breaking of the symmetry of the dynamic modes is also found. By introducing a linear temperature sweeping scheme, transient analysis is performed to capture the snapping phenomenon dynamically, which occurs with moderate heating ratio. Comparison between the analytic and finite element results shows good agreement. (C) 2003 Elsevier Ltd. All rights reserved.
引用
收藏
页码:233 / 256
页数:24
相关论文
共 32 条
[1]  
[Anonymous], 1997, AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations, user's Manual
[2]   Mode jumping in the von Karman equations [J].
Chien, CS ;
Gong, SY ;
Mei, Z .
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2000, 22 (04) :1354-1385
[3]   Tracing the buckling of a rectangular plate with the Block GMRES method [J].
Chien, CS ;
Chang, SL ;
Mei, Z .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 136 (1-2) :199-218
[4]  
Dowell E.H., 1975, AEROELASTICITY PLATE
[5]   Quasi-periodic buckling of an elastic structure under the influence of changing boundary conditions [J].
Everall, PR ;
Hunt, GW .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 455 (1988) :3041-3051
[6]   Arnold tongue predictions of secondary buckling in thin elastic plates [J].
Everall, PR ;
Hunt, GW .
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 1999, 47 (10) :2187-2206
[7]   Mode jumping in the buckling of struts and plates: a comparative study [J].
Everall, PR ;
Hunt, GW .
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2000, 35 (06) :1067-1079
[8]   Capturing mode-switching in postbuckling composite panels using a modified explicit procedure [J].
Falzon, BG ;
Hitchings, D .
COMPOSITE STRUCTURES, 2003, 60 (04) :447-453
[9]   Arnold tongues and mode-jumping in the supercritical post-buckling of an archetypal elastic structure [J].
Hunt, GW ;
Everall, PR .
PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1999, 455 (1981) :125-140
[10]   Vibration and post-buckling of in-plane loaded rectangular plates using a multiterm Galerkin's method [J].
Ilanko, S .
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2002, 69 (05) :589-592