CHAOTIC ANALYSIS OF SUBHARMONIC RESONANT WAVES IN UNDAMPED AND DAMPED STRINGS
CHAOTIC ANALYSIS OF SUBHARMONIC RESONANT WAVES IN UNDAMPED AND DAMPED STRINGS作者机构：Univ of Manitoba Winnipeg Canada
出 版 物：《Journal of Hydrodynamics》 (水动力学研究与进展B辑（英文版）)
年 卷 期：1995年第7卷第1期
页 面：92-104页
核心收录：
学科分类：080704[工学-流体机械及工程] 080103[工学-流体力学] 08[工学] 0807[工学-动力工程及工程热物理] 0801[工学-力学（可授工学、理学学位）]
主 题：chaos subharmonic resonant waves undamped and damped strings,incremental energy balance method renormalization group technique.
摘 要：The chaotic phenomena of subharmonic resonant waves in undamped and damped strings are investigated in this paper. The model consistS of a constant-tension, stretched string whose partial differential equation is derived by taking into account its exact configuration. Simplification via a Taylor series expansion of the curvature term and then employing the Galerkin method, an ordinary differential equation for the nonlinear dyamics is obtained. For the undamped case, we can formulate the Hamiltonian energy form of the conservative string, under the influence of an external periodic excitation. This permits the subharmonic resonant condition for this system to be derived. We truncate the resulting infinite number of subharmonic resonant waves to just two waves by renormalizing the Hamiltonian energy function near the subharmonic resonant orbit of the system. Adopting the renormalization group technique for the nit6raction of the two subharmonic resonant waves, an approximate chaotic condition associated with the subharmonic resonance of this system is determined. For the case fo the damped string, the minimum condition for the bifurcation of the subharmonic resonant wave is computed using the incremental energy balance method. For model verification, we carried out numerical simulations and they show good agreement with our analytical results.
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