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The Modeling of Cable-Beam Structure and Nonlinear Finite Element Analysis

Author: WangXin
Tutor: ZhaoYueYu
School: Hunan University
Course: General and Fundamental Mechanics
Keywords: cable-beam structure nonlinear dynamical nonlinear finite element subharmonic resonance multiple scale method
CLC: U441
Type: Master's thesis
Year: 2009
Downloads: 128
Quote: 1
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Abstract


Cable structure has been widely applied in engineering due to its simple forces transmitting, thus can be considered as a representative of stayed structures. Under external excitation, cables are susceptible to significant vibrations in a series of complicated forms due to its inherent characteristics, such as flexibility, structural lightness and low damp as well as its initial stretching and curvature. When its inherent frequency is close to or proportional to the inherent frequency of connection beam, resonance of the whole system will be aroused. The observation on cable-stayed bridges built or under construction shows that several cables may vibrate dramatically in breeze or drizzle. This kind of vibration can badly harm the safety and endurance of the bridge. To be exact, it may cause fatigue of the cables, crack of the anchor joint, damage to the protection system, and invalidation of the cables in severe circumstances.What’s more, the vibration of cables will undoubtedly cause the uncomfortableness of the passers-by; hence bring out their doubt to the safety of the bridge. Therefore, it is quite necessary to do more research on the cable-beam structure. Based on the above facts, this thesis has done much related research, and the main research work covers the following contents: (1)By taking the influence of bending rigidity into consideration, the three dimensional nonlinear dynamic equations of inclined cable are deduced under the Hamilton Principle. Based on the boundary conditions, the system equations are reduced to two-dimensional. Moreover, the internal resonance patterns of the plane motions and couple motions of in-planar or out-planar are analyzed respectively. The influence of bending rigidity on the internal resonance of inclined cable is also studied.(2) We establish the Mathematical model of cable-beam structure, and also establish the partial differential equations of motions of cable-beam structure by following the Hamilton principle. And a one-dimensional treatment is also given on the above equations.(3) By using Galerkin method, we change the partial differential equations of motions of cable-beam structure to the second-order ordinary differential equations. And figure out the frequency ratio of resonance of the cable-beam structure by adopting the Multi-scale method. This chapter also discusses the stability between the cable and the beam with some frequency ratio of resonance. Considering the case of k≈2, we figure out the amplitude-amplitude response curves of parametric resonance and study the influence of damp to the cable parametric vibration with numerical examples.(5) By adopting the Ansys, we build a mechanical model of the cable-beam structure, and figure out the response time history curve of the cables under main resonance and subharmonic resonance, and analyze the harmonic response of the structure.

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CLC: > Transportation > Road transport > Bridges and Culverts > Structural principles, structural mechanics
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