Theoretical analysis of dynamic behaviors of cable-stayed bridges excited by two harmonic forces

Nonlinear Dynamics - To better understand the dynamic behaviors of cable-stayed bridges, this study investigates the dynamic behaviors of a cable-stayed shallow arch subjected to two external...     

磁致伸缩光纤磁光光学双稳态

报道了一种基于磁致伸缩原理实现的全光纤结构磁光光学双稳态装置。与分立元件的磁光双稳系统相比较，该系统的双稳开关功率降低了２～３个数量级，实验结果与理论计算相符。     

Analysis of 1:1 internal resonance of a CFRP cable with an external 1/3 subharmonic resonance

Nonlinear Dynamics - Based on the non-planar vibration equations of a cable made of carbon fiber reinforced polymer (CFRP), the nonlinear behaviors of the cable are studied. The one-to-one internal...     

Stability prediction for milling process with multiple delays using an improved semi‐discretization method

Milling chatter leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Thus, it is desirable to predict and avoid the onset of this instability. Considering that the stability of milling with variable pitch cutter or tool runout case is characterized by multiple delays, in this paper, an improved semi‐discretization method is proposed to predict the stability lobes for milling processes with multiple delays. Taking the variable pitch milling, for example, a comparisonwith prior methods is conducted to verify the accuracy and efficiency of the proposed approach for the stability prediction both in low and high radial immersion ratios. In addition, the rate of convergence of the proposed method is also evaluated. The results show that the proposed method has high computational efficiency. Copyright © 2015 John Wiley & Sons, Ltd.     

Elastic cables–rigid body coupled dynamics: asymptotic modeling and analysis

An elastic cables–rigid body coupled model is proposed for investigating dynamic interactions between cables’ nonlinear transversal vibrations and boundary tower’s torsional dynamics, arising in large transmission line–tower systems and suspended cable–bridge tower systems. By introducing a weak torsion assumption and a large moment of inertia for the tower, an asymptotic expansion of cables–tower coupled dynamics is conducted in a weakly nonlinear framework, and a cables–tower reduced coupled model is eventually established. After model’s validations using direct numerical simulations, two distinct kinds of coupled dynamics are fully investigated. The first is that an external torque is applied to the tower and the two cables would both be indirectly excited, asymmetrically, by the torsional/oscillating tower. The two cables’ responses are the same in this case. The second is that only one of the two cables, i.e., the leader cable, is directly excited, and the other cable, i.e., the follower one, is only indirectly excited through cables–tower dynamic interactions. In such kind of leader–follower dynamics, the leader cable is quite different from the follower one. Nonlinear coupled frequency response diagrams for both systems are constructed using numerical continuation algorithms, mainly focused on the coupled steady solutions’ stabilities and bifurcations. Furthermore, the dynamic effects of tower’s moment of inertia, wing span and damping are thoroughly investigated.

     

大跨度斜拉桥非线性振动模型与理论研究进展

斜拉桥的非线性动力学问题一直都是力学、结构和桥梁领域的研究热点.随着新材料(如碳纤维增强聚合物索)和新施工工艺的发展,斜拉桥的跨越能力不断得到提高,从而在桥梁建设中更具有竞争力.然而,斜拉桥跨度的增大和新材料的应用使结构变得更轻和更柔,使结构的非线性振动问题比以往更为突出,可能危及桥梁安全.基于课题组近年来对斜拉桥非线性动力学的研究,围绕大跨度斜拉桥的非线性建模理论及动力学问题,较为详细地评述近十年来国内外的研究进展情况.主要从斜拉索非线性动力学模型、梁的非线性动力学模型、索-梁组合结构的非线性动力学模型、斜拉桥整体非线性动力学模型与理论、以及斜拉桥的非线性振动实验等几个方面对斜拉桥非线性建模方法、力学模型、数学模型、求解方法及相应研究成果进行评述和讨论.研究结果表明,斜拉桥由于多柔性索和大跨度梁的耦合问题,以及环境载荷的复杂性,导致其具有丰富的非线性动力学行为.同时由于高维非线性系统求解方法的欠缺,整体斜拉桥非线性动力学行为又相当复杂,深入研究面临很大困难.最后,基于未来斜拉桥的发展趋势和可能面临的突出问题,对斜拉桥非线性振动问题今后的发展方向进行了探讨和展望.      

Modal interaction activations and nonlinear dynamic response of shallow arch with both ends vertically elastically constrained for two-to-one internal resonance

This study investigates the two-to-one internal resonance of the shallow arch with both ends elastically constraining, and the primary resonance case is considered. The full-basis Galerkin method and the multi-scale method are applied to obtain the modulation equations. It is shown that the natural frequencies of the first two modes cross/avoid to each other when the stiffness of elastic supports at two ends is the same/different. Moreover, the nonlinear modal interactions between these two modes may not/may be activated. The force/frequency-response curves are employed to explore the nonlinear response of the elastically supported shallow arch. The saddle-node bifurcation points and Hopf bifurcation points are observed in these cases. Moreover, the dynamic solutions, i.e., the periodic solution, quasi-periodic solution and chaotic solution are discussed. The numerical simulations are used to illustrate the route to chaos via period-doubling bifurcation.     

裂纹转子振动特性分析

以具有刚性支承的水平Jefcott裂纹转子为研究对象,考虑涡动的影响,建立了裂纹转轴在固定坐标系中的刚度矩阵,推导了裂纹转子振动的运动方程,并通过数值方法分析了其动态特性。数值分析表明：裂纹转子振动响应中出现1X、2X、3X……分量,且当Ω=1/2,1/3…时,2X,3X…分量分别达到最大值;转子的中心轨迹形状随Ω变化而变化,当β=0-π逐渐增大时,响应中1X分量显著减小。考虑弯扭耦合振动时,振动响应中出现一些新的频率成分。同步激励的情况下,当ω＝ωN／n(n=2,3,4,…）时,扭转振动响应中nX分量也达到最大值。