【作者】 王建文；

【导师】 应祖光；

【作者基本信息】 浙江大学 ， 工程力学， 2011， 硕士

【摘要】 本文研究了斜拉索因雨、雪等改变了截面形状时受到横向风的激励而产生的多模态自激振动及其最优控制。首先通过建立拉索受风力作用的非线性运动微分方程,基于索纵向运动相对较小而导出关于索横向运动的偏微分振动方程,进一步运用Galerkin法将该方程转化为常微分方程组,用以描述索的多模态自激振动；再应用非线性振动的平均法,求解得到该系统的自激振动分析解,根据奇解的稳定性条件,分析了拉索前两阶模态耦合的自激振动以及拉索一三阶模态耦合的自激振动的临界风速和极限环的稳定性及其条件,并通过数值模拟验证,然后通过数值方法计算了拉索一二三阶模态耦合的自激振动的特性,并与拉索前两阶模态耦合的自激振动和一三阶模态耦合的自激振动的情况相比较。接着研究了各参数对拉索前两阶模态耦合的自激振动的影响。以拉索前两阶模态的耦合的自激振动为对象,研究了斜拉索多模态自激振动的最优控制问题。根据最优控制的动态规划原理确定最优非线性控制力,再应用非线性振动的平均法,求解得到该系统自激振动及其稳定性的分析解,通过分析比较和数值模拟验证控制前后极限环及其稳定性,说明该最优控制能够有效地抑制风激拉索的自激振动。然后比较了非线性最优控制与线性次最优控制控制效果的差异,结果表明：在小初始扰动条件下,非线性最优控制和线性次最优控制均能有效的抑制拉索的振荡,且控制效果基本相同；在大初始扰动条件下,非线性最优控制和线性次最优控制也均能有效的抑制拉索的振荡,但和线性次最优控制相比,非线性最优控制能够更快的减小振幅。接着研究非线性最优控制的实施,建立起拉索横向一点、两点非线性最优控制,结果表明：选取合适的控制参数,拉索横向一点、两点最优控制均能有效抑制拉索的自激振荡,但两点最优控制的效果优于一点最优控制。考虑拉索的纵向振动对拉索横向多模态振动的影响,建立起拉索面内纵向、横向二维耦合的运动微分方程组,应用非线性振动的平均法,研究了纵向一阶、横向一二阶模态的耦合振动特性,结果表明：稳态响应时,纵向一阶模态振幅与横向二阶模态振幅成正比,相位相差180°,并与第二章简化拉索纵向振动时进行比较,拉索横向一二阶模态耦合振动的极限环的稳定性及其条件具有相同的规律。更多还原

【Abstract】 The fluid-flow-induced cable vibration is an active research subject in structural engineering and has practical importance for structural improvement and vibration control. This paper focused mainly on the analysis of the self-excited oscillation of an inclined taut cable with multi-vibration modes under wind loading as the cable’s cross-section shape changes because of rain or snow. Firstly the nonlinear differential equations of motion were derived for the wind-induced vibration of the cable. Then the partial differential equation for the transverse cable vibration was obtained based on the assumption of longitudinal cable vibration comparatively small. By using the Galerkin approach, this partial differential equation was converted into ordinary differential equations which describe the self-excited oscillation of the cable as multi-modes system. The analytical solutions in self-excited oscillation were obtained further by using the averaging method for nonlinear vibration. According to the stability condition of analytical solutions, the wind-induced limit cycle of self-excited oscillation and its existence conditions and the critical wind velocities for the first two modes and the first, third modes of the cable system in self-oscillation were analytically determined finally and verified by the numerical results. Then the self-oscillation characteristics for the first three modes of the cable system were analyzed by numerical method. The effects of parameters about self-oscillation for the first two modes of the cable were researched at last.Secondly the cable control for the first two modes in self-excited oscillation was focused on. The performance index for optimal cable control was given to the polynomial control solution. Based on the dynamical programming principle, the Hamilton-Jacobi-Bellman (HJB) equation was established for the cable control with the index. The optimal nonlinear control force was determined from solving the HJB equation. By using the averaging method for nonlinear vibration, the analytical solutions, in particular, limit cycle solutions and stability of the controlled system in self-excited oscillation were obtained further. It was concluded by the analytical and numerical comparison between controlled and uncontrolled self-excited oscillations and stability that the proposed optimal control could effectively suppress the self-excited oscillation of the cable under wind loading. Then the control effectiveness was compared between the nonlinear optimal control and linear sub-optimal control. The results showed that under a small initial disturbance, the nonlinear optimal control and linear sub-optimal control could effectively suppress the cable oscillation and the control effectiveness was almost same; under the large initial disturbance, the nonlinear optimal control and linear sub-optimal control was also able to effectively suppress the cable oscillation but compared with the linear sub-optimal control, nonlinear optimal control could reduce the amplitude faster. Then the implementation of nonlinear optimal control was researched. It was established that one-point and two-point nonlinear optimal control of the cable in transverse direction. The results showed that selecting the appropriate control parameters, one-point and two-points nonlinear optimal control could both effectively suppress the self-excited oscillation of cable but the control effectiveness of two-point nonlinear optimal control was better than that of one-point nonlinear optimal control.Thirdly it was considered that the effects of the cable’s longitudinal vibration on the cable’s transverse multi-modal vibration. The differential equations of motion for the two-dimensional longitudinal and transverse coupling of cables were established. Then the self-excited oscillation characteristics for the first mode of cable longitudinal vibration and the first two modes of cable transverse vibration were analyzed by the averaging method for nonlinear vibration. The results showed that the amplitude of the longitudinal first mode was proportional to that of the transverse second mode of the cable and, the phase difference between the longitudinal first mode and the transverse second mode of the cable was 180°. Compared with those in the second chapter under the longitudinal vibration simplified, the stability of limit cycles in self-excited oscillation for the first two modes of cable transverse vibration had the same conclusion.更多还原