【作者】 杜冬；

【导师】 华宏星；

【作者基本信息】 上海交通大学 ， 机械设计与理论， 2007， 博士

【摘要】 振动控制一直是工程界和学术界努力解决的重要问题,它涉及的领域包括舰船结构及其机电设备隔振抗冲,土木结构防风减震,汽车悬架减振,等等。其中,现代军事工业的飞速进步使得舰船柴油机等动力设备向着高功率高转速的趋势发展,这意味着船体结构和设备振动问题将进一步突出,而与此同时,对舰船隐身性能,抗冲性能以及舰载灵敏设备的保护要求都更加苛刻。动力吸振器(Dynamic Vibration Absorber, i.e. DVA)是解决这一矛盾的有效手段。本论文基于船用设备振动控制这一工程背景,对动力吸振器的被动控制和主动控制都做了深入的分析研究,对减振与隔振中的动力吸振器最优设计给出了重要结论,论文还运用实验手段研究了虚拟吸振器算法的有效性,主要研究内容和成果总结如下:一、将舰船设备简化为单自由度系统,运用Lyapunov方程以及矩阵Kronecker积求解了与设备附连吸振器的最优设计。其具体方法是利用Lyapunov方程将二次型积分目标函数转化为初始状态向量的矩阵二次型,然后针对初速度或初位移条件将矩阵二次型变为多项式,最后采用Kronecker积以及列展开将多项式的系数转化为吸振器调谐频率比以及阻尼比的表达式,并令多项式取极小值,即可得到最优参数。在忽略被控结构阻尼的情况下,得到了封闭解析解;如果考虑阻尼,给出了以被控结构粘性阻尼比幂级数表达的二阶摄动解。与以往研究最大的不同是,在本文给出的最优设计中包含初速度比或初位移比变量,因此,采用不同的初速度比和初位移比可以得到各种条件下的最优设计——特殊条件下,给定初速度比为0或1可求解外力激励或基础加速度激励下的经典最优。本研究还比较了二阶摄动解与梯度寻优得到的数值最优解之间的差别,证明二阶摄动解具有较高的稳定性。H2二、在我国的某型舰艇上已经将多重调谐质量阻尼器应用于柴油机减振,本文提出运用微积分手段分析多重调谐质量阻尼器(MTMD)在TMD个数趋于无穷多条件下的性能指标和迭代寻优。以往的研究针对包含TMD个数较多的MTMD,只能通过大量数值现象来猜测其最终趋势,迭代效率低下。本研究将单个TMD视为并联的小单元,每个小单元都对被控结构产生作用力,并具有独立的传递函数,因此在TMD趋于无穷多时,每个小TMD单元相当于一个微元,将所有的微元作用积分即可得到无穷多TMD的传递函数,基于该传递函数可求出基础加速度激励或外力激励下无穷MTMD的极限性能,而且数值仿真还证明,无穷MTMD迭代效率高,它的最优设计可直接代替包含20个以上的TMD组成的MTMD设计。三、双层隔振技术在当前舰船设备隔振中有广泛应用,但它引入了二次谐振峰,这对于中频段的隔振极为不利,本文为了解决这一问题,提出了中间小质量隔振技术——其本质就是将多重调谐质量阻尼器的吸振思想扩展到隔振设计,并利用无穷维动力系统近似有限维系统的方法分析它的最优设计。在中间小质量无穷多的前提下,中间系统的传递特性可利用积分方法得到,而这也正是有限个中间小质量在个数较多时的近似。然后,基于给定的静变形上限求解简单双层隔振,多个小中间质量隔振以及无穷多小中间质量隔振的最优刚度比以及初始频率比,最后利用高频段的传递特性确定中间小质量分布的频带宽度。虽然采用多个小中间质量隔振会抬高传递率曲线的高频段,但如果容许高频段有稍许的上移,则多个小中间质量隔振可以消除简单双层隔振的二次谐振峰。最优设计为中间质量系统的质量比以及高频段容许上移量的解析表达式。四、当前舰船设备的振动控制,主动吸振器技术应用十分有限,本文针对两种具有较强抗干扰能力的主动控制技术,即滑模控制和鲁棒控制,从理论上进行了一些探索。首先,纠正了以往研究对于主动吸振器滑模控制中作动力出现直流分量的错误解释,并定量的给出了出现直流分量的判定标准。次之,给出了主动吸振器鲁棒控制权函数的选择技巧。这些对于主动吸振器在舰船振动控制领域的应用都具有一定价值。五、采用实验手段研究了虚拟吸振器算法的控制性能。结果表明,虚拟吸振器算法可以有效地抑制结构振动,它的重要优点在于对结构摄动具有相当高的稳定性,而且信号处理和反馈不需要全局处理,十分有利于大型结构的分散控制。面对舰船结构控制领域不断出现的新问题,以及当前控制理论各个方面的突破,主动或被动吸振器的振动控制也是一个不断进步的领域,所以本文也对主被动吸振器研究未来的发展做了若干展望。更多还原

【Abstract】 Vibration control is all along an important issue addressed by engineers and scholars, which covers vibration isolation and shock resistance of marine electromechanical equipments, the wind and earthquake protection of civil structures, vibration cancellation of automobile suspensions, etc. The advancement of modern military industry leads marine diesel engines to develop towards high power and high rotating velocity, which may cause more severe undesirable vibration of ship skull and equipments. Dynamic Vibration Absorber (DVA) can work as an effective strategy, which is discussed thoroughly in current study. Based on vibration control of marine equipments, some conclusions about passive and active DVA’s optimum designs in vibration suppression or isolation are drawn; moreover, the Virtual DVA control law is demonstrated experimentally. The main content and novel results are listed as following:1. The marine equipment is simplified as a SDOF mass block, and then the optimum designs of DVA attached to the SDOF primary mass are derived by the Lyapunov Equation and Matrix Kronecker Product. Firstly, using Lyapunov Equation the objective function is transformed from integration quadric form to matrix quadric one, secondly the matrix quadric form are expanded as polynomial expression under initial velocity or displacement, finally the polynomial coefficient are expressed with the Frequency Tuning Ratio and Damping Ratio using Kronecker Product. Minimizing the objective function, the optimum Frequency Tuning Ratio and Damping Ratio can be obtained. If the damping of primary structure is ignored, the closed-form analytical solution can be given. If the damping is taken into consideration, the 2-order perturbation solutions, expressed as the power series about the damping ratio, can be acquired. These optimum designs are composed of initial velocity or displacement ratio; hence various initial states can produce corresponding optimum designs, which differentiate them from previous studies. Especially, given the initial velocity ratio 0 or 1, these analytical solutions can produce the classical optimum designs under external force or base acceleration excitation. The comparison between the 2-order perturbation solutions and numerical optimum solutions by gradient search are demonstrated too, which prove that the 2-order perturbation solutions are stable enough.2. The Multiple Tuned Mass Dampers (MTMD) have been already applied for vibration cancellation of marine diesel engines, and consequently the calculus tools are proposed for performance index and iteration search of MTMD composed of infinitely multiple TMDs. In the previous study, the performance of MTMD made up of many TMDs can only be conjectured based on lots of data observation, at the same time, the iteration search is time-consuming. In current study, every single TMD, i.e. a small feedback component with independent Transform Function (TF), receives the displacement signal of the primary mass and exerts the control force on the primary mass, so the small TMD element can be regarded as an infinitesimal when the total number of TMD approaches infinity. Integrating all infinitesimal TMD elements, the TF of Infinitely Multiple Tuned Mass Damper (IMTMD) can be acquired, with the help of which the best and critical performance can be obtained. Moreover, the IMTMD method has excellent efficiency of iteration and it can give correct optimum parameters numerically for MTMD composed of more than 20 TMDs.3. The Two-Stage Vibration Isolation (TSVI) is widely used for vibration isolation of marine equipments, however, it’s well known that TSVI causes a steep resonant peak (i.e. the second resonant peak) in the middle frequency band, and hence the Multiple Small Middle Mass Vibration Isolation (MSMMVI), i.e. the MTMD introduced into vibration isolation, is proposed to address this issue in the present study. An infinite-dimension dynamic system is adopted to approximate a finite-dimension one, i.e. MSMMVI. When the number of small middle mass approaches infinity, the TF of MSMMVI can be obtained by integration, and then based on constrained static deflection of gravity, the optimum stiffness ratio and starting frequency ratio is derived for the single Two-Stage Vibration Isolation (TSVI), MSMMVI and Infinite Multiple Small Middle Mass Vibration Isolation (IMSMMVI), finally the performance in high frequency band is analyzed, by which the optimum frequency distribution bandwidth is acquired. Although introducing decentralized small middle masses blocks causes a little shift-up of Transform Ratio (TR) curve in high frequency band, the MSMMVI can flatten the second resonant peak of TSVI. Moreover, the TR curve can be improved obviously at the cost of an almost ignorable shift-up.4. It seems that the active DVA technique is rarely used for vibration suppression of marine equipments in current ship engineering, hence two active control algorithms, i.e. the Sliding Mode Control and Robust control, which both have excellent disturbance or error resistant ability, are selected for being discussed theoretically in the present study. The direct-current component of active control force in Sliding Mode Control (SMC) is explained, at the same time, some mistakes in the previous study are clarified. Finally a sufficient and necessary standard is given to avoid the direct-current component. For the Robust Control, some skills are given about weight function selection, which is of great value for industry application.5. The performance of Virtual DVA algorithm is studied experimentally, which is proved to be effective in vibration suppression. The algorithm is stable even if modeling error for the controlled system exists, more importantly, it can receive the local signal and feedback the control force to the local part, which is especially suitable for the Decentralized Control (DC) of the massive or complex structure.Confronted with various new issues appearing in ship industry field and development in modern control theory, research concerning the vibration control of marine equipments and Active/Passive DVA are advancing, as a result, some important problem, which may have great influence on the future of DVA, are listed.更多还原