Towed wheel shimmy suppression through a nonlinear tuned vibration absorber

The implementation of the nonlinear tuned vibration absorber (NLTVA) for the suppression of shimmy vibration in towed wheels is addressed in this study. We adopt a modified straight tangent tyre model of a single-degree-of-freedom towed wheel system with an attached NLTVA. Stability analysis illustrated that the NLTVA can significantly improve the stability of the equilibrium of the wheel. Bifurcation analysis highlighted the existence of large bistable regions, which undermines the system’s safety. However, numerical continuation analysis, coupled with a dynamical integrity investigation, revealed that the addition of an intentional softening nonlinearity in the absorber restoring force characteristic enables the complete suppression of the bistable regions, also reducing the amplitude of shimmy oscillations in the unstable region. Quasiperiodic motions were also identified; however, their practical relevance seems marginal.

     

The energy thresholds of nonlinear vibration absorbers

A popular means to mitigate excessive structural vibrations is the attachment of a lightweight spring-mass element, known as a vibration absorber or tuned mass damper. Designing new types of vibration absorbers that outperform the classical linear tuned mass damper is a challenging ongoing research field. This paper focuses on the absorber with a strongly nonlinear spring characteristic. A critical aspect in the design procedure of such nonlinear vibration absorber is the existence of energy thresholds below which no efficient vibration reduction is possible. This paper extends the concept of an energy threshold to a more general parameter threshold representing several threshold values. Two important contributions are obtained. First, one single bifurcation analysis covers every combination of the system parameters. Second, the results are generalized to linear main systems under impulsive load and harmonic load, nonlinear main systems, and general nonlinear spring characteristics.     

接地惯容式减振器对悬臂输流管稳定性和动态响应的影响研究

输流管道广泛应用于机械、航空、核电和石油等重要工程领域.为防止管道结构因流致振动破坏造成的损失, 很有必要对其稳定性、动力学响应及其调控进行深入研究.本文提出一种由惯容器、弹簧和阻尼器并联组成的减振器模型, 研究了这种接地惯容减振器对悬臂输流管稳定性和非线性振动的影响. 首先, 基于哈密顿原理给出了带有接地惯容减振器非保守系统的非线性动力学模型; 然后, 利用高阶伽辽金方法对非线性方程进行离散化; 最后, 分别从线性和非线性角度分析了不同减振器参数下输流管道的被动控制效果, 着重讨论了惯容系数和减振器安装位置对悬臂管稳定性和动态响应的影响机制.线性理论模型的研究结果显示, 接地惯容减振器可显著影响悬臂管的失稳临界流速, 故通过调节减振器参数能有效提高输流管道的稳定性;惯容系数和弹簧刚度对系统稳定性的控制效果还与减振器的安装位置密切相关.非线性理论模型的分析结果显示, 惯容系数和减振器位置对输流管的非线性动态响应也有显著影响, 且这种影响还依赖于管道的流速取值; 在某些参数条件下, 减振器还可使输流管道由周期运动演化为复杂的混沌行为. 本文研究结果表明, 通过设计合理的惯容式减振器参数, 可提升悬臂输流管道的稳定性并有效抑制其颤振幅值.      

Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber

This paper is the second one in the series of two papers devoted to detailed investigation of the response regimes of a linear oscillator with attached nonlinear energy sink (NES) under harmonic external forcing and assessment of possible application of the NES for vibration absorption and mitigation. In this paper, we study the performance of a strongly nonlinear, damped vibration absorber with relatively small mass attached to a periodically excited linear oscillator. We present a nonlinear absorber tuning procedure in the vicinity of (1:1) resonance which provides the best total system energy suppression, using analytical and numerical tools. A linear absorber is also tuned according to the same criterion of total system energy suppression as the nonlinear one. Both optimally tuned absorbers are compared under common parameters of damping, external forcing but different absorber stiffness characteristics; certain cases for which nonlinear absorber is preferable over the linear one are revealed and confirmed numerically.     

Vibration reduction of multi-parametric excited spring pendulum via a transversally tuned absorber

The use of passive control strategy is a common way to stabilize and control dangerous vibrations in a nonlinear spring pendulum which is describing the ship’s roll motion. In this paper, a tuned absorber in the transversal direction is connected to a spring pendulum with multi-parametric excitation forces to control the vibration due to some resonance cases on the system. The method of multiple scale perturbation technique (MSPT) is applied to study the periodic solution of the given system near simultaneous sub-harmonic and internal resonance case. The stability of the steady-state solution near the resonance case is investigated and studied using frequency response equations. The effects of the absorber and some system parameters on the vibrating system are studied numerically. Optimal working conditions of the system are extracted when applying passive control methods. Comparison with the available published work is reported.     

The tuned bistable nonlinear energy sink

A bistable nonlinear energy sink conceived to mitigate the vibrations of host structural systems is considered in this paper. The hosting structure consists of two coupled symmetric linear oscillators (LOs), and the nonlinear energy sink (NES) is connected to one of them. The peculiar nonlinear dynamics of the resulting three-degree-of-freedom system is analytically described by means of its slow invariant manifold derived from a suitable rescaling, coupled with a harmonic balance procedure, applied to the governing equations transformed in modal coordinates. On the basis of the first-order reduced model, the absorber is tuned and optimized to mitigate both modes for a broad range of impulsive load magnitudes applied to the LOs. On the one hand, for low-amplitude, in-well, oscillations, the parameters governing the bistable NES are tuned in order to make it functioning as a linear tuned mass damper (TMD); on the other, for high-amplitude, cross-well, oscillations, the absorber is optimized on the basis of the invariant manifolds features. The analytically predicted performance of the resulting tuned bistable nonlinear energy sink (TBNES) is numerically validated in terms of dissipation time; the absorption capabilities are eventually compared with either a TMD and a purely cubic NES. It is shown that, for a wide range of impulse amplitudes, the TBNES allows the most efficient absorption even for the detuned mode, where a single TMD cannot be effective.     

Competitive energy transfer between a two degree-of-freedom dynamic system and an absorber with essential nonlinearity

The background of this work is related to passive vibration control of a two degree-of-freedom master system attached to an essentially nonlinear slave absorber aimed to attenuate vibrations by irreversibly transferring energy to a localized nonlinear normal mode (nonlinear normal modes should be considered here according to the definition from Rosenberg in J. Appl. Mech., 28:275–283, 1961). Such a nonlinear absorber which has no preferential frequency is theoretically able to capture several nonlinear resonances. The main purpose is here to bring insight in what is actually going on when two linear modes are in competition for energy transfer. An original asymptotic analysis using two small parameters enables one to build a scenario that improves the understanding of resonance mechanisms and to forecast which mode will be first attenuated by means of energy transfer. Numerical benchmark simulations corroborate the reliability of obtained scenario.     

Damping of Free Elastic Vibrations in Linear Systems

The possibility of using a Mises truss as an absorber of free elastic vibrations in a linear elastic system is examined. The nonlinear normal mode method is used to analyze nonlinear vibrations. A local nonlinear normal mode is shown to be favorable for vibration damping__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 110–117, February 2005.     

动力吸振器复合非线性能量阱对线性镗杆系统的振动控制

研究了线性动力吸振器复合非线性能量阱对线性镗杆在外部简谐激励下的振动控制. 忽略镗杆系统中的非线性因素, 建立了附加线性动力吸振器和非线性能量阱的镗杆系统的三自由度运动方程, 研究了附加复合式动力吸振器的镗杆系统的受迫振动. 通过平均法得到了附加复合式动力吸振器的镗杆系统的近似解析解, 并利用数值解验证了近似解析解的准确性, 两者具有很好的一致性. 利用近似解析解详细分析了线性动力吸振器和非线性能量阱的参数对镗杆振动抑制性能的影响. 对给定质量的复合式动力吸振器进行了参数优化, 其中线性动力吸振器参数采用H_∞优化方法的近似解析解进行了优化, 非线性能量阱的阻尼利用系统的近似解析解进行了优化. 分析结果表明, 线性动力吸振器与非线性能量阱组合可以有效抑制线性镗杆系统的振动, 而且采用参数优化后的复合式动力吸振器可以获得更好的减振效果. 通过附加非线性能量阱, 不但可以提高线性动力吸振器的振动抑制效果, 而且还可以提高振动控制系统的鲁棒性.      

不同类型水平弹簧组合刚度非线性吸振器的性能分析及稳定性研究

动力吸振器作为一种振动控制单元被广泛运用于各种工程场合,但传统的线性吸振器只能实现窄带振动控制.文章在线性吸振器的基础上引入对称水平弹簧构建线性刚度与非线性刚度相结合的组合刚度非线性吸振器,以提升吸振器的吸振性能.考虑实际工程中可能的安装方式,分别建立水平弹簧接地安装和不接地安装的组合刚度非线性吸振器模型,利用谐波平衡法结合弧长延拓法解析求解动力学响应,并与数值结果相互验证,证明了求解结果的准确性.随后分析比较两种组合刚度非线性吸振器与线性吸振器以及非线性能量阱之间的吸振性能,发现水平弹簧接地安装类型的组合刚度非线性吸振器在保留线性吸振器优势的同时又改善其吸振频带窄的缺点,且与非线性能量阱相比在主共振频率附近的较宽频内吸振性能更优.在此基础上,讨论了水平弹簧参数以及吸振器阻尼对主结构振动幅频响应和稳定性的影响,最后观察分析主结构幅频响应曲线不稳定区内的复杂动力学行为.研究结果表明合适的设计参数能够使得主结构振动峰值较低的同时,频响曲线不稳定运动区域的范围也较小.     

Amplitude reduction of primary resonance of nonlinear oscillator by a dynamic vibration absorber using nonlinear coupling

The paper presents the characteristics of a new type of nonlinear dynamic vibration absorber for a main system subjected to a nonlinear restoring force under primary resonance. The absorber is connected to the main system by a link in order to be excited with twice the frequency of the motion of the main system. The natural frequency of the absorber is tuned to be twice the natural frequency of the main system, in contrast to autoparametric vibration absorber, whose natural frequency is tuned to be one-half the natural frequency of the main system. The presented absorber is not excited through the autoparametric resonance, i.e., no trivial equilibrium state exists. Therefore, the absorber always oscillates because of the motion of the main system and cannot be trapped by Coulomb friction acting on the absorber, in contrast to the autoparametric vibration absorber. Under small excitation amplitude, this absorber does not produce an overhang in the frequency response curve, which occurs because of the use of the conventional autoparametric vibration absorber; the overhang renders the response amplitude larger than that in the case without an absorber. In addition, the absorber removes the hysteresis in the frequency response curve caused by the nonlinearity of the restoring force acting on the main system. Regarding large excitation amplitude, the response amplitude in the main system can be decreased by increasing the damping of the absorber, but that decrease is limited by the nonlinearity in the restoring force acting on the main system. This paper also describes experimental validation of the absorber under small excitation amplitude using a simple apparatus.     

自适应主动共振吸振器的设计和减振性能研究

为了扩大吸振器的工作频带,减小吸振器的阻尼,最终提高吸振器的减振效果,本文设计了一种自适应主动共振吸振器。文中对几种不同种类吸振器的减振原理、动力学特性等进行了理论分析和比较,集成自调谐吸振器和主动吸振器的优点,完成了一种自适应主动共振吸振器的设计,并提出了一种变步长、双寻优的控制算法。在振动台上测试了吸振器的动力学特性并理论分析了吸振器的移频特性和阻尼特性。在两端固支梁上对吸振器的减振效果进行了实验评估。实验结果显示,相比自调谐吸振器,加入主动力控制后,自适应主动共振吸振器的阻尼比从0.04减小至0.02,减振效果得到了显著的提高。     

The effects of Coulomb friction on the performance of centrifugal pendulum vibration absorbers

We investigate analytically and experimentally the effects of Coulomb friction on the performance of centrifugal pendulum vibration absorbers (CPVAs), which are used to reduce torsional vibrations in rotating machinery. The analysis is based on perturbation methods applied to the nonlinear equations of motion for a rotor subjected to an engine order applied torque and equipped with a circular path CPVA with viscous and Coulomb damping. The experimental work is based on quantifying parameters for the damping model using free vibration measurements with a viscous and Coulomb damping identification scheme that is enhanced to better handle measurement noise, and running tests for steady-state operation under a range of loading conditions. The level of Coulomb damping is varied by adjusting the friction of the absorber connection bearing. Good agreement is found between the analytical predictions and the experimental data. It is shown that the absorber sticks up to a level of excitation that allows it to release, after which the Coulomb damping acts in the expected manner, resulting in lowered response amplitudes. The results obtained are of general use in assessing absorber performance when dry friction is present in absorber suspensions.     

Novel method for research on exposure to nonlinear vibration transferred by suspension of vehicle

The paper presents novel method for research on exposure to nonlinear vibration of passenger car suspension as nonlinear dynamical system. Also paper provides a discussion on the results of studies addressing the impact exerted by damping properties of shock absorber on the vibrations being generated. The research was conducted on the car forced to vibration by the exciter machine with changeable frequency. The paper addresses results of analysis of application of one of the time-frequency representation techniques to the identification of structure of vibration. The obtained representation of the vibration allows determining time function of separate frequency bands, which represents the isolated vibration dynamics phenomena. Considering the variability of the time and frequency distribution of the vibration even in selected analysed bands, the time function was developed as exposure to vibration estimator. The recommended method makes use of function of exposure to vibration. The advantage of these method is possibilities of precise analysis of chosen frequency bands. The investigations conducted confirm considerable susceptibility to changes in the technical condition of shock absorber with regard to the assessment of human exposure to vibrations.     

A review of development and implementation of an active nonlinear vibration absorber

Summary We present an account of an implementation of an active nonlinear vibration absorber that we have developed. The control technique exploits the saturation phenomenon that is known to occur in quadratically-coupled multi-degree-of-freedom systems subjected to primary excitation and possessing a two-to-one internal resonance. The technique is based on introducing an absorber and coupling it with the structure through a sensor and an actuator, where the feedback and control signals are quadratic. First, we consider the case of controlling the vibrations of a single-degree-of-freedom system. We develop the equations governing the response of the closed-loop system and use the method of multiple scales to obtain an approximate solution. We investigate the performance of the control strategy by studying its steady-state and transient characteristics. Additionally, we compare the performance of the quadratic absorber with that of a linear absorber. Then, we present theoretical and experimental results that demonstrate the versatility of the technique. We design an electronic circuit to emulate the absorber and use a variety of sensors and actuators to implement the active control strategy. First, we use a motor and a potentiometer to control the vibration of a rigid beam. We develop a plant model that includes Coulomb friction and demonstrate that the closed-loop system exhibits the saturation phenomenon. Second, we extend the strategy to multi-degree-of-freedom systems. We use PZT ceramics and strain gages to suppress vibrations of flexible steel beams when subjected to single- and simultaneous two-mode excitations. Third, we employ Terfenol-D, a nonlinear actuator, and accelerometers to control the vibrations of flexible beams. In all instances, the technique is successful in reducing the response amplitude of the structures. Received 3 May 1999; accepted for publication 3 June 1999     

Vibration absorbers for a rotating flexible structure with cyclic symmetry: nonlinear path design

This paper analytically investigates the nonlinear dynamics of order-tuned vibration absorbers applied to cyclic rotating flexible structures under traveling wave (TW) engine-order excitation. The primary cyclic structure is assumed to be governed by linear vibrations and the nonlinear absorber response arises from large amplitude kinematic effects. These dynamics are captured by a lumped-parameter model that consists of N blades with one blade mode and one absorber per blade, which are arranged with cyclic symmetry on a rotating disk. The governing equations of motion are formulated for arbitrary absorber paths to allow investigation of the absorber path design for nonlinear response. This paper extends previous work by the authors, which considered the linearized blade and absorber dynamics of a similar system. Several intriguing features of the dynamics were uncovered, most notably the existence of an absorber tuning range that avoids resonance at any rotation speed. Of particular interest is the existence and stability of the steady-state TW response to TW excitation, as experienced in turbomachinery, and how these are affected by selection of the absorber paths, which fix the linear and nonlinear tuning characteristics. It is shown that the TW response, which is unique for the linearized system, also exists for the weakly nonlinear model and can be captured by an equivalent two degree of freedom model obtained using the symmetry of the excitation and system response. The forced response exhibits the usual characteristics of a weakly nonlinear system, specifically, bistability and the attendant hysteresis near resonance. More significantly, it does not experience any additional instabilities associated with the symmetry. That is, the desired TW response is robust to nonlinear effects in the absorber, which allows use of the simple equivalent model for selection of absorber tuning parameters. For good performance and robustness, the linear absorber tuning should be in the “no-resonance zone” described by the linear theory and the absorber paths should have a slightly softening nonlinear characteristic.     

Design of a tuned vibration absorber for a slender hollow cylindrical structure

Abstract

In this paper, details of the design work for a tuned vibration absorber to be used on a hollow cylindrical structure is presented. The vibration problem is of resonant type and the tuned vibration absorber is designed to suppress the displacement vibration response of the free end of the slender hollow structure dominated by the contribution of its lowest transverse vibration modes. The structure is modeled using a commercial finite element software. Finite element model of the structure is verified using experimentally obtained frequency response functions and modal parameters. Effective parameters of the tuned vibration absorber design are then determined based on finite element analysis simulations of the vibration suppression performance of the tuned vibration absorber as it is used on the structure. Details of the tuned vibration absorber design are determined and a prototype is fabricated. Prototype tuned vibration absorber is then characterized experimentally both as a standalone system and also as it is used on the main structure. Vibration reduction performance of the physical prototype of the tuned vibration absorber is also compared with its vibration reduction performance estimated from finite element analysis simulations so that the analysis based design process can be validated.

Communicated by Dumitru Caruntu.     

基于非线性吸能机理的涡激振动减振理论与实验研究

流致振动现象广泛存在于机械、航空、土木和石油等重要工程领域, 为防止工程结构因流致振动行为而造成疲劳破坏, 有必要对稳定性、动力学响应及其振动控制做深入研究. 本文提出了一种由弹簧和质量块构成的非线性吸能器(nonlinear targeted energy transfer, NTET), 研究了该非线性吸能器对弹性支承圆柱体涡激振动的被动控制影响机制. 基于能量法推导了圆柱体涡激振动非线性被动控制的耦合动力学方程, 通过设计非线性弹簧?质量块构型的NTET, 进一步开展了涡激振动控制的实验研究, 并与理论预测结果进行了较好的对比, 获得提升涡激振动控制效果的最佳参数值. 研究发现, NTET的质量、弹簧刚度以及弹簧预应力等参数会对涡激振动控制效果产生显著的影响. 本文研究结果表明, 该耦合系统中圆柱体和NTET均表现出周期性的稳态振动响应, NTET质量的改变会显著影响系统的耦合频率. 在无预应力状态下, NTET质量越大、刚度越小时, 有更好的减振效果. 当弹簧预应力逐渐增大时, NTET的非线性刚度逐渐变弱, 会降低涡激振动控制性能. 参数分析表明: 随着涡激振动控制性能的提升, 圆柱体的振幅逐渐较小, NTET的振幅逐渐增大, 能量传递效率逐渐提高. 研究结果可为工程中涡激振动控制策略的高效设计提供有用的理论支撑和实验数据.      

Tuning of a vibration absorber with shunted piezoelectric transducers

In order to reduce structural vibrations in narrow frequency bands, tuned mass absorbers can be an appropriate measure. A quite similar approach which makes use of applied piezoelectric elements, instead of additional oscillating masses, are the well-known resonant shunts, consisting of resistances, inductances, and possibly negative capacitances connected to the piezoelectric element. This paper presents a combined approach, which is based on a conventional tuned mass absorber, but whose characteristics can be strongly influenced by applying shunted piezoceramics. Simulations and experimental analyses are shown to be very effective in predicting the behavior of such electromechanical systems. The vibration level of the absorber can be strongly attenuated by applying different combinations of resistant, resonant, and negative capacitance shunt circuits. The damping characteristics of the absorber can be changed by applying a purely resistive or resonant resistant shunt. Additionally, the tuning frequency of the absorber can be adapted to the excitation frequency, using a negative capacitance shunt circuit, which requires only the energy to supply the electric components.     

The application of inerter in tuned mass absorber

In this paper we investigate the dynamics of tuned mass absorber with additional viscous damper and inerter attached to the pendulum. The devices are used to damp out oscillations of non-linear Duffing oscillator. Analysis of how these devices influence the dynamics of tuned mass absorber and its damping properties is shown. We calculate the detailed bifurcation diagrams and show how by changing the parameters of damper and inerter one can eliminate dangerous dynamic instabilities from the systems. Finally, in the last section we present an optimization of TMA׳s parameters in order to achieve best efficiency in damping of the main body vibrations.