The centrifugal pendulum as a non linear torsional vibration absorber

Summary In this paper we study the centrifugal pendulum as a torsional vibrations absorber of an engine. A non-autonomous two degrees of freedom mechanical system with viscous-Coulomb damping is considered. The motion equations are written and we analyse for small oscillations of the pendulum, the effect of the non linear damping on the response curves in amplitude. Several numerical examples are ratio and the damping coefficients on the resonance peaks.

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Sommario In questo lavoro si studia il pendolo centrifugo come ammortizzatore di vibrazioni torsionali di un motore. Si considera un sistema meccanico non autonomo a due gradi di libertà con dissipazione coulombiana-viscosa. Si scrivono le equazioni del moto e si analizza, per piccole oscillazioni del pendolo, l'effetto dell'attrito non lineare sulle curve di risposta in ampiezza. Vengono presentati numerosi esempi numerici per illustrare l'influenza del rapporto di massa e dei coefficienti di attrito sui picchi di risonanza.

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This work has been realized within the activities of the Italian Council for the Research, C.N.R., G.N.F.M.     

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.

     

Suppression of chaos in nonlinear oscillators using a linear vibration absorber

Meccanica - This paper proposes a nonfeedback control to suppress the chaotic response of nonlinear oscillators. A linear vibration absorber is used as nonfeedback method, whose key idea is to find...     

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.     

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     

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.     

Stabilization of a 1/3-order subharmonic resonance using nonlinear dynamic vibration absorber

The paper proposes a stabilization method for a 1/3-order subharmonic resonance with a new type of nonlinear vibration absorber using nonlinear coupling between a main system and the absorber. The main system with nonlinear restoring force and harmonic excitation, i.e., subjected to a sinusoidally changed magnetic force, is introduced as a model which produces a 1/3-order subharmonic resonance. A damped pendulum, whose natural frequency is tuned to be in the neighborhood of twice that of the main system, is connected through a link to the main system as a nonlinear vibration absorber. Theoretical results using the method of multiple scales show that only a stable nontrivial steady state is changed into an unstable one due to the effect of absorber. In addition, we numerically confirm the validity of the proposed absorber using Runge–Kutta method.     

Longitudinal and torsional oscillations of a rod in a viscoelastic fluid

The flow of a viscoelastic fluid due to the torsional and longitudinal oscillations of an infinite circular rod is examined. The idealized equation of state to characterise this liquid is of the implicit Oldroyd-B model, for which momentum equations are solved analytically. The effect of the Weissenberg number and the viscosity ratio on the flow field are discussed. Also, the axial shear force and torque on the rod are computed. Received: 14 March 1997 Accepted: 14 May 1998     

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.     

Broadening the frequency bandwidth of a finite extensibility nonlinear vibration absorber by exploiting its internal resonances

Nonlinear Dynamics - In this paper, the dynamics response of a finite extensibility nonlinear elastic (FENE) absorber attached to a nonlinear primary system is investigated by writing the modal...     

Radial and torsional vibration characteristics of a rub rotor

The nonlinear dynamics characteristics of a vertical Jeffcott rotor with radial rub-impact are investigated in this paper. Considering the influence of speed whirling, the radial-torsional coupling model of the rub rotor in polar coordinate system is established. With the improved model, the dynamics characteristics of radial vibration, whirl and torsional vibration are analyzed under no rub, full annual rub and partial rub conditions. The radial harmonic frequency is obtained by the harmonic balance method. The torsional vibration has the harmonic frequency component similar to the radial vibration. The new harmonic frequency is useful to help diagnose the occurrence of rub fault. A reasonable explanation of backward whirl instability is presented in this paper. With development of partial rub, the backward whirl will occur. When the backward whirling frequency is near the natural frequency, the instability is observed. The numerical method gives the quantitative results and reveals the backward whirl instability process of rub.     

Numerical analysis of nonlinear modes of piecewise linear systems torsional vibrations

The nonlinear modes of essentially nonlinear piecewise-linear finite degrees of freedom systems are calculated by the numerical methods, which are suggested in this paper. The basis of these methods is numerical solutions of the equations of the systems motions in configuration space. The numerical method for the nonlinear modes of essentially nonlinear piecewise-linear systems forced vibrations is suggested. The basis of this approach is the combination of the Rauscher method and the calculations of the autonomous system nonlinear modes. The nonlinear modes of the diesel engine transmission torsional vibrations are analyzed numerically. The vibrations are described by essentially nonlinear piecewise-linear system with fifteen degrees of freedom. The NNMs of this system forced vibrations are observed in the resonance regions. Both NNMs and the motions, which are essentially differ from NNMs, are observed in the distance from the resonances. NNMs of the forced vibrations of the systems with dissipation are close to NNMs of the system without dissipation.