A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008

Shaw, Steven W.; Balachandran, Balakumar

doi:10.1299/jsdd.2.611

Cited by 30 publications

(23 citation statements)

References 220 publications

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“…This work was expanded in [54] to a dual-wheel configuration, which allowed for the assessment of the effects of gyroscopic forces and axle width on shimmy behavior of the NLG. Finally, we remark that although shimmy oscillations are a well-documented phenomenon in aircraft ground dynamics, as Shaw and Balachandran point out in the review paper [43], shimmy oscillations may appear in mechanical systems outside of an aerospace context-for example, in the dynamics of motorcycles [5,27]. These mechanical systems have also attracted research interest, and examples of shimmy research employing numerical continuation techniques include the studies of an automobile under steady cornering conditions [12], the dynamics of a pulled wheel system [49], and the active steering control of a car [8].…”

mentioning

confidence: 62%

Influence of Variable Side-Stay Geometry on the Shimmy Dynamics of an Aircraft Dual-Wheel Main Landing Gear

Howcroft¹,

Krauskopf²,

Lowenberg

et al. 2013

SIAM J. Appl. Dyn. Syst.

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Copyright © by SIAM. Unauthorized reproduction of this article is prohibited. Abstract.Commercial aircraft are designed to fly but also need to operate safely and efficiently as vehicles on the ground. During taxiing, take-off, and landing the landing gear must operate reliably over a wide range of forward velocities and vertical loads. Specifically, it must maintain straight rolling under a wide variety of operating conditions. It is well known, however, that under certain conditions the wheels of the landing gear may display unwanted oscillations, referred to as shimmy oscillations, during ground maneuvers. Such oscillations are highly unwanted from a safety and a ride-comfort perspective. In this paper we conduct a study into the occurrence of shimmy oscillations in a main landing gear (MLG) of a typical midsize passenger aircraft. Such a gear is characterized by a main strut attached to the wing spar with a side-stay that connects the main strut to an attachment point closer to the fuselage center line. Nonlinear equations of motion are developed for the specific case of a two-wheeled MLG configuration and allow for large angle deflections within the geometrical framework of the system. The dynamics of the MLG are expressed in terms of three degrees of freedom: torsional motion, in-plane motion, and out-of-plane motion (with respect to the side-stay plane). These are modeled by oscillators that are coupled directly through the geometric configuration of the system as well as through the tire/ground interface, which is modeled here by the von Schlippe stretched string approximation of the tire dynamics. The mathematical model is fully parameterized and parameters are chosen to represent a generic (rather than a specific) landing gear. In particular, the positions of the attachment points are fully parameterized so that any orientation of the side-stay plane can be considered. The occurrence of shimmy oscillations is studied by means of a two-parameter bifurcation analysis of the system in terms of the forward velocity of the aircraft and the vertical force acting on the gear. 1. Introduction. The technical term shimmy is generally used to describe the self-sustained oscillations of a system with one or more rolling wheels and represents a relatively well-studied problem in engineering. Typical examples of shimmy with which the reader may be familiar range from the weaving of a towed trailer at high speeds to the sudden oscillation of a loose trolley wheel. The phenomenon first began to attract research interest in connection with the undesirable oscillation of the steering mechanism of early automobiles. These vehicles shared the common design elements of a single front axle rigidly connected to the front wheels, and the severity of the problem increased further with the development...

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mentioning

confidence: 62%

Influence of Variable Side-Stay Geometry on the Shimmy Dynamics of an Aircraft Dual-Wheel Main Landing Gear

Howcroft¹,

Krauskopf²,

Lowenberg

et al. 2013

SIAM J. Appl. Dyn. Syst.

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“…For instance, the nonlinear energy sink, an essentially nonlinear absorber, can extract energy from any mode of a host structure, a result that has never been obtained with linear absorbers [4]. This unconventional way of thinking renders the state of affairs in nonlinear dynamics particularly exciting, as pointed out in [5].…”

Section: Introductionmentioning

confidence: 99%

“…Although nonlinear absorbers can absorb disturbances in wide ranges of frequencies due to their increased bandwidth, their performance depends critically on motion amplitude [5]. One important observation is that all previously developed nonlinear absorbers are designed without considering the frequency-energy dependence of the nonlinear oscillations of the host structure.…”

Section: Introductionmentioning

confidence: 99%

The Nonlinear Tuned Vibration Absorber

Viguié

Kerschen

2013

Topics in Nonlinear Dynamics, Volume 1

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Abstract. The objective of this paper is to introduce a new nonlinear dynamical absorber, the nonlinear tuned vibration absorber, through a rigorous nonlinear extension of the tuning rule for the linear tuned vibration absorber. This nonlinear tuning methodology combined with the increased suppression bandwidth brought by the intentional use of nonlinearity leads to the development of an absorber that is effective in wide ranges of frequencies and motion amplitudes. The results are illustrated using a one-degree-of-freedom primary system.

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“…Impacting structures have been studied extensively [1][2][3][4][5][6], as these systems are relevant to macroscale and microscale dynamical problems, including gear rattling, milling operations, tapping mode AFM operations, and so on. A special situation arises when these impacts have a "zero-speed" or of the grazing type.…”

Section: Introductionmentioning

confidence: 99%

Noise influenced elastic cantilever dynamics with nonlinear tip interaction forces

Chakraborty

Balachandran

2011

Nonlinear Dyn

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In this work, the authors study the influence of noise on the dynamics of base-excited elastic cantilever structures at the macroscale and microscale by using experimental, numerical, and analytical means. The macroscale system is a base excited cantilever structure whose tip experiences nonlinear interaction forces. These interaction forces are constructed to be similar in form to tip interaction forces in tapping mode atomic force microscopy (AFM). The macroscale system is used to study nonlinear phenomena and apply the associated findings to the chosen AFM application. In the macroscale experiments, the tip of the cantilever structure experiences long-range attractive and short-range repulsive forces. There is a small magnet attached to the tip, and this magnet is attracted by another one mounted to a high-resolution translatory stage. The magnet fixed to the stage is covered by a compliant material that is periodically impacted by the cantilever's tip. Building on their earlier work, wherein the authors showed that perioddoubling bifurcations associated with near-grazing impacts occur during off-resonance base excitations of macroscale and microscale cantilevers, in the present work, the authors focus on studying the influence of Gaussian white noise when it is included as an addition to a deterministic base excitation input. The repulsive forces are modeled as Derjaguin-MullerToporov (DMT) contact forces in both the macroscale and microscale systems, and the attractive forces are modeled as van der Waals attractive forces in the microscale system and magnetic attractive forces in the macroscale system. A reduced-order model, based on a single mode approximation is used to numerically study the response for a combined deterministic and random base excitation. It is experimentally and numerically found that the addition of white Gaussian noise to a harmonic base excitation facilitates contact between the tip and the sample, when there was previously no contact with only the harmonic input, and results in a response that is nominally close to a period-doubled orbit. The qualitative change observed with the addition of noise is associated with neargrazing impacts between the tip and the sample. The numerical and experimental results further motivate the formulation of a general analytical framework, in which the Fokker-Planck equation is derived for the cantilever-impactor system. After making a set of approximations, the moment evolution equations are derived from the Fokker-Planck equation and numerically solved. The resulting findings support the experimental results and demonstrate that noise can be added to the input to facilitate contact between the cantilever's tip and the surface, when there was previously no contact with only a harmonic input. The effects of Gaussian white noise are numerically studied for a tapping mode AFM application, and it is shown that contact between the tip and the sample can be realized by 428 I. Chakraborty, B. Balachandran adding noise of an appropriate level to a harmonic ex...

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A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008

Cited by 30 publications

References 220 publications

Influence of Variable Side-Stay Geometry on the Shimmy Dynamics of an Aircraft Dual-Wheel Main Landing Gear

Influence of Variable Side-Stay Geometry on the Shimmy Dynamics of an Aircraft Dual-Wheel Main Landing Gear

The Nonlinear Tuned Vibration Absorber

Noise influenced elastic cantilever dynamics with nonlinear tip interaction forces

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