scholarly journals A nonlinear model of the hand-arm system and parameters identification using vibration transmissibility

2018 ◽  
Vol 241 ◽  
pp. 01014
Author(s):  
Nahid Hida ◽  
Mohamed Abid ◽  
Faouzi Lakrad
Keyword(s):  
Nonlinear Model ◽  
Harmonic Balance ◽  
Grip Force ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Single Degree Of Freedom ◽  
Identification Process ◽  
Harmonic Vibrations ◽  
Single Degree ◽  
Vibration Transmissibility

In the present paper a lumped single degree-of-freedom nonlinear model is used to study biodynamic responses of the hand arm system (HAS) under harmonic vibrations. Then, the harmonic balance method is implemented to derive the vibration transmissibility. Furthermore,Padé approximations are used in the identification process of biodynamic characteristics of the HAS model. This process is based on minimizing the distance between the theoretical and the experimentally measured transmissibilities. The proposed identification workflow is applied to vibrations at the wrist in two cases: 1) the transmissibility versus the grip force for fixed excitation frequencies, and 2) the transmissibility versus the excitation frequency for fixed grip force.

A Harmonic Balance Approximation of Dynamic Snap-Through Boundaries in a Single-Degree-of-Freedom Structure

2013 ◽  
Author(s):  
Richard Wiebe ◽  
Lawrence N. Virgin
Keyword(s):  
Large Amplitude ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Nonlinear Phenomena ◽  
Amplitude Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Analytical Approximations

Under dynamic loading, systems with the requisite condition for snap-through buckling, that is co-existing equilibria, typically exhibit either small amplitude response about a single equilibrium configuration, or large amplitude response that transits between the static equilibria. Dynamic snap-through is the name given to the large amplitude response, which, in the context of structural systems, is obviously undesirable. Structures with underlying snap-through static behavior may exhibit highly nonlinear and unpredictable oscillations. Such systems rarely lend themselves to investigation by analytical means. This is not surprising as nonlinear phenomena such as chaos run counter to the predictability of an analytical closed form solution. However, many unexpected analytical approximations of global stability may be obtained for simple systems using the harmonic balance method. In this paper a simple single-degree-of-freedom arch is studied using the harmonic balance method. The equations developed with the harmonic balance approach are then solved using an arc-length method and an approximate snap-through boundary in forcing parameter space is obtained. The method is shown to exhibit excellent agreement with numerical results. Arches present an ideal avenue for the investigation of snap-through as they typically have multiple, often tunable, stable and unstable equilibria. They also have many applications in both civil engineering, where arches are a canonical structural element, and mechanical/aerospace engineering, where arches may be used to approximate the behavior of curved plates and panels such as those used on aircraft.

scholarly journals A Nonlinear Model to Study Selectively Deformable Wing of an Aircraft

2015 ◽  
Vol 4 (4) ◽  
pp. 316
Author(s):  
Deiva Ganesh A
Keyword(s):  
Structural Dynamics ◽  
Nonlinear Model ◽  
Final Section ◽  
Excitation Frequency ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Deformable Structure ◽  
Prime Movers ◽  
Overall Performance ◽  
Future Work

<p>Aeroelasticity of an aircraft includes the study of dynamics of prime movers, structural dynamics, and aerodynamics. Research efforts are on in every area to improve the overall performance of an aircraft. In this paper preliminary studies conducted on the dynamics of selectively deformable wing using an under actuated nonlinear model is reported. First, the literature related to the design and analysis of selectively deformable structure (SDS) wing is reviewed. Second, a single degree of freedom (DOF) model to represent a fixed wing and a two DOF under-actuated model to represent SDS are discussed and their mathematical models are derived. Third, the effect of deformable wing portion on the wing dynamics is studied by varying the excitation frequency and stiffness of the model. Fourth, an experimental setup consisting of two rigid links connected by spring and subjected to sinusoidal displacement is investigated. Final section summarizes the research and provides directions for future work.</p>

Harvesting Energy From Time-Limited Harmonic Vibrations: Mechanical Considerations

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. J. Brennan ◽  
G. Gatti
Keyword(s):  
Mechanical Design ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Considerable Effect ◽  
Mechanical Vibrations ◽  
Single Degree Of Freedom ◽  
Harmonic Vibrations ◽  
Single Degree ◽  
Mechanical Oscillators ◽  
Analytical Expressions

Single-degree-of-freedom (SDOF) mechanical oscillators have been the most common type of generators used to harvest energy from mechanical vibrations. When the excitation is harmonic, optimal performance is achieved when the device is tuned so that its natural frequency coincides with the excitation frequency. In such a situation, the harvested energy is inversely proportional to the damping in the system, which is sought to be very low. However, very low damping means that there is a relatively long transient in the harvester response, both at the beginning and at the end of the excitation, which can have a considerable effect on the harvesting performance. This paper presents an investigation into the mechanical design of a linear resonant harvester to scavenge energy from time-limited harmonic excitations to determine an upper bound on the energy that can be harvested. It is shown that when the product of the number of excitation cycles and the harvester damping ratio is greater (less) than about 0.19, then more (less) energy can be harvested from the forced phase of vibration than from the free phase of vibration at the end of the period of excitation. The analytical expressions developed are validated numerically on a simple example and on a more practical example involving the harvesting of energy from trackside vibrations due to the passage of a train.

Two Groups of Chaotic Vibrations in a Single-Degree-of-Freedom Maglev System

1997 ◽  
Author(s):  
Zhixiang Xu ◽  
Hideyuki Tamura
Keyword(s):  
Magnetic Levitation ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Period Doubling ◽  
Excitation Amplitude ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Period Doubling Bifurcations

Abstract In this paper, a single-degree-of-freedom magnetic levitation dynamic system, whose spring is composed of a magnetic repulsive force, is numerically analyzed. The numerical results indicate that a body levitated by magnetic force shows many kinds of vibrations upon adjusting the system parameters (viz., damping, excitation amplitude and excitation frequency) when the system is excited by the harmonically moving base. For a suitable combination of parameters, an aperiodic vibration occurs after a sequence of period-doubling bifurcations. Typical aperiodic vibrations that occurred after period-doubling bifurcations from several initial states are identified as chaotic vibration and classified into two groups by examining their power spectra, Poincare maps, fractal dimension analyses, etc.

Beating Effects in a Single Nonlinear Dynamical System in a Neighborhood of the Resonance

2016 ◽  
Vol 849 ◽  
pp. 76-83
Author(s):  
Jiří Náprstek ◽  
Cyril Fischer
Keyword(s):  
Harmonic Balance ◽  
Excitation Frequency ◽  
Nonlinear Dynamical System ◽  
Numerical Continuation ◽  
System Response ◽  
Algebraic Equations ◽  
Single Degree Of Freedom ◽  
Nonlinear Dynamical ◽  
The Difference ◽  
Eigen Frequency

The exact coincidence of external excitation and basic eigen-frequency of a single degree of freedom (SDOF) nonlinear system produces stationary response with constant amplitude and phase shift. When the excitation frequency differs from the system eigen-frequency, various types of quasi-periodic response occur having a character of a beating process. The period of beating changes from infinity in the resonance point until a couple of excitation periods outside the resonance area. Theabove mentioned phenomena have been identified in many papers including authors’ contributions. Nevertheless, investigation of internal structure of a quasi-period and its dependence on the difference of excitation and eigen-frequency is still missing. Combinations of harmonic balance and small parameter methods are used for qualitative analysis of the system in mono- and multi-harmonic versions. They lead to nonlinear differential and algebraic equations serving as a basis for qualitativeanalytic estimation or numerical description of characteristics of the quasi-periodic system response. Zero, first and second level perturbation techniques are used. Appearance, stability and neighborhood of limit cycles is evaluated. Numerical phases are based on simulation processes and numerical continuation tools. Parametric evaluation and illustrating examples are presented.

Stochastic Dynamics of a Variable Inertia System via Lyapunov Exponents

2008 ◽  
Author(s):  
S. F. Asokanthan ◽  
X. H. Wang ◽  
W. V. Wedig ◽  
S. T. Ariaratnam
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Stochastic Dynamics ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Excitation ◽  
The Stability

Torsional instabilities in a single-degree-of-freedom system having variable inertia are investigated by means of Lyapunov exponents. Linearised analytical model is used for the purpose of stability analysis. Numerical schemes for simulating the top Lyapunov exponent for both deterministic and stochastic systems are established. Instabilities associated with the primary and the secondary sub-harmonic resonances have been identified by studying the sign of the top Lyapunov exponent. Predictions for the deterministic and the stochastic cases are compared. Instability conditions have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. The effects of fluctuation density as well as that of damping on the stability behaviour of the system have been examined. Predicted instability conditions are adequate for the design of a variable-inertia system so that a range of critical speeds of operation may be avoided.

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