scholarly journals Dynamic response of multi-degree-of-freedom systems with a Coulomb friction contact under harmonic excitation

2021 ◽  
Author(s):  
Luca Marino ◽  
Alice Cicirello
Keyword(s):  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Friction Contact ◽  
Engineering Structures ◽  
Stick Slip ◽  
State Response ◽  
Mdof Systems ◽  
Analytical Response ◽  
Dynamic Performances ◽  
Stick Slip Motion

Abstract This paper investigates the steady-state response of a multi-degree-of-freedom (MDOF) system with a Coulomb contact to harmonic excitation. Although discrete MDOF models are commonly used at early design stages to analyse the dynamic performances of engineering structures, the current understanding of the friction damping effects on MDOF behaviour is still limited due to the absence of analytical solutions. In this contribution, closed-form expressions of the continuous time response, the displacement transmissibility and the phase angle of each mass of the system are derived and validated numerically for 2DOF and 5DOF systems. Moreover, the features of the analytical response are investigated, obtaining the following results: (i) the determination of the minimum amounts of friction for which the resonant peaks become finite and (ii) for which stick-slip motion can be observed at high frequencies; (iii) an equation for the evaluation of invariant points for the displacement transmissibilities; (iv) a better understanding of phenomena such as the inversions of the transmissibility curves and the onset of additional resonant peaks due to the permanent sticking of the mass in contact. All these results show that MDOF systems exhibit significantly different dynamic behaviours depending on whether the friction contact and the harmonic excitation are applied to the same or different masses.

scholarly journals Multi-degree-of-freedom systems with a Coulomb friction contact: analytical boundaries of motion regimes

2021 ◽  
Author(s):  
Luca Marino ◽  
Alice Cicirello
Keyword(s):  
Ad Hoc ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Physical Parameters ◽  
Dimensional Parameter ◽  
Stick Slip ◽  
State Response ◽  
Mdof Systems ◽  
Two Degree Of Freedom

AbstractThis paper proposes an approach for the determination of the analytical boundaries of continuous, stick-slip and no motion regimes for the steady-state response of a multi-degree-of-freedom (MDOF) system with a single Coulomb contact to harmonic excitation. While these boundaries have been previously investigated for single-degree-of-freedom (SDOF) systems, they are mostly unexplored for MDOF systems. Closed-form expressions of the boundaries of motion regimes are derived and validated numerically for two-degree-of-freedom (2DOF) systems. Different configurations are observed by changing the mass in contact and by connecting the rubbing wall to: (i) the ground, (ii) the base or (iii) the other mass. A procedure for extending these results to systems with more than 2DOFs is also proposed for (i)–(ii) and validated numerically in the case of a 5DOF system with a ground-fixed contact. The boundary between continuous and stick-slip regimes is obtained as an extension of Den Hartog’s formulation for SDOF systems with Coulomb damping (Trans Am Soc Mech Eng 53: 107–115, 1931). The boundary between motion and no motion regimes is derived with an ad hoc procedure, based on the comparison between the overall dynamic load and the friction force acting on the mass in contact. The boundaries are finally represented in a two-dimensional parameter space, showing that the shape and the extension of the regions associated with the three motion regimes can change significantly when different physical parameters and contact configurations are considered.

Stability Analysis of a Multi-Degree of Freedom System Limit Cycles and Close Trajectories

2010 ◽  
Author(s):  
Jir´i´ Na´prstek
Keyword(s):  
Steady State ◽  
Limit Cycles ◽  
Theoretical Background ◽  
Degree Of Freedom ◽  
Steady State Response ◽  
Stability Assessment ◽  
Open Problems ◽  
Linear Dynamics ◽  
State Response ◽  
Mdof Systems

Limit cycles (LC) are important steady state response types of multi-degree of freedom (MDOF) systems. Problems of LC basic existence, their emerging and extinction are closely related with their stable/unstable character. A new analytical/iterative method of LC identification and portrait investigation has been developed together with a technique of stability assessment. It enables to distinguish the stable/unstable limit cycles and consequently to define the attractive and repulsive response fields. LC investigation and transition processes from/to the wide attractor are carried out in subspace which is normal to the limit cycle trajectory. Special orthogonal subsystem is constructed. It enables an effective investigation of an LC behavior in a close neighborhood of the basic trajectory. Some analogies and relations with Lyapunov exponent procedure are mentioned. The general theoretical background is demonstrated on an SDOF and later DDOF systems. Links with related areas of non-linear dynamics and some open problems are outlined.

scholarly journals A model of processive walking and slipping of kinesin-8 molecular motors

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ping Xie
Keyword(s):  
Single Molecule ◽  
Molecular Motors ◽  
External Load ◽  
Molecular Motor ◽  
Velocity Versus ◽  
Stick Slip ◽  
Load Dependence ◽  
Chemomechanical Coupling ◽  
Similarities And Differences ◽  
Stick Slip Motion

AbstractKinesin-8 molecular motor can move with superprocessivity on microtubules towards the plus end by hydrolyzing ATP molecules, depolymerizing microtubules. The available single molecule data for yeast kinesin-8 (Kip3) motor showed that its superprocessive movement is frequently interrupted by brief stick–slip motion. Here, a model is presented for the chemomechanical coupling of the kinesin-8 motor. On the basis of the model, the dynamics of Kip3 motor is studied analytically. The analytical results reproduce quantitatively the available single molecule data on velocity without including the slip and that with including the slip versus external load at saturating ATP as well as slipping velocity versus external load at saturating ADP and no ATP. Predicted results on load dependence of stepping ratio at saturating ATP and load dependence of velocity at non-saturating ATP are provided. Similarities and differences between dynamics of kinesin-8 and that of kinesin-1 are discussed.

scholarly journals Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 850-856 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Yun-Yun Xu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Vibration System ◽  
Derivative Operator ◽  
Vibration Equation ◽  
State Response ◽  
Frequency Relation

Abstract The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator ${}_{-\infty} D_t^\beta,$where the order β is a real number satisfying 0 ≤ β ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < β < 1, while it contributes to the viscous inertia if 1 < β < 2. Thus the fractional derivative can represent the “spring-pot” element and also the “inerterpot” element proposed in the present article. The viscosity contribution coefficient, elasticity contribution coefficient, inertia contribution coefficient, amplitude-frequency relation, phase-frequency relation, and influence of the order are discussed in detail. The results show that fractional derivatives are applicable for characterizing the viscoelasticity and viscous inertia of materials.

A Resonance Chart for Damped Vibration

1955 ◽  
Vol 59 (540) ◽  
pp. 850-852 ◽  
Author(s):  
R. E. D. Bishop
Keyword(s):  
Linear System ◽  
Convenient Method ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Viscous Damping ◽  
Similar Form ◽  
Hysteretic Damping ◽  
Resonance Curves ◽  
Phase Angles

A convenient method is pointed out for calculating the response of a damped linear system with one degree of freedom to harmonic excitation. Results of such calculations are usually represented by the familiar “ resonance curves ”—one curve being plotted for each intensity of damping. These curves are not particularly convenient to use and Yates has overcome several of their defects by throwing them into a nomographic form. Yates' nomogram is based upon the concept of viscous damping and it does not give the information of a conventional set of resonance curves in that it relates to the velocity of vibration. By changing over to hysteretic damping, a nomogram of somewhat similar form may be constructed such that it gives amplitudes and phase angles of displacements while retaining the advantages, over resonance curves, of this form of representation.

Energy Balancing Method to Identify Nonlinear Damping of Bolted-Joint Interface

2016 ◽  
Vol 693 ◽  
pp. 318-323 ◽  
Author(s):  
Xin Liao ◽  
Jian Run Zhang
Keyword(s):  
Dry Friction ◽  
Harmonic Excitation ◽  
Joint Interface ◽  
Damping Factor ◽  
Viscous Damping ◽  
Bolted Joint ◽  
Energy Balancing ◽  
Stick Slip ◽  
Non Linear ◽  
Linear Damping

The interface of bolted joint commonly focuses on the research of non-linear damping and stiffness, which affect structural response. In the article, the non-linear damping model of bolted-joint interface is built, consisting of viscous damping and Coulomb friction. Energy balancing method is developed to identify the dry-friction parameter and viscous damping factor. The corresponding estimation equations are acquired when the input is harmonic excitation. Then, the vibration experiments with different bolted preloads are conducted, from which amplitudes in various input levels are used to work out the interface parameters. Also, the fitting curves of dry-friction parameters are also obtained. Finally, the results illustrate that the most interface of bolted joint in lower excitation levels occurs stick-slip motion, and the feasibility of the identification approach is demonstrated.

Dynamics of stick–slip motion, Whillans Ice Stream, Antarctica

2011 ◽  
Vol 305 (3-4) ◽  
pp. 283-289 ◽  
Author(s):  
J. Paul Winberry ◽  
Sridhar Anandakrishnan ◽  
Douglas A. Wiens ◽  
Richard B. Alley ◽  
Knut Christianson
Keyword(s):  
Stick Slip ◽  
Ice Stream ◽  
Whillans Ice Stream ◽  
Stick Slip Motion ◽  
Slip Motion

GRANULAR FAILURE: THE ORIGIN OF EARTHQUAKES?

2009 ◽  
Vol 23 (28n29) ◽  
pp. 5374-5382 ◽  
Author(s):  
MASSIMO PICA CIAMARRA ◽  
LUCILLA DE ARCANGELIS ◽  
EUGENIO LIPPIELLO ◽  
CATALDO GODANO
Keyword(s):  
Confining Pressure ◽  
Stick Slip ◽  
Slip Regime ◽  
Constant Rate ◽  
Large Fluctuations ◽  
System Flow ◽  
System Phase Diagram ◽  
Dynamics Simulations ◽  
Stick Slip Motion ◽  
System Phase

Via Molecular Dynamics simulations, we investigate the stick-slip motion in a model of fault, where two surfaces subject to a constant confining pressure P, and enclosing granular particles, are subject a shear stress σ. When the system sticks, the stress increases with a constant rate [Formula: see text], while the stress decreases when the system flow. We dermine the system 'phase diagram' in the pressure P load velocity [Formula: see text] plane, locating the transition form the continuos flow regime to the stick-slip regimes, and show that the transition between these two regimes is characterized by the presence of large fluctuations. In the stick-slip regime, the system reproduces the behaviour of a segment of a fault of fixed lenght.

Dynamic simulation of stick–slip motion of a flexible solar array

2008 ◽  
Vol 16 (6) ◽  
pp. 724-735 ◽  
Author(s):  
Yasushi Kojima ◽  
Shigemune Taniwaki ◽  
Yoshiaki Okami
Keyword(s):  
Dynamic Simulation ◽  
Solar Array ◽  
Stick Slip ◽  
Stick Slip Motion ◽  
Slip Motion
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