scholarly journals Passive Shock Isolation Utilising Dry Friction

2017 ◽  
Vol 2017 ◽  
pp. 1-21 ◽  
Author(s):  
Mohd Ikmal Ismail ◽  
Neil Stuart Ferguson
Keyword(s):  
Degree Of Freedom ◽  
Experimental Results ◽  
Maximum Displacement ◽  
Natural Period ◽  
Single Degree Of Freedom ◽  
Excited System ◽  
Theoretical Predictions ◽  
Shock Isolation ◽  
Two Degree Of Freedom ◽  
Experimental Rig

A novel shock isolation strategy for base excited system is presented by introducing a two-degree-of-freedom model with passive friction, where the friction is applied to an attached mass instead of directly to the primary isolated mass. The model is evaluated against the benchmark case of single-degree-of-freedom system with friction applied directly to the primary isolated mass. The performances of the models are compared in terms of the maximum displacement response and the acceleration during the application of the shock input for the case when the shock input duration is approximately equal to the natural period of the system (amplification region). From the results, the two-degree-of-freedom model can produce both maximum displacement reduction and smoother acceleration at the point of motion transition. An experimental rig was built to validate the theoretical results against the experimental results; it is found that the experimental results closely match the theoretical predictions.

On the Natural Modes and Their Stability in Nonlinear Two-Degree-of-Freedom Systems

1959 ◽  
Vol 26 (3) ◽  
pp. 377-385
Author(s):  
R. M. Rosenberg ◽  
C. P. Atkinson
Keyword(s):  
Free Vibrations ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Natural Modes ◽  
Theoretical Predictions ◽  
Stability Chart ◽  
The Stability ◽  
Two Parameters ◽  
Two Degree Of Freedom

Abstract The natural modes of free vibrations of a symmetrical two-degree-of-freedom system are analyzed theoretically and experimentally. This system has two natural modes, one in-phase and the other out-of-phase. In contradistinction to the comparable single-degree-of-freedom system where the free vibrations are always orbitally stable, the natural modes of the symmetrical two-degree-of-freedom system are frequently unstable. The stability properties depend on two parameters and are easily deduced from a stability chart. For sufficiently small amplitudes both modes are, in general, stable. When the coupling spring is linear, both modes are always stable at all amplitudes. For other conditions, either mode may become unstable at certain amplitudes. In particular, if there is a single value of frequency and amplitude at which the system can vibrate in either mode, the out-of-phase mode experiences a change of stability. The experimental investigation has generally confirmed the theoretical predictions.

The Dynamics of a Nonharmonically Excited System Having Rigid Amplitude Constraints

1992 ◽  
Vol 59 (3) ◽  
pp. 693-695 ◽  
Author(s):  
Pi-Cheng Tung
Keyword(s):  
Dynamic Response ◽  
Bifurcation Analysis ◽  
Piecewise Linear ◽  
Coefficient Of Restitution ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Chaotic Motions ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Excited System

We consider the dynamic response of a single-degree-of-freedom system having two-sided amplitude constraints. The model consists of a piecewise-linear oscillator subjected to nonharmonic excitation. A simple impact rule employing a coefficient of restitution is used to characterize the almost instantaneous behavior of impact at the constraints. In this paper periodic and chaotic motions are found. The amplitude and stability of the periodic responses are determined and bifurcation analysis for these motions is carried out. Chaotic motions are found to exist over ranges of forcing periods.

scholarly journals Experimental investigation of a single-degree-of-freedom system with Coulomb friction

2020 ◽  
Vol 99 (3) ◽  
pp. 1781-1799
Author(s):  
Luca Marino ◽  
Alice Cicirello
Keyword(s):  
Experimental Investigation ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Systematic Observation ◽  
Stick Slip ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Set Up

AbstractThis paper presents an experimental investigation of the dynamic behaviour of a single-degree-of-freedom (SDoF) system with a metal-to-metal contact under harmonic base or joined base-wall excitation. The experimental results are compared with those yielded by mathematical models based on a SDoF system with Coulomb damping. While previous experiments on friction-damped systems focused on the characterisation of the friction force, the proposed approach investigates the steady response of a SDoF system when different exciting frequencies and friction forces are applied. The experimental set-up consists of a single-storey building, where harmonic excitation is imposed on a base plate and a friction contact is achieved between a steel top plate and a brass disc. The experimental results are expressed in terms of displacement transmissibility, phase angle and top plate motion in the time and frequency domains. Both continuous and stick-slip motions are investigated. The main results achieved in this paper are: (1) the development of an experimental set-up capable of reproducing friction damping effects on a harmonically excited SDoF system; (2) the validation of the analytical model introduced by Marino et al. (Nonlinear Dyn, 2019. https://doi.org/10.1007/s11071-019-04983-x) and, particularly, the inversion of the transmissibility curves in the joined base-wall motion case; (3) the systematic observation of stick-slip phenomena and their validation with numerical results.

The Active Control of Forced Vibration Produced by Arbitrary Disturbances

1985 ◽  
Vol 107 (1) ◽  
pp. 33-37 ◽  
Author(s):  
J. S. Burdess ◽  
A. V. Metcalfe
Keyword(s):  
Vibration Control ◽  
Active Control ◽  
Forced Vibration ◽  
Disturbance Observer ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impact Forces ◽  
Mass Spring

This paper considers the vibration control of a single degree of freedom mass-spring-damper system when subjected to an arbitrary, unmeasurable disturbance. The idea of a disturbance observer is introduced and it is shown how an estimate of the excitation can be derived and used to generate a control, which reduces the vibration. This control is shown to be robust with respect to the parameters describing the behavior of the system. Experimental results are presented which show the efficacy of the method when the system is excited by periodic, random, and impact forces. Comments are made on the application of the method.

Development of a Single-Degree-of-Freedom Mechanical Model for Predicting Strain-Based Brain Injury Responses

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Lee F. Gabler ◽  
Hamed Joodaki ◽  
Jeff R. Crandall ◽  
Matthew B. Panzer
Keyword(s):  
Brain Injury ◽  
Degree Of Freedom ◽  
Deformation Model ◽  
Maximum Magnitude ◽  
Natural Period ◽  
Single Degree Of Freedom ◽  
Head Kinematics ◽  
Single Degree ◽  
Brain Deformation ◽  
Deformation Mechanics

Linking head kinematics to injury risk has been the focus of numerous brain injury criteria. Although many early forms were developed using mechanics principles, recent criteria have been developed using empirical methods based on subsets of head impact data. In this study, a single-degree-of-freedom (sDOF) mechanical analog was developed to parametrically investigate the link between rotational head kinematics and brain deformation. Model efficacy was assessed by comparing the maximum magnitude of displacement to strain-based brain injury predictors from finite element (FE) human head models. A series of idealized rotational pulses covering a broad range of acceleration and velocity magnitudes (0.1–15 krad/s2 and 1–100 rad/s) with durations between 1 and 3000 ms were applied to the mechanical models about each axis of the head. Results show that brain deformation magnitude is governed by three categories of rotational head motion each distinguished by the duration of the pulse relative to the brain's natural period: for short-duration pulses, maximum brain deformation depended primarily on angular velocity magnitude; for long-duration pulses, brain deformation depended primarily on angular acceleration magnitude; and for pulses relatively close to the natural period, brain deformation depended on both velocity and acceleration magnitudes. These results suggest that brain deformation mechanics can be adequately explained by simple mechanical systems, since FE model responses and experimental brain injury tolerances exhibited similar patterns to the sDOF model. Finally, the sDOF model was the best correlate to strain-based responses and highlighted fundamental limitations with existing rotational-based brain injury metrics.

Instabilities Arising From the Frictional Interaction of a Pin-Disk System Resulting in Noise Generation

1976 ◽  
Vol 98 (1) ◽  
pp. 81-86 ◽  
Author(s):  
S. W. E. Earles ◽  
C. K. Lee
Keyword(s):  
Angular Speed ◽  
Degree Of Freedom ◽  
Noise Generation ◽  
Disk System ◽  
Single Degree Of Freedom ◽  
Disk Brake ◽  
Thin Steel ◽  
Three Degree Of Freedom ◽  
Squeal Noise ◽  
Experimental Rig

A steel pin, supported on a flexible cantilever, is pressed against a thin steel disk which rotates at a uniform angular speed. The orientation of the pin’s central axis to the plane of the disk, the bending and torsional stiffnesses of the pin support, the stiffness of the disk, and the line of action of the resultant interactive force are all shown to affect the self-induced coupled frequencies and modes generated. The analysis of the experimental arrangement in terms of a three-degree-of-freedom pin subsystem and a single-degree-of-freedom disk element suggests that the system is unstable for certain combinations of the variables. The instabilities are shown to belong to a class of “geometrically induced” or “kinematic constraint” instability. The region of squeal-noise generation within the experimental rig is shown to correspond to the oscillatory unstable region predicted theoretically. The noise generated is similar to disk-brake squeal, and so the work furthers the understanding of this practical problem.

Decentralized Control of Active Vehicle Suspensions With Preview

1995 ◽  
Vol 117 (4) ◽  
pp. 478-483 ◽  
Author(s):  
Aleksander Hac´
Keyword(s):  
Decentralized Control ◽  
The Body ◽  
Degree Of Freedom ◽  
Vehicle Model ◽  
Fast Subsystem ◽  
Interconnected System ◽  
Single Degree Of Freedom ◽  
Vehicle Suspensions ◽  
Slow Subsystem ◽  
Two Degree Of Freedom

In this paper, decentralized control of active vehicle suspensions with preview of road irregularities is considered using a two-degree-of-freedom vehicle model. It is shown that by taking advantage of the separation between the eigenvalues of the slow subsystem representing the body mode, and the fast subsystem corresponding to the wheel mode, the design of the preview controller can be decoupled. Since decentralized preview controllers are synthesized independently for two single-degree-of-freedom systems, analytical solutions are obtained. The results of the analysis and simulations demonstrate that the performance of the system with the proposed controller is comparable to that of the optimal preview controller based on a fully interconnected system.

Forced Nonlinear Oscillations of an Autoparametric System—Part 2: Chaotic Responses

1983 ◽  
Vol 50 (3) ◽  
pp. 663-668 ◽  
Author(s):  
H. Hatwal ◽  
A. K. Mallik ◽  
A. Ghosh
Keyword(s):  
Statistical Analysis ◽  
Nonlinear Oscillations ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Forced Oscillations ◽  
Mean Square ◽  
Chaotic Oscillations ◽  
System Part ◽  
The Mean ◽  
Two Degree Of Freedom

Chaotic oscillations arising in forced oscillations of a two degree-of-freedom autoparametric system are studied. Statistical analysis of the numerically integrated nonperiodic responses is shown to be a meaningful description of the mean square values and the frequency contents of the responses. Some qualitative experimental results are presented to substantiate the necessity of performing the statistical analysis of the responses even though the system and the input are deterministic.

Chaotic Responses of a Two-Degree-of-Freedom Elastic-Plastic Beam Model to Short Pulse Loading

1992 ◽  
Vol 59 (4) ◽  
pp. 711-721 ◽  
Author(s):  
J.-Y. Lee ◽  
P. S. Symonds ◽  
G. Borino
Keyword(s):  
Short Pulse ◽  
Direct Method ◽  
Degree Of Freedom ◽  
Beam Model ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Arch Action ◽  
Time Histories ◽  
Energy Plane ◽  
Two Degree Of Freedom

The paper discusses chaotic response behavior of a beam model whose ends are fixed, so that shallow arch action prevails after moderate plastic straining has occurred due to a short pulse of transverse loading. Examples of anomalous displacement-time histories of a uniform beam are first shown. These motivated the present study of a two-degree-of-freedom model of Shanley type. Calculations confirm these behaviors as symptoms of chaotic unpredictability. Evidence of chaos is seen in displacement-time histories, in phase plane and power spectral diagrams, and especially in extreme sensitivity to parameters. The exponential nature of the latter is confirmed by calculations of conventional Lyapunov exponents and also by a direct method. The two-degree-of-freedom model allows use of the energy approach found helpful for the single-degree-of-freedom model (Borino et al., 1989). The strain energy is plotted as a surface over the displacement coordinate plane, which depends on the plastic strains. Contrasting with the single-degree-of-freedom case, the energy diagram illuminates the possibility of chaotic vibrations in an initial phase, and the eventual transition to a smaller amplitude nonchaotic vibration which is finally damped out. Properties of the response are further illustrated by samples of solution trajectories in a fixed total energy plane and by related Poincare section plots.

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