Vibration analysis of an oscillator with non-smooth dry friction constraint

2015 ◽  
Vol 23 (14) ◽  
pp. 2328-2344 ◽  
Author(s):  
Yali Ma ◽  
Shudong Yu ◽  
Delun Wang
Keyword(s):  
Dry Friction ◽  
Harmonic Excitation ◽  
Dynamical Problem ◽  
Single Degree Of Freedom ◽  
Current State ◽  
Newmark Scheme ◽  
Friction Oscillator ◽  
Coulomb Type ◽  
The Time Domain ◽  
Event Based

Global vibrational behaviour of a single degree-of-freedom (SDOF) oscillator subjected to Coulomb type of dry frictional constraint and harmonic excitation is investigated in this paper. To obtain a numerical solution to the non-smooth dynamical problem, the equation of motion is discretized in the time domain by means of the implicit Bozzak-Newmark scheme. An algebraic equation governing the current state of the system is obtained in terms of its velocity. Utilizing the fact that the frictional constraint can be completely characterized by two scenarios - (i) forward sliding or stiction with a tendency to move forward, and (ii) backward sliding or stiction with a tendency to move backward, two coupled linear complementary equations are deduced. With the reduction of the non-smooth dynamical problem to a linear complementarity problem (LCP) in terms of supremum velocities and slack forces, the rapid and endless switches from sliding to stiction, and vice versa, in a vibration problem, are automatically detected and handled effectively. This is superior to the event-based methods and analytical methods available in the literature. Numerical results obtained using the proposed method are compared with the analytical solutions for harmonically excited dry-friction oscillator with ordinary behaviour; excellent agreement is observed. The proposed method is then employed for determining the global chaotic and deterministic behaviour of a harmonically excited dry-friction oscillator with system and excitation parameters varying in wide ranges.

scholarly journals Asymmetric and chaotic responses of dry friction oscillators with different static and kinetic coefficients of friction

Meccanica ◽  
2021 ◽  
Author(s):  
Gábor Csernák ◽  
Gábor Licskó
Keyword(s):  
Dry Friction ◽  
Continuation Method ◽  
Friction Model ◽  
Lugre Friction Model ◽  
Kinetic Coefficients ◽  
Friction Oscillator ◽  
Lugre Friction ◽  
Friction Parameters ◽  
Two Parameter ◽  
Parameter Bifurcation

AbstractThe responses of a simple harmonically excited dry friction oscillator are analysed in the case when the coefficients of static and kinetic coefficients of friction are different. One- and two-parameter bifurcation curves are determined at suitable parameters by continuation method and the largest Lyapunov exponents of the obtained solutions are estimated. It is shown that chaotic solutions can occur in broad parameter domains—even at realistic friction parameters—that are tightly enclosed by well-defined two-parameter bifurcation curves. The performed analysis also reveals that chaotic trajectories are bifurcating from special asymmetric solutions. To check the robustness of the qualitative results, characteristic bifurcation branches of two slightly modified oscillators are also determined: one with a higher harmonic in the excitation, and another one where Coulomb friction is exchanged by a corresponding LuGre friction model. The qualitative agreement of the diagrams supports the validity of the results.

scholarly journals A Review of Algorithms and Hardware Implementations for Spiking Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 23
Author(s):  
Duy-Anh Nguyen ◽  
Xuan-Tu Tran ◽  
Francesca Iacopi
Keyword(s):  
Neural Networks ◽  
Computational Cost ◽  
Superior Performance ◽  
Training Algorithms ◽  
Current State ◽  
Hardware Implementations ◽  
Neuromorphic Hardware ◽  
High Level ◽  
Event Based ◽  
Hardware Platforms

Deep Learning (DL) has contributed to the success of many applications in recent years. The applications range from simple ones such as recognizing tiny images or simple speech patterns to ones with a high level of complexity such as playing the game of Go. However, this superior performance comes at a high computational cost, which made porting DL applications to conventional hardware platforms a challenging task. Many approaches have been investigated, and Spiking Neural Network (SNN) is one of the promising candidates. SNN is the third generation of Artificial Neural Networks (ANNs), where each neuron in the network uses discrete spikes to communicate in an event-based manner. SNNs have the potential advantage of achieving better energy efficiency than their ANN counterparts. While generally there will be a loss of accuracy on SNN models, new algorithms have helped to close the accuracy gap. For hardware implementations, SNNs have attracted much attention in the neuromorphic hardware research community. In this work, we review the basic background of SNNs, the current state and challenges of the training algorithms for SNNs and the current implementations of SNNs on various hardware platforms.

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.

Two-Frequency Oscillation With Combined Coulomb and Viscous Frictions

2002 ◽  
Vol 124 (4) ◽  
pp. 537-544 ◽  
Author(s):  
Gong Cheng ◽  
Jean W. Zu
Keyword(s):  
Steady State ◽  
Dry Friction ◽  
Single Frequency ◽  
Friction Oscillator ◽  
One Stop ◽  
Frequency Excitation ◽  
Stop Motion ◽  
The One ◽  
Coulomb Dry Friction ◽  
Mass Spring

In this paper, a mass-spring-friction oscillator subjected to two harmonic disturbing forces with different frequencies is studied for the first time. The friction in the system has combined Coulomb dry friction and viscous damping. Two kinds of steady-state vibrations of the system—non-stop and one-stop motions—are considered. The existence conditions for each steady-state motion are provided. Using analytical analysis, the steady-state responses are derived for the two-frequency oscillating system undergoing both the non-stop and one-stop motions. The focus of the paper is to study the influence of the Coulomb dry friction in combination with the two frequency excitations on the dynamic behavior of the system. From the numerical simulations, it is found that near the resonance, the dynamic response due to the two-frequency excitation demonstrates characteristics significantly different from those due to a single frequency excitation. Furthermore, the one-stop motion demonstrates peculiar characteristics, different from those in the non-stop motion.

Vibration Isolation From Harmonic Disturbances Through Use of Internally Rotating Masses

2015 ◽  
Author(s):  
Eric Smith ◽  
Al Ferri
Keyword(s):  
Kinetic Energy ◽  
Vibration Isolation ◽  
Harmonic Excitation ◽  
Impulsive Loading ◽  
Qualitative Behavior ◽  
Single Degree Of Freedom ◽  
Transmitted Force ◽  
A Chain ◽  
Isolation Systems ◽  
Parameter Values

This paper considers the use of a chain of translating carts or housings having internally rotating eccentric masses in order to accomplish vibration isolation. First a single degree-of-freedom system is harmonically excited to uncover the qualitative behavior of each rotating mass. The simple model is then expanded into a chain of housings, containing rotating eccentric masses, which are interconnected with springs. The internal rotating eccentric masses are damped along their circular pathway by means of linear viscous damping. Due to the lack of elastic or gravitational constraint on the rotating eccentric masses, they provide a nonlinear inertial coupling to their housings. Previous research has shown that such systems are capable of reducing shock or impulsive loading by converting some of the translational kinetic energy into rotational kinetic energy of the internal masses. This paper examines the potential for vibration isolation of a chain of such systems subjected to persistent, harmonic excitation. It is seen that the dynamics of these systems is very complicated, but that trends are observed which have implications for practical isolation systems. Using simulation studies, tradeoffs are examined between displacement and transmitted force for a range of physical parameter values.

Vibration Damping by Friction Forces: Theory and Applications

2003 ◽  
Vol 9 (3-4) ◽  
pp. 419-448 ◽  
Author(s):  
Karl Popp ◽  
Lars Panning ◽  
Walter Sextro
Keyword(s):  
Three Dimensional ◽  
Friction Damping ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Practical Applications ◽  
Linear Friction ◽  
Solution Methods ◽  
Friction Oscillator ◽  
Contact Models

In this paper, we deal with the vibrational behavior of mechanical structures interconnected by contacts with friction. The focus is set on the utilization of friction forces that are generated in the contact interfaces with the objective to increase damping and to reduce vibration amplitudes in order to prevent structures from failures owing to high resonance stresses. We present a comparison and classification of different contact models that are most commonly used, including the derivation of a three-dimensional contact model under consideration of rough surfaces. We give different solution methods for problems with non-linear friction elements. The effectiveness of friction damping devices is pointed out by a single-degree-of-freedom friction oscillator, beam-like structures with frictional interfaces and different underplatform dampers in turbo-machinery applications. It can be shown that in many practical applications friction damping devices provide a remarkable decrease of vibration amplitudes.

Forced Response of a SDOF Friction Oscillator Colliding With a Hysteretic Obstacle

2001 ◽  
Author(s):  
Ugo Andreaus ◽  
Paolo Casini
Keyword(s):  
Constant Velocity ◽  
Driving Force ◽  
Practical Interest ◽  
Forced Response ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Moving Base ◽  
Friction Oscillator ◽  
Sample Application ◽  
Made In

Abstract The forced dynamics of non-smooth oscillators have not yet been sufficiently investigated, when damping is simultaneously due to friction and impact. Because of the theoretical and practical interest of this type of systems, an effort is made in this paper to lighten the behaviour of a single-degree-of-freedom oscillator colliding with a hysteretic obstacle and excited by an harmonic driving force and by a moving base with constant velocity. A friction-contact model has been proposed which allows simulating an exponential velocity-dependent friction law, and a deformable (hysteretic) obstacle. This model has been numerically tested via a sample application.

Distribution of Maxima of Non-Linear Rolling in Case of Coupled Sway and Roll Motions of a Floating Body in Irregular Waves

2008 ◽  
Author(s):  
Ignace D. Mendoume Minko ◽  
Marc Prevosto ◽  
Marc Le Boulluec
Keyword(s):  
Irregular Waves ◽  
Floating Body ◽  
Time Domain Simulation ◽  
Single Degree Of Freedom ◽  
Simulation Based ◽  
Non Linear ◽  
Circular Frequency ◽  
The Time Domain ◽  
Gaussian Closure ◽  
Made In

The so-called Linearize & Match (L&M), which gives a good approximation of the exact distribution of maxima roll angle of non-linear systems, was studied some years ago by Armand and Duthoit (1990) and by Prevosto (2001). The developments within this method were made in the case of single degree of freedom dynamic systems. Moreover, the terms (mass, damping, stiffness) of the non-linear transfer function did not depend on the circular frequency. In this paper, first, the L&M method is improved by adding a last step in the procedure which correct the Gaussian closure technique of the method, secondly is generalized to a coupled sway and roll dynamic system in which the hydrodynamic coefficients are frequency-dependent. The system is modelled by a set of ordinary differential equations in which the non linearity is only in the roll motion. In order to validate the results obtained in this case by the L&M method, a Monte Carlo method with long simulations of the response of the system was carried out. Hence, some aspects of the time domain simulation, based on Cummins equations, are also discussed.

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