Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part I — Single-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Damping Ratio ◽  
Strong Dependence ◽  
Time Integration ◽  
Single Mode ◽  
Stick Slip ◽  
Friction Forces ◽  
Equivalent Damping ◽  
Damping Characteristics ◽  
Parameter Values

Abstract The dynamic behavior of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent dry friction force is examined. In Part I, the beam is modeled by a single mode while Part II considers multi-mode representations. The displacement dependence in each case is caused by a ramp configuration that allows the normal force across the sliding interface to increase linearly with slip displacement. The system is studied first by using first-order harmonic balance and then by using a time integration method. The stick-slip behavior of the system is also studied. Even though the only source of damping is dry friction, the system is seen to exhibit “viscous-like” damping characteristics. A strong dependence of the equivalent natural frequency and damping ratio on the displacement amplitude is an interesting result. It is shown that for a given set of parameter values, an optimal ramp angle exists that maximizes the equivalent damping ratio. The appearance of two dynamic response solutions at certain system and forcing parameter values is also seen. Results suggest that the overall characteristics of mechanical systems may be improved by properly configuring frictional interfaces to allow normal forces to vary with displacement.

Analysis of Beam-Like Structures With Displacement-Dependent Friction Forces: Part II — Multi-Degree-of-Freedom Model

1995 ◽  
Author(s):  
Wayne E. Whiteman ◽  
Aldo A. Ferri
Keyword(s):  
Dry Friction ◽  
Time Integration ◽  
Degree Of Freedom ◽  
Mode Analysis ◽  
Friction Damper ◽  
Compressor Blades ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Damping Characteristics

Abstract A multi-mode analysis of a beam-like structure undergoing transverse vibration and subjected to a displacement-dependent friction force is conducted. The level of displacement-dependence is governed by a ramp angle and spring arrangement as discussed in Part I. The system is studied by using harmonic balance as an approximate analytical solution and then by using a time integration method. The damping characteristics of the system are studied in detail. The results qualitatively agree with those obtained using a single-degree-of-freedom analysis of this system reported in Part I. Interesting findings include the appearance of internal resonance peaks when multiple modes are considered. Also, as with the earlier single-degree-of-freedom study, two dynamic response solutions exist at certain parameter values. It is found that the ability to control the amplitude of the response is a function of the frequency range considered. In general, near modal resonance peaks, the amplitude of the response decreases with increasing ramp angle. However, in an “overlapping” region between resonance peaks, the amplitude of the response actually increases with increasing ramp angle. Detailed analysis of the damping characteristics indicate that the dry friction damper is most effective in damping the fundamental mode. The other critical observation is that the damping contribution from the displacement-dependent dry friction damper is “viscous-like” in nature and relatively insensitive to the amplitude of the response. This result suggests that in the case of turbine or compressor blades, this type of damping arrangement may be effective in the suppression of flutter.

Stick-Slip Vibrations of Layered Structures Undergoing Large Deflection and Dry Friction at the Interface

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Hamid M. Sedighi ◽  
Kourosh H. Shirazi ◽  
Khosro Naderan-Tahan
Keyword(s):  
Dry Friction ◽  
Large Deflection ◽  
Dynamical Behavior ◽  
Single Mode ◽  
Layered Structures ◽  
Order Mode ◽  
Chaotic Motions ◽  
Stick Slip ◽  
Coupled Equations ◽  
Mode Method

The present study focuses on the nonlinear analysis of the dynamical behavior of layered structures, including interfacial friction in the presence of the stick-slip phenomenon and large deformation. To achieve a proper outlook for the two-layer structure's behavior, it is essential to precisely realize the mechanisms of motion. Taking the dry friction into account, coupled equations of the transversal and longitudinal large vibration of two-layers are derived and nondimensionalized. Furthermore, the free and forced vibration of the aforementioned system is investigated. From the results of the numerical simulation, it is observed that there exist quasi-periodic and stick–slip chaotic motions in the system. The results demonstrate that the single mode method usually utilized may lead to incorrect conclusions and, instead, the higher order mode method should be employed. A comparative study with ANSYS is developed to verify the accuracy of the proposed approach.

scholarly journals Micro-Slip as a Loss of Determinacy in Dry-Friction Oscillators

2019 ◽  
Vol 29 (06) ◽  
pp. 1930015 ◽  
Author(s):  
S. Webber ◽  
M. R. Jeffrey
Keyword(s):  
Differential Equations ◽  
Dry Friction ◽  
Dynamical Theory ◽  
Stick Slip ◽  
Friction Forces ◽  
Mechanical Oscillators ◽  
The Stability ◽  
Stick Slip Motion ◽  
Friction Oscillators ◽  
Slip Motion

Dry-friction contacts in mechanical oscillators can be modeled using nonsmooth differential equations, and recent advances in dynamical theory are providing new insights into the stability and uniqueness of such oscillators. A classic model is that of spring-coupled masses undergoing stick-slip motion on a rough surface. Here, we present a phenomenon in which multiple masses transition from stick to slip almost simultaneously, but suffer a brief loss of determinacy in the process. The system evolution becomes many-valued, but quickly collapses back down to an infinitesimal set of outcomes, a sort of “micro-indeterminacy”. Though fleeting, the loss of determinacy means masses may each undergo different microscopic sequences of slipping events, before all masses ultimately slip. The microscopic loss of determinacy is visible in local changes in friction forces, and in creating a bistability of global stick-slip oscillations. If friction forces are coupled between the oscillators then the effect is more severe, as solutions are compressed instead onto two (or more) macroscopically different outcomes.

Attenuation of Free Vibration Using Particle Impact Damper

2007 ◽  
Author(s):  
Hamid R. Hamidzadeh
Keyword(s):  
Free Vibration ◽  
Damping Ratio ◽  
Particle Impact ◽  
Constrained Layer Damping ◽  
Equivalent Viscous Damping ◽  
Impact Damper ◽  
Equivalent Damping ◽  
Vibrating System ◽  
Damping Characteristics ◽  
Moving Particle

The particle impact damper is an effective vibration damping treatment that can be used in the cases where visco-elastic constrained layer damping fails due to excessive surrounding temperature. In this type of passive damping, particles move in a container attached to the vibrating system resulting in plastic impact with the container. In the presented theoretical study, the damping characteristics of free oscillation for a vertical system with an initial displacement are considered and a governing equation for the system under free vibration with a particle damper is derived. To evaluate the damping characteristics for the free vibrating system, the equivalent damping ratio is determined by considering both kinematics and kinetics of the particle motion and its impacts with the container. The presented solution concludes that in general damping effectiveness can be enhanced by increasing the mass of the particle in comparison with total mass of the system. Mathematical optimum clearance for the moving particle and the equivalent viscous damping ratio are determined for the best performance of the particle impact damper.

A View to the Energy Dissipation Mechanism of a Gas Foil Bearing’s Structure due to Dry Friction

2012 ◽  
Author(s):  
José A. Matute ◽  
Rafael O. Ruiz ◽  
Sergio E. Diaz
Keyword(s):  
Energy Dissipation ◽  
Dry Friction ◽  
Nonlinear Behavior ◽  
Excitation Amplitude ◽  
Equivalent Model ◽  
Stick Slip ◽  
Friction Forces ◽  
Energy Dissipation Mechanism ◽  
Variable Function ◽  
Dissipation Mechanism

The purpose of the present work consists on improving the understanding of the energy dissipation mechanism in the structure of a gas foil bearing. The analysis is based on an analytical model capable of predicting bumps deformation due to a load on the top coupled with dry friction forces at the top and bump ends. Models of mass-individual bump and mass-bump foil subject to a harmonic force are predicted numerically. The nonlinear behavior due to dry friction results in the possibility of stick-slip conditions over the surfaces in contact. The Variation of parameters such as excitation amplitude, mass magnitude, coefficient of friction, and bump geometry were considered. Equivalent dynamic coefficients of stiffness and damping are estimated through a least squares curve fitting, which constitutes a linearization of the system with dry friction. A computer program was developed in order to consider the effect of stick-slip. As a final product of this research the nonlinear model of the structure support was used to obtain a linear and simplified equivalent model. In most studied cases it is possible to represent the system with a linearized model of constant stiffness and viscous damping which is a variable function of the studied parameters and the frequency.

scholarly journals A Prediction Method with Altering Equivalent Stiffness for Damping Evaluation of Shrouded Bladed Disk Dynamic Systems

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 413
Author(s):  
Shimin Gao ◽  
Yanrong Wang ◽  
Zhiwei Sun ◽  
Siyuan Chen
Keyword(s):  
Contact Surface ◽  
Contact Stiffness ◽  
Damping Ratio ◽  
Characteristic Curve ◽  
Prediction Method ◽  
Blade Vibration ◽  
Stick Slip ◽  
Bladed Disk ◽  
Damping Characteristics ◽  
Vibration Stress

In turbomachinery bladed disks are typical cyclic symmetric structures where high-cycle fatigue of the blades can easily occur. Increasing the shroud structure is an effective blade vibration reduction method using the dry friction of the shroud contact surface to dissipate vibration energy. During one vibration cycle of the blade, the contact surface of the shroud may have one or several states of stick, slip, and separation due to the different amplitude of blade, which affects not only the damping, but also the stiffness of the system. This paper proposes a method to analyze the damping characteristics of blades with shroud considering the change of equivalent contact stiffness of the shroud by using the finite element method. With a 2D contact model, this method calculates the equivalent damping and obtains the damping characteristic curve to evaluate the damping of shroud. During the design phase, the objective is that when resonance occurs, the shroud can provide the optimal damping ratio under the allowable vibration stress of the blade. The parameter sensitivity of the damping characteristic for one bladed disk with parallel shroud is investigated. It is shown that vibration phase angle, contact stiffness, contact force, friction coefficient significantly influence the damping characteristics.

Stick-Slip Effect in a Vibration-Driven System With Dry Friction: Sliding Bifurcations and Optimization

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
Hongbin Fang ◽  
Jian Xu
Keyword(s):  
Steady State ◽  
Bifurcation Diagram ◽  
Dry Friction ◽  
Classical Mechanics ◽  
System Optimization ◽  
Physical Parameters ◽  
Stick Slip ◽  
Friction Forces ◽  
Driven System ◽  
Different Types

Vibration-driven systems can move progressively in resistive media owing to periodic motions of internal masses. In consideration of the external dry friction forces, the system is piecewise smooth and has been shown to exhibit different types of stick-slip motions. In this paper, a vibration-driven system with Coulomb dry friction is investigated in terms of sliding bifurcation. A two-parameter bifurcation problem is theoretically analyzed and the corresponding bifurcation diagram is presented, where branches of the bifurcation are derived in view of classical mechanics. The results show that these sliding bifurcations organize different types of transitions between slip and sticking motions in this system. The bifurcation diagram and the predicted stick-slip transitions are verified through numerical simulations. Considering the effects of physical parameters on average steady-state velocity and utilizing the sticking feature of the system, optimization of the system is performed. Better performance of the system with no backward motion and higher average steady-state velocity can be achieved, based on the proposed optimization procedures.

A Historical Review on Dry Friction and Stick-Slip Phenomena

1998 ◽  
Vol 51 (5) ◽  
pp. 321-341 ◽  
Author(s):  
Brian Feeny ◽  
Arde´shir Guran ◽  
Nikolaus Hinrichs ◽  
Karl Popp
Keyword(s):  
Dry Friction ◽  
Historical Review ◽  
Review Article ◽  
Stick Slip ◽  
Daily Lives ◽  
Friction Forces ◽  
Sliding Surfaces ◽  
Highly Nonlinear ◽  
History Of ◽  
Friction Oscillators

This article gives a historical overview of structural and mechanical systems with friction. Friction forces between sliding surfaces arise due to complex mechanisms and lead to mathematical models which are highly nonlinear, discontinuous and nonsmooth. Humankind has a long history of magnificent usage of friction in machines, buildings and transportation. Regardless, our state of knowledge of the friction-influenced dynamics occurring in such systems as well as in our daily lives was, until recently, rather primitive. To represent our understanding of friction in nonlinear dynamics, we first trace examples from the earliest prehistoric technologies and the formulation of dissipation laws in mechanics. The work culminates with examples of friction oscillators and stick-slip. This review article contains 304 references.

scholarly journals Design of elastic and dissipation joints in bearing structures of electronic packages

2021 ◽  
Vol 351 ◽  
pp. 01012
Author(s):  
Igor Kovtun ◽  
Juliy Boiko ◽  
Svitlana Petrashchuk ◽  
Michał Liss
Keyword(s):  
Dry Friction ◽  
Dynamic Stress ◽  
Oscillation Amplitude ◽  
Viscous Friction ◽  
Dynamic Force ◽  
Electronic Packages ◽  
Friction Damper ◽  
Friction Forces ◽  
Damping Characteristics ◽  
Liquid Dampers

Mathematical modeling and experimental research represented in this paper is aimed at dynamic force analysis of circuit cards in order to eliminate or reduce dynamic stress and deflection to an acceptable level and to provide strength and reliability in design of circuit card assemblies subjected to vibration. In conditions when viscous friction forces are negligible and viscous friction dampers, such as liquid dampers, cannot be used reduction of oscillation amplitude in critical frequencies was proposed by creating dry friction damper. On the base of mathematical model, the method for reducing dynamic stress and deflection in critical section of circuit cards in resonance conditions has been developed by inserting additional elastic and dissipation joint introduced by dry friction damper. The dry friction damper device is introduced in three variants of design. The effectiveness of dry friction damper is characterized by its elastic and damping characteristics and especially by the stiffness.

Beneficial performance of a quasi-zero stiffness vibration isolator with generalized geometric nonlinear damping

2020 ◽  
pp. 095745652097238
Author(s):  
Chun Cheng ◽  
Ran Ma ◽  
Yan Hu
Keyword(s):  
Damping Ratio ◽  
Nonlinear Damping ◽  
Vibration Isolator ◽  
Equivalent Damping ◽  
Frequency Responses ◽  
Geometric Nonlinear ◽  
Resonant Region ◽  
Force Transmissibility ◽  
Isolation Performance ◽  
Force And Displacement Transmissibility

Generalized geometric nonlinear damping based on the viscous damper with a non-negative velocity exponent is proposed to improve the isolation performance of a quasi-zero stiffness (QZS) vibration isolator in this paper. Firstly, the generalized geometric nonlinear damping characteristic is derived. Then, the amplitude-frequency responses of the QZS vibration isolator under force and base excitations are obtained, respectively, using the averaging method. Parametric analysis of the force and displacement transmissibility is conducted subsequently. At last, two phenomena are explained from the viewpoint of the equivalent damping ratio. The results show that decreasing the velocity exponent of the horizontal damper is beneficial to reduce the force transmissibility in the resonant region. For the case of base excitation, it is beneficial to select a smaller velocity exponent only when the nonlinear damping ratio is relatively large.

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