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.

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.

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.

Influence of Friction Dampers on Torsional Blade Flutter

1986 ◽  
Vol 108 (2) ◽  
pp. 313-318 ◽  
Author(s):  
A. Sinha ◽  
J. H. Griffin ◽  
R. E. Kielb
Keyword(s):  
Dry Friction ◽  
Fluid Velocity ◽  
Supersonic Flows ◽  
Degree Of Freedom ◽  
Lumped Parameter Model ◽  
Single Degree Of Freedom ◽  
Friction Dampers ◽  
Single Degree ◽  
Lumped Parameter ◽  
Blade Flutter

This paper deals with the stabilizing effects of dry friction on torsional blade flutter. A lumped parameter model with single degree of freedom per blade has been used to represent the rotor stage. The well-known cascade theories for incompressible and supersonic flows have been used to determine the allowable increase in fluid velocity relative to the blade. It has been found that the effectiveness of friction dampers in controlling flutter can be substantial.

The Estimation of Viscous and Coulomb Damping in Harmonically Excited Oscillators

1999 ◽  
Author(s):  
J.-W. Liang ◽  
B. F. Feeny
Keyword(s):  
Free Vibration ◽  
Numerical Simulations ◽  
Dry Friction ◽  
Mechanical Vibration ◽  
Degree Of Freedom ◽  
Identification Algorithm ◽  
Single Degree Of Freedom ◽  
Coulomb Damping ◽  
Single Degree

Abstract This paper proposes a simple identification algorithm for estimating both viscous and dry friction in harmonically forced single-degree-of-freedom mechanical vibration systems. The method is especially suitable for the identification of systems for which the traditional free-vibration scheme is difficult to implement. Numerical simulations are included to show the effectiveness of the proposed algorithm. A numerical perturbation study is also included for insight on the robustness of the algorithm.

Simplified seismic code design procedure for friction-damped steel frames

1999 ◽  
Vol 26 (1) ◽  
pp. 55-71 ◽  
Author(s):  
Yaomin Fu ◽  
Sheldon Cherry
Keyword(s):  
Design Procedure ◽  
Steel Structures ◽  
Lateral Force ◽  
Building Codes ◽  
Degree Of Freedom ◽  
Friction Damper ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Damped System ◽  
Seismic Force

This paper describes the development of a proposed seismic design procedure for friction-damped steel structures, which employs the lateral force provisions used in many modern building codes. Closed-form expressions are first derived that relate the normalized response of a single degree of freedom friction-damped system with the system parameters, such as bracing stiffness ratio, damper slip ratio, and frame member ductility. A parametric analysis is then used to reveal that the seismic displacement of a friction-damped frame can be controlled by combining the frame stiffness with the bracing stiffness of the friction damper component, while the seismic force can be controlled by the damper slip force. A force modification factor (equivalent to the code R-factor) and displacement estimate for a friction-damped system are next determined. The single degree of freedom results are subsequently used to develop expressions for dealing with the multi degree of freedom situation, which permits the seismic lateral force design procedure adopted by many current building codes to be applied to friction-damped systems. The proposed procedure allows the frame response to be controlled so that the displacement can be limited to small magnitudes and the overall structural shape to an essentially straight-line deformation. Design examples illustrate that friction-damped frame systems are economical and offer a better overall response performance than that provided by conventional systems under the design earthquake.Key words: passive energy dissipation system, friction damper, steel frame, design procedure, static analysis.

The Effect of Circumferential Aerodynamic Detuning on Coupled Bending-Torsion Unstalled Supersonic Flutter

1986 ◽  
Vol 108 (2) ◽  
pp. 253-260 ◽  
Author(s):  
D. Hoyniak ◽  
S. Fleeter
Keyword(s):  
Stability Analysis ◽  
Natural Frequency ◽  
Frequency Ratio ◽  
Center Of Gravity ◽  
Degree Of Freedom ◽  
Mode Analysis ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Unsteady Aerodynamic ◽  
Supersonic Flutter

A mathematical model is developed to predict the enhanced coupled bending-torsion unstalled supersonic flutter stability due to alternate circumferential spacing aerodynamic detuning of a turbomachine rotor. The translational and torsional unsteady aerodynamic coefficients are developed in terms of influence coefficients, with the coupled bending-torsion stability analysis developed by considering the coupled equations of motion together with the unsteady aerodynamic loading. The effect of this aerodynamic detuning on coupled bending-torsion unstalled supersonic flutter as well as the verification of the modeling are then demonstrated by considering an unstable twelve-bladed rotor, with Verdon’s uniformly spaced Cascade B flow geometry as a baseline. It was found that with the elastic axis and center of gravity at or forward of the airfoil midchord, 10 percent aerodynamic detuning results in a lower critical reduced frequency value as compared to the baseline rotor, thereby demonstrating the aerodynamic detuning stability enhancement. However, with the elastic axis and center of gravity at 60 percent of the chord, this type of aerodynamic detuning has a minimal effect on stability. For both uniform and nonuniform circumferentially spaced rotors, a single degree of freedom torsion mode analysis was shown to be appropriate for values of the bending-torsion natural frequency ratio lower than 0.6 and higher than 1.2. However, for values of this natural frequency ratio between 0.6 and 1.2, a coupled flutter stability analysis is required. When the elastic axis and center of gravity are not coincident, the effect of detuning on cascade stability was found to be very sensitive to the location of the center of gravity with respect to the elastic axis. In addition, it was determined that when the center of gravity was forward of an elastic axis located at midchord, a single degree of freedom torsion model did not accurately predict cascade stability.

scholarly journals Analysis of Single-degree-of-freedom Systems Containing Multi-functional Friction Damper

2014 ◽  
Vol 79 ◽  
pp. 500-505
Author(s):  
Chia-Shang Chang Chien ◽  
Lyan-Ywan Lu ◽  
Yu-Lin Tsai
Keyword(s):  
Degree Of Freedom ◽  
Friction Damper ◽  
Single Degree Of Freedom ◽  
Single Degree

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.

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