A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Bin Tang ◽  
M. J. Brennan
Keyword(s):  
Free Vibration ◽  
Equations Of Motion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree ◽  
Dependent Term ◽  
Quadratic Damping

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration.

The Measurement of Nonlinear Damping in Single-Degree-of-Freedom Systems

1991 ◽  
Vol 113 (1) ◽  
pp. 132-140 ◽  
Author(s):  
H. J. Rice ◽  
J. A. Fitzpatrick
Keyword(s):  
Nonlinear Distortion ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Crucial Importance ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Wide Range ◽  
Impulse Excitation ◽  
Excitation Techniques ◽  
Quadratic Damping

The measurement and correct modelling of damping is of crucial importance in the prediction of the dynamical performance of systems for a wide range of engineering applications. In most cases, however, the experimental methods used to measure damping coefficients are extremely basic and, in general, poorly reported. This paper shows that damping is a deceptive parameter which is prone to subtle nonlinear distortion which often appears to satisfy general linear criteria. An efficient experimental method which provides for the measurement of both the linear and nonlinear damping for a single-degree-of-freedom system is proposed. The results from a numerical simulation study of a model with “drag” type quadratic damping are shown to give reliable estimates of parameters of the system when both random and impulse excitation techniques are used.

An Approximate Method for the Dynamic Analysis of Elastic Linkages

1977 ◽  
Vol 99 (2) ◽  
pp. 449-455 ◽  
Author(s):  
A. Midha ◽  
A. G. Erdman ◽  
D. A. Frohrib
Keyword(s):  
Exact Analytical Solution ◽  
Equations Of Motion ◽  
Numerical Procedure ◽  
Degree Of Freedom ◽  
Suggested Approach ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
System A ◽  
Suggested Technique ◽  
Particular Solution

A new numerical procedure based on an iterative technique is progressively developed in this paper for obtaining an approximate particular solution from the equations of motion of an elastic linkage with small damping and at subresonant speeds. The method is introduced by employing a simple vibrating system, a single degree-of-freedom mass-dashpot-spring model under both harmonic forcing and periodic forcing. A harmonically excited two degree-of-freedom model is also solved by the suggested approach. Error functions are developed for each case to give an estimation of the order of error between the exact analytical solution and the approximate technique. The suggested technique is then extended to solve an elastic linkage problem where the uncoupled equations of motion are treated as a series of single degree-of-freedom problems and solved. These are retransformed into the physical coordinate system to obtain the particular solution. The first and second derivatives of the forcing functions (involving rigid-body inertia) are approximated utilizing the finite difference method.

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.

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