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.

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.

Application of the Random Melnikov Method for Single-Degree-of-Freedom Vessel Rolls Motion

2010 ◽  
Author(s):  
Kaiye Hu ◽  
Yong Ding ◽  
Hongwei Wang ◽  
Jide Li
Keyword(s):  
Global Stability ◽  
Global Bifurcation ◽  
Melnikov Method ◽  
Threshold Value ◽  
Homoclinic Orbits ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Bounded Noise ◽  
Single Degree Of Freedom ◽  
Single Degree

Basing on the nonlinear dynamics theory, the global stability of ship in stochastic beam sea is researched by the global bifurcation method. In this paper, bounded noise is first briefly introduced. Bounded noise is a harmonic function with constant random frequency and phase. It has finite power and its spectral shape can be made to fit a target spectrum, such as Pierson-Moskowitz spectrum, by adjusting its parameters. This paper considered the stochastic excitation term as bounded noise and the influence of nonlinear damping and nonlinear righting moment, setup the random single degree of freedom nonlinear rolling equation. Then the random Melnikov process for the nonlinear system with homoclinic orbits under both dissipative and bounded noise perturbations is derived. The random Melnikov mean-square criterion is used to analysis the global stability of this system. The research indicates that the bounded noise can approximately simulate the wave excitation and if the noise exceeds the threshold value, the ship will undergo stochastic chaotic motion. That will lead ships to instability and even to capsizing.

scholarly journals Dynamical analysis of a single degree-of-freedom impact oscillator with impulse excitation

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401771661 ◽  
Author(s):  
Jun Wang ◽  
Yongjun Shen ◽  
Shaopu Yang
Keyword(s):  
Periodic Motion ◽  
Dynamical Behavior ◽  
Degree Of Freedom ◽  
Dynamical Response ◽  
Restitution Coefficient ◽  
Impact Oscillator ◽  
Vibration Period ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Impulse Excitation

In this article, the dynamical behavior of a single degree-of-freedom impact oscillator with impulse excitation is studied, where the mass impacts at one stop and is shocked with impulse excitation at the other stop. The existing and stability conditions for periodic motion of the oscillator are established. The effects of system parameters on dynamical response are discussed under different initial velocities. It is found that smaller shock gap than impact gap could make the periodic motion more stable. The decrease in natural frequency would consume less impact energy, make the vibration frequency smaller, and reduce the vibration efficiency. Finally, the dynamical properties are further analyzed under a special case, that is, the shock gap approaches zero. It could be seen that the larger shock coefficient and impact restitution coefficient would make vibration period smaller. Based on the stability condition, there are an upper limit for the product of shock coefficient and impact restitution coefficient, so that a lower limit of corresponding vibration period exists.

The Virtual Cam – Hexagon Method Authentication on Locating Key Instant Centers of All Planar Single Degree of Freedom Kinematically Indeterminate Linkages up to Ten-Bar

2018 ◽  
Author(s):  
Zhengqi Liu ◽  
Yin-ping Chang
Keyword(s):  
Degree Of Freedom ◽  
Universal Method ◽  
Single Degree Of Freedom ◽  
Graphical Approach ◽  
Single Degree ◽  
Wide Range ◽  
Different Types ◽  
Limited Application ◽  
Complete Sets ◽  
Improved Technique

At this moment all the methods which had been proposed have extremely limited application to only several specific constructions of kinematically indeterminate linkages, i.e. their complete sets of instant centers cannot be obtained simply from Kennedy Theorem due to lack of enough four-bar loop information in their constructions. Planar single degree of freedom linkages up to ten-bar include two different types of mechanisms, i.e. pure bar linkages, such as four-, six-, eight-, and ten-bar; and geared-bar linkages, i.e. geared-five, seven, and nine-bar. The huge varieties of different types and constructions can serve as great testbeds for these methods. This research systematically investigates and modifies the graphical approach, i.e. virtual cam method, whose employment will show it to be an almost-universal method which can be compliantly applied on very wide range of kinematically indeterminate linkages. The procedures and criteria of the methodology are proposed and examined thoroughly to help locate key instant centers of all planar single degree of freedom kinematically indeterminate linkages up to ten-bar so that their complete sets of instant centers can be located successfully. We call this modified and improved technique as Virtual Cam – Hexagon Method. The results are verified carefully against traditional Kennedy Theorem approach and CAD modeling.

Effectiveness of neoprene pad vibration isolators at high frequencies

2021 ◽  
Vol 263 (4) ◽  
pp. 2172-2183
Author(s):  
Jerry Lilly
Keyword(s):  
Natural Frequency ◽  
Insertion Loss ◽  
Dynamic Stiffness ◽  
Degree Of Freedom ◽  
Frequency Wave ◽  
Single Degree Of Freedom ◽  
High Frequencies ◽  
Vibration Isolators ◽  
Single Degree ◽  
Wide Range

The natural frequency, dynamic stiffness, and insertion loss of commercially available neoprene pad vibration isolators have been measured in a simple, single degree of freedom system over a wide range of pad loadings out to a maximum frequency of 10 kHz. The results reveal that dynamic stiffness can vary significantly with pad loading as well as the durometer of the material. It will also be shown that insertion loss follows the theoretical single degree of freedom curve only out to a frequency that is about 5 to 10 times the natural frequency, depending upon the pad durometer rating. Above that frequency wave resonances in the material cause the insertion loss to deteriorate significantly out to a frequency near 1 kHz, above which the insertion loss maintains a relatively constant value, again depending upon the pad durometer rating. In some instances the insertion loss values can approach 0 dB or even become negative at specific frequencies in the frequency region that is 10 to 20 times the natural frequency of the system.

Probability Distribution of Bilinear System Response to Impulse Excitation

1966 ◽  
Vol 33 (2) ◽  
pp. 384-386
Author(s):  
Stephen F. Felszeghy ◽  
William T. Thomson
Keyword(s):  
Probability Distribution ◽  
Bilinear System ◽  
Degree Of Freedom ◽  
System Response ◽  
Single Degree Of Freedom ◽  
Peak Response ◽  
Single Degree ◽  
Impulse Excitation ◽  
Peak Value

A single-degree-of-freedom system with a bilinear spring is excited by a rectangular impulse of constant value, but whose amplitude has a probability distribution which is Gaussian. The peak response of the system under this excitation is determined, and its probability distribution is plotted as a function of its peak value.

An Experimental Study of a Single-Degree-of-Freedom Impact Oscillator

2021 ◽  
Author(s):  
Shun Zhong ◽  
Jingyuan Tan ◽  
Zhicheng Cui ◽  
Tanghong Xu ◽  
Liqing Li
Keyword(s):  
Dynamical Behavior ◽  
Degree Of Freedom ◽  
Experimental Results ◽  
Physical Parameters ◽  
Impact Oscillator ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Design Choice ◽  
Wide Range ◽  
Simulation Results

Purpose. Impacts appear in a wide range of mechanical systems. To study the dynamical behavior introduced by impact in practical way, a single-degree-of-freedom impact oscillator rig is designed. Originality. A simple piece-wise linear system with symmetrical flexible constraints is designed and manufactured to carry out a wide range of experimental dynamic analysis and ultimately to validate piece-wise models. The new design choice is based on the following criteria: accuracy in representing the mathematical model, manufacturing simplicity, flexibility in terms of parameter changes and cost effectiveness as well avoidance of the delay introduced by the structure. Meanwhile, the new design provides the possibility of the applications of the complex control algorithms. Design/methodology/approach. The design process is described in detail. The initial experimental results of the rig as well as numerical simulation results are given. In this rig, the mass driven force is generated by electromagnet, which can be adjusted and control easily. Also, most of the physical parameters can be varied in a certain range to enhance flexibility of the system allowing to observe subtle phenomena. Findings. Compared with the simulation results, the designed rig is proved to be validated. Then, the initial experimental results demonstrate potentials of this rig to study fundamental impact phenomena, which have been observed in various engineering systems. They also indicate that this rig can be a good platform for investigating nonlinear control methods.

A Mechanical Analyzer for the Solution of Vibration Problems of a Single Degree of Freedom

1948 ◽  
Vol 15 (2) ◽  
pp. 146-150
Author(s):  
E. E. Weibel ◽  
N. M. Cokyucel ◽  
R. E. Blau
Keyword(s):  
Generalized Solution ◽  
Nonlinear Damping ◽  
Degree Of Freedom ◽  
Simple Construction ◽  
Dimensionless Form ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Constant Magnitude ◽  
Linear Damping ◽  
Vibration Problems

Abstract A mechanical-analogy-type analyzer is described which is of relatively simple construction being limited to single-degree-of-freedom problems. Whithin this limitation solutions may be obtained for systems which include various types of nonlinear elasticity and of nonlinear damping. Included is a generalized solution obtained on the analyzer giving in dimensionless form the maximum displacements and forces in a system having nonlinear (linear plus cubic) elasticity and linear damping caused by a force pulse of constant magnitude and finite duration. The bearing of the results on the starting torques in nonlinear systems is indicated.

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