Natural Vibration with Damping Force Proportional to a Power of the Velocity

1963 ◽  
Vol 67 (630) ◽  
pp. 381-385 ◽  
Author(s):  
A. W. Morley ◽  
W. D. Bryce
Keyword(s):  
Experimental Data ◽  
Natural Vibration ◽  
Dissipated Energy ◽  
Approximate Theory ◽  
Internal Damping ◽  
Damping Force ◽  
Solid Materials ◽  
Single Degree Of Freedom ◽  
Physical Systems ◽  
Single Degree

SummaryThe friction force in many physical systems has been found to depend on a power of the velocity, the magnitude of which varies according to the damping mechanism. This note employs an approximate theory applicable to small damping to examine the free vibration of a single degree of freedom system in which the damping force is proportional to an unspecified power of the velocity.Correlation with experimental data on the internal damping of solid materials shows that this phenomenon also tends to obey a power law although discrepancies exist between the expected and observed behaviours. These arise from the interpretation of the damping coefficient and from the frequency dependence of the dissipated energy.

scholarly journals Orthogonal contrasts: definitions and concepts

2004 ◽  
Vol 61 (1) ◽  
pp. 118-124 ◽  
Author(s):  
Maria Cristina Stolf Nogueira
Keyword(s):  
Experimental Data ◽  
Statistical Analysis ◽  
Interaction Effects ◽  
Degree Of Freedom ◽  
Extensive Review ◽  
Single Degree Of Freedom ◽  
Orthogonal Contrasts ◽  
Single Degree ◽  
Definite Structure

The single degree of freedom of orthogonal contrasts is a useful technique for the analysis of experimental data and helpful in obtaining estimates of main, nested and interaction effects, for mean comparisons between groups of data and in obtaining specific residuals. Furthermore, the application of orthogonal contrasts is an alternative way of doing statistical analysis on data from non-conventional experiments, whithout a definite structure. To justify its application, an extensive review is made on the definitions and concepts involving contrasts.

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.

An Experimental Hand/Arm Model for Human Interaction With a Telemanipulation System

2001 ◽  
Author(s):  
John E. Speich ◽  
Liang Shao ◽  
Michael Goldfarb
Keyword(s):  
Experimental Data ◽  
Second Order ◽  
Degree Of Freedom ◽  
Human Interaction ◽  
Haptic Interfaces ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Lumped Parameter ◽  
Mass Spring ◽  
System 1

Abstract This paper describes the development of a linear single degree-of-freedom lumped-parameter hand/arm model for the operator of a telemanipulaton system. The model form and parameters were determined from experimental data taken from a single degree-of-freedom telemanipulation system. Typically, the human is modeled as a second order mass-spring-damper system [1, 2]. The model developed in this paper, however, includes an additional spring and damper to better approximate the dynamics of the human while interacting with the manipulator. This model can be used in the design and simulation of control architectures for telemanipulation systems and haptic interfaces.

On Free Vibrations With Combined Viscous and Coulomb Damping

1980 ◽  
Vol 102 (4) ◽  
pp. 283-286 ◽  
Author(s):  
P. H. Markho
Keyword(s):  
Decay Curve ◽  
Closed Form Solution ◽  
Free Vibrations ◽  
Form Solution ◽  
Forced Response ◽  
Experimental Plot ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Coulomb Damping ◽  
Single Degree

A closed-form solution of the governing, nonlinear equation for free vibrations of a single-degree-of-freedom system, without stops, under combined viscous and Coulomb damping is first obtained. This is much less involved than forced-response considerations of the same system (with or without stops) the solution of which problem was first obtained by Den Hartog [1]. This note contains the first derivation, as far as the author is aware of, of the equation for the amplitude decay curve (or envelope) for such a system vibrating freely under no-stop conditions. This equation is presented in a form which enables the components of the damping force to be determined from the system’s experimental plot (or record) of displacement versus time.

An improved constant deceleration control method with extended shock velocity range for magnetorheological energy absorber

2021 ◽  
pp. 1045389X2110572
Author(s):  
Zhongqiang Feng ◽  
Dong Yu ◽  
Zhaobo Chen ◽  
Xudong Xing ◽  
Hui Yan
Keyword(s):  
Control Algorithm ◽  
Control Method ◽  
Velocity Range ◽  
Damping Force ◽  
Isolation System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Shock Mitigation ◽  
Energy Absorbers ◽  
Feasible Solutions

This paper proposed an extended constant deceleration (ECD) control method that can be used in the shock mitigation system with magnetorheological energy absorbers (MREAs). The ECD control method has three sections: zero controllable force (ZCF) section, constant deceleration (CD) section, and maximum damping force (MDF) section. Under the control of ECD, the system can stop at the end of MREA stroke without exceeding the maximum allowable deceleration. The ECD control algorithm is derived in a single-degree-of-freedom (SDOF) system. The controllable velocity range and the required controllable damping force of ECD control method are also derived, which can provide feasible solutions for the design of shock isolation system with MREAs. The performance of ECD control method is shown by applying to the drop-induced shock mitigation system with different drop velocities, different maximum controllable damping force, and MREA stroke. The results shows that the ECD control method not only has a large controllable velocity range and small controllable damping force requirement, but also can minimize the load transmitted to the system.

Response of Systems With Damping Materials Modeled Using Fractional Calculus

1995 ◽  
Vol 48 (11S) ◽  
pp. S118-S126 ◽  
Author(s):  
L. Suarez ◽  
A. Shokooh
Keyword(s):  
Fractional Calculus ◽  
Series Solution ◽  
Operator Method ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Kelvin Model ◽  
Single Degree ◽  
Damping Materials ◽  
Derivatives Of ◽  
Laplace And Fourier Transform

The mathematical modeling of damping materials based on fractional calculus has been shown to be very effective in representing the frequency dependence of the properties of these materials. In this model, the integer order derivatives in the constitutive equations of the Kelvin model are replaced by derivatives of fractional order. In this paper, we examine the response of a single degree-of-freedom system in which the damping force is proportional to a derivative of order α < 1 of the displacements. Three methods are proposed to obtain the response: the Laplace and Fourier transform methods, and an operator method that results in a series solution. Some interesting features exhibited by the oscillator’s response due to the fractional representation of the damping are unveiled.

Analysis of the Quality Factor and Response Time of Resonant Biosensor

2016 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Response Time ◽  
Quality Factor ◽  
Governing Equation ◽  
Dynamic Effect ◽  
Equation Of Motion ◽  
Measured Parameter ◽  
Damping Force ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
The Relationship

The relationship between the overall damping and response time of resonant biosensors is investigated in this paper. The governing equation of motion is derived using a single degree-of-freedom model of the resonator considering the dynamic effect of adsorption of the measured parameter. It is shown that the adsorption leads to a damping force on the resonant sensor. If not taken into account, this damping force results in misinter-pretation of the sensor readings.

Response of Linear Systems to Magnitude Limited Random Excitation

1969 ◽  
Vol 91 (4) ◽  
pp. 991-996 ◽  
Author(s):  
P. Y. Hu
Keyword(s):  
Linear Systems ◽  
Gaussian Distribution ◽  
Random Vibration ◽  
Random Excitation ◽  
Experimental Results ◽  
Single Degree Of Freedom ◽  
Physical Systems ◽  
Single Degree ◽  
Random Source ◽  
Instantaneous Values

In many situations, encountered both in the field and in the laboratory, the excitation produced by a broadband random source has many of the characteristics of a signal having a Gaussian distribution of instantaneous values except that the higher values predicted by the theory do not appear. Therefore, in all cases, physical systems are really excited by a magnitude limited Gaussian random vibration rather than a strictly Gaussian random vibration. Analytical as well as experimental results on the response of the single-degree-of-freedom system subject to magnitude limited random vibration are presented.

Nonlinear Structural Damping Described by the Masing Model and the Method of Slowly Varying Amplitude and Phase

1995 ◽  
Author(s):  
Ulrich Gutzer ◽  
Wolfgang Seemann ◽  
Peter Hagedorn
Keyword(s):  
Standing Waves ◽  
Free Vibrations ◽  
Dissipated Energy ◽  
Continuous Systems ◽  
Structural Damping ◽  
Single Degree Of Freedom ◽  
One Dimensional ◽  
Single Degree ◽  
Explicit Formulae ◽  
Good Agreement

Abstract In this paper we investigate vibrations of discrete and continuous systems with damping of the MASING type. For free vibrations the method of the slowly varying amplitude and phase shows good agreement with numerical results, especially if the damping is small. The equations resulting from this method allow a faster identification of the parameters of a physical model. First, a single degree of freedom system is studied. Explicit formulae are obtained for the changing amplitude and frequency. The results are useful since damping laws of the type under consideration are well suited to describe the energy dissipation in a variety of real structures. In the second part we consider a one dimensional continuum with a distributed MASING model. An explicit formula is found for the dissipated energy per cycle and wavelength in standing waves.

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