Free Vibration of Systems with a Single Degree of Freedom

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.

Free Vibration of Single Degree of Freedom Systems

Mechanical Engineering Series - Theory of Vibration ◽

10.1007/978-1-4684-0362-6_3 ◽

1991 ◽

pp. 54-124

Author(s):

A. A. Shabana

Keyword(s):

Free Vibration ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree

Free-Vibration Response of Single-Degree-Of-Freedom Systems

Basic Structural Dynamics ◽

10.1002/9781118279137.ch3 ◽

2012 ◽

pp. 51-76

Keyword(s):

Free Vibration ◽

Vibration Response ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree ◽

Free Vibration Response

Demonstrator to show the effects of negative stiffness on the natural frequency of a simple oscillator

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/09544062jmes1012 ◽

2008 ◽

Vol 222 (7) ◽

pp. 1189-1192 ◽

Cited By ~ 14

Author(s):

A Carrella ◽

M J Brennan ◽

T P Waters

Keyword(s):

Free Vibration ◽

Natural Frequency ◽

Degree Of Freedom ◽

Negative Stiffness ◽

Test Rig ◽

Single Degree Of Freedom ◽

Single Degree ◽

Horizontal Beam ◽

Additional Correction

This article describes a demonstrator to show the effects of negative stiffness on the free vibration of a simple oscillator. The test rig consists of a horizontal beam that is hinged at one end and is supported by two coil springs to form a single-degree-of-freedom system. Additional correction springs, which provide negative stiffness, can be attached to lower the natural frequency of the system. The effect of the change in natural frequency can be easily seen visually, and it is shown that for one of the configurations of correction springs, the natural frequency can be reduced by a factor of about 4.

Exact Solutions for Free Vibration in a Single-Degree-of-Freedom System Having a Spring with an Arbitrary Cubic Function. Introductory Remarks.

TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C ◽

10.1299/kikaic.62.1 ◽

1996 ◽

Vol 62 (593) ◽

pp. 1-8

Author(s):

Hideyuki TAMURA ◽

Youichiro HARA ◽

Tadashi OKABE ◽

Ken-ichiro MATSUZAKI

Keyword(s):

Free Vibration ◽

Exact Solutions ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree ◽

Cubic Function

Free Vibration of Single Degree of Freedom System

Conceptual Theories in Structural Dynamics - Advanced Structured Materials ◽

10.1007/978-981-15-5440-7_3 ◽

2020 ◽

pp. 29-59

Author(s):

Farzad Hejazi ◽

Tan Kar Chun

Keyword(s):

Free Vibration ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree

The Estimation of Viscous and Coulomb Damping in Harmonically Excited Oscillators

Volume 7B: 17th Biennial Conference on Mechanical Vibration and Noise ◽

10.1115/detc99/vib-8183 ◽

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.

Free vibration of single-degree-of-freedom systems (undamped) in relation to structural dynamics during earthquakes

Structural Dynamics of Earthquake Engineering ◽

10.1533/9781845695736.1.9 ◽

2009 ◽

pp. 9-42

Author(s):

S. Rajasekaran

Keyword(s):

Free Vibration ◽

Structural Dynamics ◽

Degree Of Freedom ◽

Single Degree Of Freedom ◽

Single Degree

Free Vibration of Single Degree of Freedom Linear Oscillator

Structural Dynamics and Static Nonlinear Analysis From Theory to Application - Advances in Civil and Industrial Engineering ◽

10.4018/978-1-7998-4399-3.ch001 ◽

2021 ◽

pp. 1-40

Keyword(s):

Free Vibration ◽

Degree Of Freedom ◽

Linear Oscillator ◽

Single Degree Of Freedom ◽

Single Degree ◽

Translational Vibration ◽

Mathematical Equations ◽

Damped Oscillator

This chapter is dedicated to understanding and studying a didactic case represented by a free vibration of a linear oscillator with a single degree of freedom. Mathematical equations of the problem will be detailed as well as the solution that goes with single degree of freedom oscillator for translational vibration for all cases: free undamped oscillator, as well as free damped oscillator, and torsional free undamped vibration passing by critical, subcritical, and over damping system. At the end of the chapter, some examples will be treated.