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.

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.

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.

Effect of Waveform on the Effectiveness of Tangential Dither Forces to Cancel Friction-Induced Oscillations

2005 ◽  
Author(s):  
Michael A. Michaux ◽  
Aldo A. Ferri ◽  
Kenneth A. Cunefare
Keyword(s):  
Numerical Integration ◽  
High Frequency ◽  
Frictional Contact ◽  
Degree Of Freedom ◽  
System Response ◽  
Periodic Signal ◽  
Method Of Averaging ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree

High-frequency dither forces are often used to reduce unwanted vibration in frictional systems. This paper examines how the effectiveness of these dither-cancellation techniques is influenced by the type of periodic signal employed. The paper uses the method of averaging as well as numerical integration to study a single-degree-of-freedom (SDOF) system consisting of a mass in frictional contact with a translating surface. Recently, it was found that sinusoidal dither forces had the ability to stabilize or destabilize such a system, depending on the system and frictional characteristics as well as the amplitude and frequency of the dither signal [1]. This paper extends this analysis to general, periodic dither forces. In particular, the system response for sinusoidal dither waveforms is compared to that of triangular dither waveforms and square dither waveforms. It is found that, for a given amplitude and frequency of the dither signal, square waveforms are much more effective in canceling friction-induced oscillations than sinusoidal dither; likewise, sinusoidal waveforms are more effective than triangular waveforms for a given amplitude and frequency. A criterion is developed that relates the effectiveness of the waveform to the properties of the integral of the dither signal.

Some Shock Spectra Characteristics and Uses

1958 ◽  
Vol 25 (3) ◽  
pp. 365-372
Author(s):  
Y. C. Fung ◽  
M. V. Barton
Keyword(s):  
Shock Wave ◽  
High Frequency ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Close Approximation ◽  
Single Degree Of Freedom ◽  
Peak Response ◽  
Single Degree ◽  
Frequency Oscillator ◽  
The Individual

Abstract A shock spectrum is a plot showing the peak response of a linear variable-frequency oscillator (of single degree of freedom) to a specific shock wave, as a function of the frequency of the oscillator. Such a spectrum may be measured, for example, by multifrequency reed gages and is sometimes used as a basis either for specifying the shock wave or for computing the response of a multi-degree-of-freedom structure to such a shock. In this paper these applications of the shock spectrum are discussed. In particular, it is shown that, if the fundamental frequency (f1, cps) of the structure is sufficiently high, a close approximation of the peak response of a multi-degree-of-freedom system can be obtained by the algebraic sum (not the sum of absolute values) of the peak responses of the individual degrees of freedom. Numerical results for a uniform cantilever beam subjected to a shock load uniformly distributed over its span show that the high-frequency requirement is satisfied if 2f1tm ≥ 1, where tm(sec) is the rise time of the pulse.

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