Approximate Analytical Mean-Square Response of an Impacting Stochastic System Oscillator With Fractional Damping

2017 ◽  
Vol 3 (3) ◽  
Author(s):  
D. Yurchenko ◽  
A. Burlon ◽  
M. Di Paola ◽  
G. Failla ◽  
A. Pirrotta
Keyword(s):  
Fractional Derivative ◽  
Stochastic System ◽  
Stochastic Dynamics ◽  
Gaussian White Noise ◽  
Mean Square ◽  
Fractional Damping ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Mean Square Response ◽  
Hard Type

The paper deals with the stochastic dynamics of a vibroimpact single-degree-of-freedom system under a Gaussian white noise. The system is assumed to have a hard type impact against a one-sided motionless barrier, located at the system's equilibrium. The system is endowed with a fractional derivative element. An analytical expression for the system's mean squared response amplitude is presented and compared with the results of numerical simulations.

scholarly journals Deterministic and Probabilistic Foundation Forces Resulting From an Unbalanced Turbine

1976 ◽  
Author(s):  
L. Boyce ◽  
T. J. Kozik
Keyword(s):  
Root Mean Square ◽  
Center Of Mass ◽  
Random Variable ◽  
Degree Of Freedom ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Principal Mode ◽  
Single Degree ◽  
Rotating Machine ◽  
Mean Square Response

This paper considers the problem of the unbalanced rotating turbine as a single degree of freedom system, wherein the principal mode of vibration is a translation in the direction of the machine supports. The distance from the center of mass of the rotating mass to the geometric axis, also known as the effective eccentricity, is modeled as a random variable. The expression for the root mean square response of the rotating machine is derived and related to the statistical analog for the deterministic expression for the foundation force. These results are numerically compared to their equivalent deterministic values.

Frequency Domain Analysis of a Fractional Derivative SDOF System

2005 ◽  
Author(s):  
Silvio Sorrentino ◽  
Luigi Garibaldi
Keyword(s):  
Magnetic Material ◽  
Fractional Derivative ◽  
Frequency Response ◽  
Frequency Domain ◽  
Dynamic Behaviour ◽  
Frequency Domain Analysis ◽  
Response Functions ◽  
Single Degree Of Freedom ◽  
Sdof System ◽  
Single Degree

This paper presents a study of the frequency domain behaviour of a single degree of freedom (SDOF) system with a fractional derivative model, named Fractional Kelvin-Voigt. Frequency response functions (FRFs) as receptance and transmissibility are analytically studied. Then the model is applied to describe the dynamic behaviour of a magneto-mechanic system in the frequency domain, consisting of a body of para or dia-magnetic material vibrating in a field created by a pair of magnets.

Stochastic Dynamics of a Variable Inertia System via Lyapunov Exponents

2008 ◽  
Author(s):  
S. F. Asokanthan ◽  
X. H. Wang ◽  
W. V. Wedig ◽  
S. T. Ariaratnam
Keyword(s):  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Stochastic Systems ◽  
Stochastic Dynamics ◽  
Excitation Frequency ◽  
Excitation Amplitude ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Excitation ◽  
The Stability

Torsional instabilities in a single-degree-of-freedom system having variable inertia are investigated by means of Lyapunov exponents. Linearised analytical model is used for the purpose of stability analysis. Numerical schemes for simulating the top Lyapunov exponent for both deterministic and stochastic systems are established. Instabilities associated with the primary and the secondary sub-harmonic resonances have been identified by studying the sign of the top Lyapunov exponent. Predictions for the deterministic and the stochastic cases are compared. Instability conditions have been presented graphically in the excitation frequency-excitation amplitude-top Lyapunov exponent space. The effects of fluctuation density as well as that of damping on the stability behaviour of the system have been examined. Predicted instability conditions are adequate for the design of a variable-inertia system so that a range of critical speeds of operation may be avoided.

Mean-Square Response of Simple Mechanical Systems to Nonstationary Random Excitation

1969 ◽  
Vol 36 (2) ◽  
pp. 221-227 ◽  
Author(s):  
R. L. Barnoski ◽  
J. R. Maurer
Keyword(s):  
White Noise ◽  
Random Noise ◽  
Random Excitation ◽  
Correlated Noise ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Step Functions ◽  
Unit Step ◽  
Mean Square Response ◽  
The Mean

This paper concerns the mean-square response of a single-degree-of-freedom system to amplitude modulated random noise. The formulation is developed in terms of the frequency-response function of the system and generalized spectra of the nonstationary random excitation. Both the unit step and rectangular step functions are used for the amplitude modulation, and both white noise and noise with an exponentially decaying harmonic correlation function are considered. The time-varying mean-square response is shown not to exceed its stationary value for white noise. For correlated noise, however, it is shown that the system mean-square response may exceed its stationary value.

Dynamics of a Free Play Type of Nonlinearity System Under Deterministic and Random Excitations

1995 ◽  
Author(s):  
Ismail I. Orabi
Keyword(s):  
Gaussian White Noise ◽  
Harmonic Excitation ◽  
Free Play ◽  
Nonlinear Structures ◽  
Single Degree Of Freedom ◽  
Linearization Technique ◽  
Single Degree ◽  
Nonlinear Responses ◽  
Digital Simulations ◽  
Good Agreement

Abstract The dynamics of nonlinear structures under harmonic and random excitations is studied. The harmonic excitation is modeled by periodic loadings while the random excitations is modeled by segments of stationary Gaussian white noise processes. Transient responses of a single-degree-of-freedom model is studied to illustrate the characteristic of nonlinear responses. A free play type of nonlinearity is considered. The effects of nonlinearities on the overall dynamics of structure is investigated. The linearization technique is used to calculate the response statistics. To check the accuracy of the linearization technique, the results are compared with Monte-Carlo digital simulations and good agreement are observed.

On Equivalent Linearization Using Wavelet Transform

1999 ◽  
Vol 121 (4) ◽  
pp. 429-432 ◽  
Author(s):  
B. Basu ◽  
V. K. Gupta
Keyword(s):  
Wavelet Transform ◽  
Duffing Oscillator ◽  
Time Dependent ◽  
Equivalent Linearization ◽  
Equivalent System ◽  
Mean Square ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
The Mean ◽  
The Given

This paper proposes a wavelet-based formulation for linearizing a base-excited single-degree-of-freedom nonlinear system to a time-variant linear (TVL) system. The given system is assumed to be nonlinear in stiffness, and the time-dependent natural frequency of the equivalent system is proposed to he estimated through instantaneous minimization of the mean-square error. A duffing oscillator has been considered to illustrate the performance of the proposed TVL system.

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