Free Oscillations—One Degree of Freedom

2015 ◽  
pp. 35-69
Author(s):  
Mohammad Samiullah
Keyword(s):  
Degree Of Freedom ◽  
Free Oscillations

scholarly journals An Investigation of Fractional Bagley–Torvik Equation

Entropy ◽  
2019 ◽  
Vol 22 (1) ◽  
pp. 28 ◽  
Author(s):  
Azhar Ali Zafar ◽  
Grzegorz Kudra ◽  
Jan Awrejcewicz
Keyword(s):  
Fractional Derivative ◽  
Mechanical System ◽  
Caputo Fractional Derivative ◽  
Integral Transform ◽  
Rolling Bearing ◽  
Degree Of Freedom ◽  
Free Oscillations ◽  
Derivative Operator ◽  
Transform Method ◽  
Integral Transform Method

In this article, we will solve the Bagley–Torvik equation by employing integral transform method. Caputo fractional derivative operator is used in the modeling of the equation. The obtained solution is expressed in terms of generalized G function. Further, we will compare the obtained results with other available results in the literature to validate their usefulness. Furthermore, examples are included to highlight the control of the fractional parameters on he dynamics of the model. Moreover, we use this equation in modelling of real free oscillations of a one-degree-of-freedom mechanical system composed of a cart connected with the springs to the support and moving via linear rolling bearing block along a rail.

Approximating power for significance tests with one degree of freedom.

1997 ◽  
Vol 2 (2) ◽  
pp. 186-191 ◽  
Author(s):  
William P. Dunlap ◽  
Leann Myers
Keyword(s):  
Degree Of Freedom ◽  
Significance Tests

Free oscillations of the sun and the giant planets

1981 ◽  
Vol 134 (8) ◽  
pp. 675 ◽  
Author(s):  
S.V. Vorontsov ◽  
V.N. Zharkov
Keyword(s):  
Giant Planets ◽  
The Sun ◽  
Free Oscillations

Performance analysis of global local mean square error criterion of stochastic linearization for nonlinear oscillator

2019 ◽  
Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung
Keyword(s):  
Performance Analysis ◽  
Mean Square Error ◽  
Nonlinear Oscillators ◽  
Degree Of Freedom ◽  
Equivalent Linearization ◽  
Mean Square ◽  
Error Criterion ◽  
Stochastic Linearization ◽  
Local Mean ◽  
Mean Square Error Criterion

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).

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