Non-stationary approximate response of non-linear multi-degree-of-freedom systems subjected to combined periodic and stochastic excitation

2022 ◽  
Vol 166 ◽  
pp. 108420
Author(s):  
Fan Kong ◽  
Renjie Han ◽  
Shujin Li ◽  
Wei He
Keyword(s):  
Degree Of Freedom ◽  
Stochastic Excitation ◽  
Non Linear

Non-linear torsional oscillation of a two-degree-of-freedom system incorporating a Hooke joint

1964 ◽  
Vol 277 (1368) ◽  
pp. 92-106 ◽  
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Torsional Oscillation ◽  
Degree Of Freedom ◽  
Non Linear ◽  
Two Degree Of Freedom

The non-linear torsional oscillation of the system is analyzed by means of a variant of Kryloff and Bogoliuboff’s method. It is shown that each mode of the system can perform oscillations of large amplitude in a number of critical speed ranges, and that hysteresis effects and discontinuous jumps in amplitude are to be expected in these speed ranges if the damping is light.

Bifurcations of a Nonlinear Two-Degree-of-Freedom System Under Narrow-Band Stochastic Excitation

1992 ◽  
Vol 114 (1) ◽  
pp. 24-31
Author(s):  
R. Lin ◽  
K. Huseyin ◽  
C. W. S. To
Keyword(s):  
Relaxation Time ◽  
Correlation Time ◽  
Averaging Method ◽  
Narrow Band ◽  
Singularity Theory ◽  
Random Parameter ◽  
Degree Of Freedom ◽  
Stochastic Excitation ◽  
Static Approach ◽  
Two Degree Of Freedom

In this paper, bifurcations of a nonlinear two-degree-of-freedom system subjected to a narrow-band stochastic excitation are investigated. Under the assumption that the correlation time greatly exceeds the relaxation time, a quasi-static approach combined with averaging method is adopted to obtain the bifurcation equations, and the singularity theory is applied to analyze the bifurcations. It is demonstrated that bifurcation patterns jump from one to another due to the influence of a random parameter. The probabilities of the jumping bifurcation patterns are given.

scholarly journals Performance Barriers for Single-Degree-of-Freedom Energy Harvesters Under Generic Stochastic Excitation

2014 ◽  
Author(s):  
Han Kyul Joo ◽  
Themistoklis P. Sapsis
Keyword(s):  
Degree Of Freedom ◽  
Performance Criteria ◽  
Relative Distribution ◽  
Stochastic Excitation ◽  
Excitation Spectra ◽  
Response Level ◽  
Single Degree Of Freedom ◽  
Energy Harvesters ◽  
Single Degree ◽  
Input Spectrum

We develop performance criteria for the objective comparison of different classes of single-degree-of-freedom oscillators under stochastic excitation. For each family of oscillators, these objective criteria take into account the maximum possible energy harvested for a given response level, which is a quantity that is directly connected to the size of the harvesting configuration. We prove that the derived criteria are invariant with respect to magnitude or temporal rescaling of the input spectrum and they depend only on the relative distribution of energy across different harmonics of the excitation. We then compare three different classes of linear and nonlinear oscillators and using stochastic analysis tools we illustrate that in all cases of excitation spectra (monochromatic, broadband, white-noise) the optimal performance of all designs cannot exceed the performance of the linear design.

A Convenient Way of Taking Wing (and Fuselage) Flexibility into Account in Calculating Undercarriage Loads

1968 ◽  
Vol 72 (688) ◽  
pp. 353-355
Author(s):  
D. Williams
Keyword(s):  
Dynamic System ◽  
Ab Initio ◽  
Normal Modes ◽  
Degree Of Freedom ◽  
Concentrated Mass ◽  
Natural Approach ◽  
Non Linear ◽  
Lumped Masses

The crudest way of taking account of the airframe superstructure in calculating undercarriage performance is to represent it by a single concentrated mass. Crude as this method is, it is often used by aircraft firms because the only alternative known to them, apparently, is something they hesitate to face. And no wonder, because it means having to represent the wing-fuselage system by a large number of lumped masses and springs, each of which means an extra degree of freedom. This complicated dynamic system has then to be integrated with the undercarriage system, itself complicated by its non-linear characteristics. The natural approach that suggests itself is not to consider the w/f (wing-fuselage) structure ab initio but to make use of its (usually known) normal modes and frequencies. But this is just what cannot be done by existing techniques—hence the present impasse.

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