scholarly journals Non-stationary response power spectrum determination of linear/non-linear systems endowed with fractional derivative elements via harmonic wavelet

2022 ◽  
Vol 162 ◽  
pp. 108024
Author(s):  
Fan Kong ◽  
Yixin Zhang ◽  
Yuanjin Zhang
Keyword(s):  
Power Spectrum ◽  
Fractional Derivative ◽  
Linear Systems ◽  
Stationary Response ◽  
Non Linear ◽  
Harmonic Wavelet ◽  
Non Linear Systems

Algorithm for the Determination of the Resonances of Anharmonic Damped Oscillators

1987 ◽  
Vol 42 (8) ◽  
pp. 803-807 ◽  
Author(s):  
G. Reiser ◽  
A. Hübler ◽  
E. Lüscher
Keyword(s):  
Linear Systems ◽  
New Method ◽  
Resonance Spectroscopy ◽  
Driving Mechanism ◽  
Non Linear ◽  
Non Linear Systems ◽  
Damped Oscillators ◽  
The Way

Non-linear damped oscillators can be resonantly driven by an aperiodic force. An algorithm is described which shows how such a driving mechanism can be calculated. This new method paves the way for resonance spectroscopy in non-linear systems.

The practical use of variation principles in the determination of the stability of non linear systems

1961 ◽  
Vol 2 (2) ◽  
pp. 153-188 ◽  
Author(s):  
J. N. Lyness ◽  
J. M. Blatt
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
Mathieu Equation ◽  
Iteration Procedure ◽  
Variation Principle ◽  
Non Linear ◽  
Non Linear Systems ◽  
The Stability ◽  
Special Case

AbstractWe are interested in the motion of non linear systems. In this paper we use a variation principle and an iteration procedure in order to treat the stability of free oscillations against small disturbances of the initial conditions. It is found that approximations to the low lying stability lines can be obtained using the Rayleigh-Ritz variation principle and that these approximations can be consistently improved using an iteration procedure. These approximations are compared with the tabulated values in the special case of the Mathieu Equation. The results are in general a considerable improvement on those obtained using the usual Perturbation Theory, and have a much wider range of validity.

Probabilistic criterion for Gausian equivalent linearization

1996 ◽  
Vol 18 (2) ◽  
pp. 1-6
Author(s):  
N. D. Anh ◽  
W. Schiehlen
Keyword(s):  
White Noise ◽  
Linear Systems ◽  
Equivalent Linearization ◽  
Stationary Response ◽  
Probabilistic Criterion ◽  
Non Linear ◽  
Equivalent Equation ◽  
Non Linear Systems

Within the scope of Gaussian equivalent linearization, a new probabilistic criterion for determining the coefficients of the linearized equivalent equation is proposed to treat stationary response of non-linear systems under zero mean Gaussian ro.nd.om excitation. Application to the Duffing oscillate subjected to white noise is presented that shows significant improvement over corresponding accuracy of the classical Gaussian equivalent linearization for both weak and strong non-linear.

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