Parametric Identification of Nonlinear Systems Using Higher-Order Spectra

1997 ◽  
Author(s):  
Khalil A. Khan ◽  
B. Balachandran
Keyword(s):  
Nonlinear Systems ◽  
Nonlinear Oscillator ◽  
Transfer Functions ◽  
Nonlinear Oscillators ◽  
Parametric Identification ◽  
Higher Order ◽  
Numerical Results ◽  
Higher Order Spectra

Abstract A novel procedure to parametrically identify the nonlinearities in a system is presented. In this procedure, the relationships among higher-order transfer functions and higher-order spectra are utilized and expressions are derived for coefficients of non-linearities. Two different nonlinear oscillators are considered as examples to illustrate the procedure. Numerical results are also provided for a nonlinear oscillator.

Accurate numerical solutions of conservative nonlinear oscillators

2014 ◽  
Vol 3 (4) ◽  
Author(s):  
Najeeb Alam Khan ◽  
Khan Nasir Uddin ◽  
Khan Nadeem Alam
Keyword(s):  
Differential Equation ◽  
Plasma Physics ◽  
Nonlinear Oscillator ◽  
Numerical Solutions ◽  
Arbitrary Order ◽  
Nonlinear Oscillators ◽  
Higher Order ◽  
Algebraic Equations ◽  
Restoring Force ◽  
Arbitrary Power

AbstractThe objective of this paper is to present an investigation to analyze the vibration of a conservative nonlinear oscillator in the form u" + lambda u + u^(2n-1) + (1 + epsilon^2 u^(4m))^(1/2) = 0 for any arbitrary power of n and m. This method converts the differential equation to sets of algebraic equations and solve numerically. We have presented for three different cases: a higher order Duffing equation, an equation with irrational restoring force and a plasma physics equation. It is also found that the method is valid for any arbitrary order of n and m. Comparisons have been made with the results found in the literature the method gives accurate results.

Lagging Motion of Forced Nonlinear Oscillators

2003 ◽  
Author(s):  
Sand Woo Karng ◽  
Ki Young Kim ◽  
Ho-Young Kwak
Keyword(s):  
Nonlinear Systems ◽  
Applied Field ◽  
Nonlinear Oscillator ◽  
Phase Plane ◽  
Inverted Pendulum ◽  
Duffing Oscillator ◽  
Nonlinear Oscillators ◽  
Expansion Ratio ◽  
Amplitude Response ◽  
Calculation Results

The lagging motion of nonlinear oscillators with respect to the externally driven field was treated analytically and the calculation results were compared with observed results. Such lagging problem may occur in nonlinear systems whose behavior crucially depends on the frequency of the applied force. The lagging motion of the nonlinear oscillator with respect to the harmonically driven field made the oscillator respond in a way that reduced the effect of the applied field. The calculation considering the lagging motion yielded proper results in the expansion ratio of the bubble under ultrasound and trajectories in phase plane, the frequency spectrum for a forced inverted pendulum, and the amplitude response of the Duffing oscillator.

scholarly journals The Computation of the Magnitude of the Far Field for an Eccentric Circular Cylinder

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Bülent Yılmaz
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Radiation Condition ◽  
Higher Order ◽  
Numerical Results ◽  
Surface Radiation ◽  
Far Field ◽  
Condition Method ◽  
Radiation Conditions

The specific case of scattering of a plane wave by a two-layered penetrable eccentric circular cylinder has been considered and it is about the validity of the on surface radiation condition method and its applications to the scattering of a plane wave by a two-layered penetrable eccentric circular cylinder. The transformation of the problem of scattering by the eccentric circular cylinder to the problem of scattering by the concentric circular cylinder by using higher order radiation conditions, is observed. Numerical results presented the magnitude of the far field.

Bifurcation Trees of Periodic Motions to Chaos in a Parametric, Quadratic Nonlinear Oscillator

2014 ◽  
Vol 24 (05) ◽  
pp. 1450075 ◽  
Author(s):  
Albert C. J. Luo ◽  
Bo Yu
Keyword(s):  
Fourier Series ◽  
Nonlinear Systems ◽  
Analytical Solutions ◽  
Nonlinear Oscillator ◽  
Series Solution ◽  
Parametric Oscillator ◽  
Periodic Motions ◽  
Parametric Oscillators ◽  
Harmonic Term ◽  
Nonlinear Behaviors

In this paper, bifurcation trees of periodic motions to chaos in a parametric oscillator with quadratic nonlinearity are investigated analytically as one of the simplest parametric oscillators. The analytical solutions of periodic motions in such a parametric oscillator are determined through the finite Fourier series, and the corresponding stability and bifurcation analyses for periodic motions are completed. Nonlinear behaviors of such periodic motions are characterized through frequency–amplitude curves of each harmonic term in the finite Fourier series solution. From bifurcation analysis of the analytical solutions, the bifurcation trees of periodic motion to chaos are obtained analytically, and numerical illustrations of periodic motions are presented through phase trajectories and analytical spectrum. This investigation shows period-1 motions exist in parametric nonlinear systems and the corresponding bifurcation trees to chaos exist as well.

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