scholarly journals Accurate Solutions of Conservative Nonlinear Oscillators by the Enhanced Cubication Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Alex Elías-Zúñiga ◽  
Oscar Martínez-Romero
Keyword(s):  
Nonlinear Oscillators ◽  
Approximate Solutions ◽  
Angular Frequency ◽  
Time Response ◽  
Response Curves ◽  
Relative Errors

The enhanced cubication method is applied to develop approximate solutions for the most common nonlinear oscillators found in the literature. It is shown that this procedure leads to amplitude-time response curves and angular frequency values with maximum relative errors lower than those found by previously developed approximate solutions.

scholarly journals Approximate Solution for the Duffing-Harmonic Oscillator by the Enhanced Cubication Method

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Alex Elías-Zúñiga ◽  
Oscar Martínez-Romero ◽  
René K. Córdoba-Díaz
Keyword(s):  
Approximate Solution ◽  
Harmonic Oscillator ◽  
Relative Error ◽  
Oscillation Amplitude ◽  
Approximate Solutions ◽  
Angular Frequency ◽  
Duffing Equation ◽  
Maximum Relative Error ◽  
Relative Errors

The cubication and the equivalent nonlinearization methods are used to replace the original Duffing-harmonic oscillator by an approximate Duffing equation in which the coefficients for the linear and cubic terms depend on the initial oscillation amplitude. It is shown that this procedure leads to angular frequency values with a maximum relative error of 0.055%. This value is 21% lower than the relative errors attained by previously developed approximate solutions.

203. Note: On Estimating Time-Response Curves

Biometrics ◽  
1964 ◽  
Vol 20 (3) ◽  
pp. 643 ◽  
Author(s):  
R. C. Elston
Keyword(s):  
Time Response ◽  
Response Curves

Free and Forced Vibrations of the Strongly Nonlinear Cubic-Quintic Duffing Oscillators

2017 ◽  
Vol 72 (1) ◽  
pp. 59-69 ◽  
Author(s):  
M.M. Fatih Karahan ◽  
Mehmet Pakdemirli
Keyword(s):  
Numerical Simulations ◽  
Numerical Solutions ◽  
Multiple Scales ◽  
Approximate Solutions ◽  
Response Curves ◽  
Strongly Nonlinear ◽  
Free And Forced Vibrations ◽  
Approximate Analytical Solutions ◽  
Strongly Nonlinear Oscillators ◽  
Good Agreement

AbstractStrongly nonlinear cubic-quintic Duffing oscillatoris considered. Approximate solutions are derived using the multiple scales Lindstedt Poincare method (MSLP), a relatively new method developed for strongly nonlinear oscillators. The free undamped oscillator is considered first. Approximate analytical solutions of the MSLP are contrasted with the classical multiple scales (MS) method and numerical simulations. It is found that contrary to the classical MS method, the MSLP can provide acceptable solutions for the case of strong nonlinearities. Next, the forced and damped case is treated. Frequency response curves of both the MS and MSLP methods are obtained and contrasted with the numerical solutions. The MSLP method and numerical simulations are in good agreement while there are discrepancies between the MS and numerical solutions.

scholarly journals On the properties of numerical solutions of dynamical systems obtained using the midpoint method

2019 ◽  
Vol 27 (3) ◽  
pp. 242-262 ◽  
Author(s):  
Vladimir P. Gerdt ◽  
Mikhail D. Malykh ◽  
Leonid A. Sevastianov ◽  
Yu Ying
Keyword(s):  
Difference Scheme ◽  
Coupled Oscillators ◽  
Numerical Solutions ◽  
Nonlinear Oscillators ◽  
Approximate Solutions ◽  
Algebraic Equations ◽  
Integrals Of Motion ◽  
Midpoint Method ◽  
Nonlinear Algebraic Equations ◽  
The Difference

The article considers the midpoint scheme as a finite-difference scheme for a dynamical system of the form ̇ = (). This scheme is remarkable because according to Cooper’s theorem, it preserves all quadratic integrals of motion, moreover, it is the simplest scheme among symplectic Runge-Kutta schemes possessing this property. The properties of approximate solutions were studied in the framework of numerical experiments with linear and nonlinear oscillators, as well as with a system of several coupled oscillators. It is shown that in addition to the conservation of all integrals of motion, approximate solutions inherit the periodicity of motion. At the same time, attention is paid to the discussion of introducing the concept of periodicity of an approximate solution found by the difference scheme. In the case of a nonlinear oscillator, each step requires solving a system of nonlinear algebraic equations. The issues of organizing computations using such schemes are discussed. Comparison with other schemes, including those symmetric with respect to permutation of and .̂

Effects of Additional Mass on Modal Experimental Analysis of 3-Dimension and 5-Direction Braided Composites

2010 ◽  
Vol 34-35 ◽  
pp. 1467-1470
Author(s):  
Yan Gao ◽  
Jia Lu Li
Keyword(s):  
Natural Frequency ◽  
Influence Factor ◽  
Damping Ratio ◽  
Force Response ◽  
Braided Composites ◽  
Additional Mass ◽  
Response Curves ◽  
Ratio Increase ◽  
Modal Test ◽  
Relative Errors

The work of vibration test has significant meanings for the researches and applications of 3-dimension and 5-direction braided composites. This article discusses the effects of added mass with different weight on the modal test of 3-dimension and 5-direction braided composites. The comparison of the modal parameters of 3-dimension and 5-direction braided composites tested by different weight of mass reveals that the additional mass is a mostly influence factor for vibration property of 3-dimension and 5-direction braided composites. The results of frequency response and force response curves show that smaller mass accelerometer is more effective for a wider range of frequencies around the resonance frequency, a higher natural frequency and a larger peak in these points. Force-response curves show that force response amplitude increases with the increase of additional mass weight, and the larger additional mass, the shorter time taken for reaching stationary state. The errors of natural frequency and damping ratio increase when the weight of additional mass increases. With the increase of modal orders, relative errors of modal characteristics have slighter decreasing degrees. The results derived from this article will provide a useful reference for precise modal analysis of 3-dimension and 5-direction braided composites.

scholarly journals Optimal Variational Method for Truly Nonlinear Oscillators

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herişanu
Keyword(s):  
Variational Method ◽  
Numerical Solution ◽  
Periodic Solutions ◽  
Nonlinear Oscillators ◽  
Approximate Solutions ◽  
Convergence Of Approximate Solutions ◽  
Good Agreement

The Optimal Variational Method (OVM) is introduced and applied for calculating approximate periodic solutions of “truly nonlinear oscillators”. The main advantage of this procedure consists in that it provides a convenient way to control the convergence of approximate solutions in a very rigorous way and allows adjustment of convergence regions where necessary. This approach does not depend upon any small or large parameters. A very good agreement was found between approximate and numerical solution, which proves that OVM is very efficient and accurate.

Magnesium CSF concentrations following intravenous administration in healthy adults:dose and time response curves

2001 ◽  
Vol 18 (Supplement 21) ◽  
pp. 64
Author(s):  
E. Amadeu ◽  
A. Meireles ◽  
E. Lopes ◽  
J. Barbot ◽  
P. Amorim
Keyword(s):  
Intravenous Administration ◽  
Time Response ◽  
Response Curves
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