scholarly journals Harmonic balance approach to the periodic solutions of the (an)harmonic relativistic oscillator

2007 ◽  
Vol 371 (4) ◽  
pp. 291-299 ◽  
Author(s):  
Augusto Beléndez ◽  
Carolina Pascual
Keyword(s):  
Periodic Solutions ◽  
Harmonic Balance ◽  
Balance Approach ◽  
Relativistic Oscillator

scholarly journals APPROXIMATE ANALYTICAL SOLUTIONS FOR THE RELATIVISTIC OSCILLATOR USING A LINEARIZED HARMONIC BALANCE METHOD

2009 ◽  
Vol 23 (04) ◽  
pp. 521-536 ◽  
Author(s):  
A. BELÉNDEZ ◽  
D. I. MÉNDEZ ◽  
M. L. ALVAREZ ◽  
C. PASCUAL ◽  
T. BELÉNDEZ
Keyword(s):  
Periodic Solutions ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Oscillation Period ◽  
Analytical Approximations ◽  
Method Of Harmonic Balance ◽  
Approximate Analytical Solutions ◽  
Approximate Frequency ◽  
Relativistic Oscillator ◽  
Odd Nonlinearity

The analytical approximate technique developed by Wu et al. for conservative oscillators with odd nonlinearity is used to construct approximate frequency-amplitude relations and periodic solutions to the relativistic oscillator. By combining Newton's method with the method of harmonic balance, analytical approximations to the oscillation period and periodic solutions are constructed for this oscillator. The approximate periods obtained are valid for the complete range of oscillation amplitudes, A, and the discrepancy between the second approximate period and the exact one never exceeds 1.24%, and it tends to 1.09% when A tends to infinity. Excellent agreement of the approximate periods and periodic solutions with the exact ones are demonstrated and discussed.

Finding Periodic Solutions of Forced Systems With Local Nonlinearities: A Mixed Shooting Harmonic Balance Method

2015 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco Leine
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Balance Method ◽  
Pros And Cons ◽  
Numerical Approaches

Several numerical approaches have been developed to capture nonlinear effects of dynamical systems. In this paper we present a mixed shooting-harmonic balance method to solve large mechanical systems with local nonlinearities efficiently. The Harmonic Balance Method as well as the shooting method have both their pros and cons. The proposed mixed shooting-HBM approach combines the efficiency of HBM and the accuracy of the shooting method and has therefore advantages of both.

Harmonic Balance Approach for an Airfoil with a Freeplay Control Surface

AIAA Journal ◽  
2005 ◽  
Vol 43 (4) ◽  
pp. 802-815 ◽  
Author(s):  
Liping Liu ◽  
Earl H. Dowell
Keyword(s):  
Harmonic Balance ◽  
Control Surface ◽  
Balance Approach
Sign in / Sign up

Export Citation Format

Share Document