A Global Residue Harmonic Balance Method for a Class of Nonlinear Jerk Equation

2013 ◽  
Vol 353-356 ◽  
pp. 3324-3327
Author(s):  
Xin Xue ◽  
Pei Jun Ju ◽  
Dan Sun
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Oscillators ◽  
Solution Procedure ◽  
High Accuracy ◽  
New Approach ◽  
Strongly Nonlinear ◽  
Accuracy Comparison ◽  
Comparison Of The Results ◽  
Strongly Nonlinear Oscillators

A new approach, namely the global residue harmonic balance, was developed to determine the accurately approximate periodic solution of a class of nonlinear Jerk equation containing velocity times acceleration-squared and velocity. Unlike other improved harmonic balance methods, all the forward harmonic residuals were considered in the present approximation to improve the accuracy. Comparison of the results obtained using this approach with the exact one and the existing results reveals that the high accuracy, simplicity and efficiency of the presented solution procedure. The method can be easily extended to other strongly nonlinear oscillators.

scholarly journals Application of a modified rational harmonic balance method for a class of strongly nonlinear oscillators

2008 ◽  
Vol 372 (39) ◽  
pp. 6047-6052 ◽  
Author(s):  
A. Beléndez ◽  
E. Gimeno ◽  
M.L. Álvarez ◽  
D.I. Méndez ◽  
A. Hernández
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Oscillators ◽  
Balance Method ◽  
Strongly Nonlinear ◽  
Strongly Nonlinear Oscillators

scholarly journals An Optimal Iteration Method for Strongly Nonlinear Oscillators

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herişanu
Keyword(s):  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Oscillators ◽  
Approximate Solutions ◽  
High Accuracy ◽  
Restoring Force ◽  
Strongly Nonlinear ◽  
Convergence Of Approximate Solutions ◽  
Strongly Nonlinear Oscillators ◽  
Good Agreement

We introduce a new method, namely, the Optimal Iteration Perturbation Method (OIPM), to solve nonlinear differential equations of oscillators with cubic and harmonic restoring force. We illustrate that OIPM is very effective and convenient and does not require linearization or small perturbation. Contrary to conventional methods, in OIPM, only one iteration leads to high accuracy of the solutions. The main advantage of this approach 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. A very good agreement was found between approximate and numerical solutions, which prove that OIPM is very efficient and accurate.

scholarly journals Global Residue Harmonic Balance Method for a System of Strongly Nonlinear Oscillator

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Huaxiong Chen ◽  
Wei Liu
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Oscillator ◽  
Order Approximation ◽  
Harmonic Balance Method ◽  
High Accuracy ◽  
Balance Method ◽  
Strongly Nonlinear ◽  
Improve Accuracy ◽  
Residual Errors ◽  
Strongly Nonlinear Oscillator

In this paper, the global residue harmonic balance method is applied to obtain the approximate periodic solution and frequency for a well-known system of strongly nonlinear oscillator in engineering. This method can improve accuracy by considering all the residual errors in deriving each order approximation. With this procedure, the expressions of the higher-order approximate solution and corresponding frequency for the considered system can be determined easily. The comparison of the obtained results with previously existing and corresponding exact solutions shows the high accuracy and efficiency of the method.

A Scalable Time-Parallel Solution of Periodic Rotor Dynamics in X3D

2021 ◽  
Author(s):  
Mrinalgouda Patil ◽  
Anubhav Datta
Keyword(s):  
Harmonic Balance ◽  
Large Scale ◽  
Structural Model ◽  
Three Dimensional ◽  
Harmonic Balance Method ◽  
Flight Test ◽  
Solution Procedure ◽  
Balance Method ◽  
Computational Time ◽  
Near Resonance

A time-parallel algorithm is developed for large-scale three-dimensional rotor dynamic analysis. A modified harmonic balance method with a scalable skyline solver forms the kernel of this algorithm. The algorithm is equipped with a solution procedure suitable for large-scale structures that have lightly damped modes near resonance. The algorithm is integrated in X3D, implemented on a hybrid shared and distributed memory architecture, and demonstrated on a three-dimensional structural model of a UH-60A-like fully articulated rotor. Flight-test data from UH-60A Airloads Program transition flight C8513 are used for validation. The key conclusion is that the new solver converges to the time marching solution more than 50 times faster and achieves a performance greater than 1 teraFLOPS. The significance of this conclusion is that the principal barrier of computational time for trim solution using high-fidelity three-dimensional structures can be overcome with the scalable harmonic balance method demonstrated in this paper.

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