scholarly journals Comparison Analysis Based on the Cubic Spline Wavelet and Daubechies Wavelet of Harmonic Balance Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Jing Gao
Keyword(s):  
Theoretical Analysis ◽  
Harmonic Balance ◽  
Jacobian Matrix ◽  
Harmonic Balance Method ◽  
Cubic Spline ◽  
Nonlinear Circuits ◽  
Balance Method ◽  
Daubechies Wavelet ◽  
Comparison Analysis ◽  
Spline Wavelet

This paper develops a theoretical analysis of harmonic balance method, based on the cubic spline wavelet and Daubechies wavelet, for steady state analysis of nonlinear circuits under periodic excitation. The properties of the resulting Jacobian matrix for harmonic balance are analyzed. Numerical experiments illustrate the theoretical analysis.

scholarly journals Harmonic Balance Method for Chaotic Dynamics in Fractional-Order Rössler Toroidal System

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Huijian Zhu
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Harmonic Balance ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Chaotic Motions ◽  
Behavior Based

This paper deals with the problem of determining the conditions under which fractional order Rössler toroidal system can give rise to chaotic behavior. Based on the harmonic balance method, four detailed steps are presented for predicting the existence and the location of chaotic motions. Numerical simulations are performed to verify the theoretical analysis by straightforward computations.

Laser induced microwave oscillator under the influence of interference

2014 ◽  
Vol 6 (6) ◽  
pp. 581-590 ◽  
Author(s):  
Arindum Mukherjee ◽  
Somnath Chatterjee ◽  
Nikhil Ranjan Das ◽  
Baidyanath Biswas
Keyword(s):  
Theoretical Analysis ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Microwave Oscillator ◽  
Experimental Results ◽  
Balance Method ◽  
Optoelectronic Oscillator ◽  
System Equation ◽  
Novel Technique ◽  
Weak Interference

An optoelectronic oscillator (OEO) under the influence of a weak interference has been investigated. The system equation of the OEO under the influence of interference has been derived. A novel technique for calculating the lock range of the oscillator using the harmonic balance method in presence of interference has been demonstrated. Theoretical analysis coupled with experimental results has been presented.

Nonlinear vibration analysis of forced response for rubbing problems using the automatic differential frame

2021 ◽  
pp. 095440892110396
Author(s):  
Tianyuan Liu ◽  
Lei Sun ◽  
Yonghui Xie
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance ◽  
Vibration Analysis ◽  
Automatic Differentiation ◽  
Jacobian Matrix ◽  
Harmonic Balance Method ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Time Marching ◽  
Marching Method

The multi-harmonic balance method is widely applied to obtain the forced responses of nonlinear systems undergoing rubbing problems. Despite large-scale time savings compared with the time marching method, it suffers from the complicated derivations of the Jacobian matrix. To solve this problem, this paper focuses on applying the automatic differentiation frame to the multi-harmonic balance method to implement the nonlinear vibration analysis of systems subjected to the rub phenomena. By establishing computational graph and utilizing the automatic differentiation process, tedious works such as the derivations of the complicated analytical expressions of the Jacobian matrix are avoided, which guarantees the efficiency and applicability of the presented method. A single-degree-of-freedom system with nonlinear force in the form of cubic is used to verify the accuracy of the method, and numerical analysis results reveal that the method is accurate enough compared with the time marching method. Furthermore, for the purpose of application, the responses of two common friction models, which are of great concern in some practical engineering fields, including a two-degree-of-freedom system containing a friction damper and a rotor disk system with circumferential rubbing, are obtained utilizing the presented approach. The influences of several model parameters on their responses are investigated as well. Numerical investigations demonstrate that the automatic differential solution framework developed in this research for solving nonlinear vibration equations has high accuracy and eliminates the need for a complicated partial derivative analytical formula derivation.

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