Development of a new adaptive harmonic balance method and its comparison

Date

2018

Author

Sert, Onur

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Nonlinear systems are encountered in many areas of science. In order to study these systems on a theoretical level, many approaches regarding the solution of nonlinear equation systems have been developed. Harmonic Balance Method (HBM) is one of the most powerful and popular methods for solving nonlinear differential equations in frequency domain. The main idea of the method is representation of the time-periodic response and nonlinear internal forces in terms of Fourier series and balancing each harmonic term. In order to avoid solving an infinite system of equations, one needs to truncate this series at some point. The number of terms to be included in the series is a compromise between the computational effort and the required solution accuracy. In order to overcome this challenge, numerous adaptive algorithms for automatically selecting the harmonics to be included in the solution are developed. These methods are called Adaptive Harmonic Balance Methods (AHBMs). In this thesis, it is aimed to investigate and compare the effectiveness of AHBMs that are currently in use for mechanical vibration problems and to introduce new AHBMs vi as an alternative to the existing ones. For this purpose, firstly the mathematical backgrounds of all the methods are investigated in detail. Then, using the scripts developed in MATLAB®, AHBMs and the classical HBM are employed in order to perform nonlinear response analysis of selected lumped parameter systems. Error analyses are done and comparisons of computational time requirements are obtained in order to show the differences between various methods and effectiveness of the newly proposed methods.

Subject Keywords

Nonlinear systems., Harmonic analysis., Equilibrium., Vibration.

URI

http://etd.lib.metu.edu.tr/upload/12621915/index.pdf
https://hdl.handle.net/11511/27119

Collections

Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

O. Sert, “Development of a new adaptive harmonic balance method and its comparison,” M.S. - Master of Science, Middle East Technical University, 2018.