A novel two-step pseudo-response based adaptive harmonic balance method for dynamic analysis of nonlinear structures

Date

2019-09-01

Author

Sert, Onur
Ciğeroğlu, Ender

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

285
views

0
downloads

Harmonic balance method (HBM) is one of the most popular and powerful methods, which is used to obtain response of nonlinear vibratory systems in frequency domain. The main idea of the method is to express the response of the system in Fourier series and converting the nonlinear differential equations of motion into a set of nonlinear algebraic equations. System response can be obtained by solving this nonlinear equation set in terms of the unknown Fourier coefficients. The accuracy of the solution is greatly affected by the number of harmonics included in the method and it is enhanced as the number of harmonics increases at the expense of computational time; hence, advantage of HBM over time integration method is lost. Therefore, it is desirable to use an adaptive algorithm where the number of harmonics can be optimized in terms of both accuracy and computational effort. In this paper a new adaptive harmonic balance method (AHBM) for the dynamic analysis of nonlinear structures is developed. The new method employs a two-step harmonic selection procedure where the criteria used are based on simple magnitude comparisons that make it easy to understand and program the method. A novel pseudo-response calculation method, which is used at the second harmonic selection step, is developed in order to estimate the response of the nonlinear system with, approximately, no additional computational cost. Due to the two-step harmonic selection procedure, the method eliminates unnecessary harmonics in the response calculation; hence, it is capable of increasing the computational efficiency of HBM significantly. Several case studies are given in order to show the applicability of the proposed adaptive harmonic balance method.

Subject Keywords

Control and Systems Engineering, Signal Processing, Mechanical Engineering, Civil and Structural Engineering, Aerospace Engineering, Computer Science Applications

URI

https://hdl.handle.net/11511/34708

Journal

MECHANICAL SYSTEMS AND SIGNAL PROCESSING

DOI

https://doi.org/10.1016/j.ymssp.2019.05.028

Collections

Department of Mechanical Engineering, Article

Suggestions

OpenMETU
Core

A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes Ferhatoglu, Erhan; Ciğeroğlu, Ender; Özgüven, Hasan Nevzat (Elsevier BV, 2018-07-01) In this paper, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the n...
A frequency domain nonparametric identification method for nonlinear structures: Describing surface method Karaagacli, Taylan; Özgüven, Hasan Nevzat (Elsevier BV, 2020-10-01) In this paper a new method called 'Describing Surface Method' (DSM) is developed for nonparametric identification of a localized nonlinearity in structural dynamics. The method makes use of the Nonlinearity Matrix concept developed in the past by using classical describing function theory, which assumes that nonlinearity depends mainly on the response amplitude and frequency dependence is negligible for almost all of the standard nonlinear elements. However, this may not always be the case for complex nonli...
Model updating of nonlinear structures from measured FRFs Canbaloglu, Guvenc; Özgüven, Hasan Nevzat (Elsevier BV, 2016-12-01) There are always certain discrepancies between modal and response data of a structure obtained from its mathematical model and experimentally measured ones. Therefore it is a general practice to update the theoretical model by using experimental measurements in order to have a more accurate model. Most of the model updating methods used in structural dynamics are for linear systems. However, in real life applications most of the structures have nonlinearities, which restrict us applying model updating techn...
A novel modal superposition method with response dependent nonlinear modes for periodic vibration analysis of large MDOF nonlinear systems Ferhatoglu, Erhan; Ciğeroğlu, Ender; Özgüven, Hasan Nevzat (Elsevier BV, 2020-01-01) Design of complex mechanical structures requires to predict nonlinearities that affect the dynamic behavior considerably. However, finding the forced response of nonlinear structures is computationally expensive, especially for large ordered realistic finite element models. In this paper, a novel approach is proposed to reduce computational time significantly utilizing Response Dependent Nonlinear Mode (RDNM) concept in determining the steady state periodic response of nonlinear structures. The method is ap...
Identification of structural non-linearities using describing functions and the Sherman-Morrison method Ozer, Mehmet Bulent; Özgüven, Hasan Nevzat; Royston, Thomas J. (Elsevier BV, 2009-01-01) In this study, a new method for type and parametric identification of a non-linear element in an otherwise linear structure is introduced. This work is an extension of a previous study in which a method was developed to localize non-linearity in multi-degree of freedom systems and to identify type and parameters of the non-linear element when it is located at a ground connection of the system. The method uses a describing function approach for representing the non-linearity in the structure. The describing ...

Citation Formats

O. Sert and E. Ciğeroğlu, “A novel two-step pseudo-response based adaptive harmonic balance method for dynamic analysis of nonlinear structures,” MECHANICAL SYSTEMS AND SIGNAL PROCESSING, pp. 610–631, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34708.