A numerically efficient frequency domain method for analysis of non Linear multi degree of freedom systems

Date

2012-08-15

Author

Özer, Mehmet Bülent

Metadata

Show full item record

Item Usage Stats

161
views

0
downloads

Linear structural models contain mass, stiffness and damping matrices as well as a forcing vector. Once these matrices and the forcing vector are known, the response can be calculated through the methods of linear algebra. The system matrices of the linear model do not contain any terms that depend on the system response vector, therefore the calculation of the system response do not require an iterative procedure. On the other hand, frequency domain analysis of non-linear structural models generally contain terms that are non-linear functions of the system response vector. Therefore these terms make the system matrices become dependent on the non-linear system response vector itself. This forces one to employ an iterative solution. The disadvantage of the iterative solution is more pronounced when large degree of freedom systems are analyzed. For each frequency value, the iterative procedure requires solution of large system of equations to be evaluated several times until the iterative procedure converges to a value. Therefore the numerical cost significantly increases as the model size gets larger. This study introduces a method which requires one-time calculation of response of the linear part of the system. After finding the response of the linear part, no further matrix inversions are needed to iteratively find the non-linear system response. In the case studies it will be shown that the proposed method has significant computation time advantages to conventional time domain and frequency domain methods for solution of large non-linear structural models. In order to employ this numerically efficient method, describing function theory is used to obtain a non-linearity matrix which contains the non-linear terms. Also, a computationally efficient recursive method is used to evaluate the inverse of the sum of the linear system impedance and the non-linearity matrix. In order to employ this recursive method the non-linearity matrix is decomposed into summation of rank-one matrices.

URI

https://hdl.handle.net/11511/72411
http://apps.webofknowledge.com/full_record.do?product=UA&search_mode=GeneralSearch&qid=3&SID=E4CTPfwdICKbGfMFVPa&page=1&doc=1

Conference Name

4th Conference on Mechanical Vibration and Noise (12 - 15 Ağustos 2012)

Collections

Department of Mechanical Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

AN EMPIRICAL TORQUE NOISE AND SPIN-UP MODEL FOR ACCRETION-POWERED X-RAY PULSARS Baykal, Altan (1993-01-01) By using the first order autoregressive time series model, rotation histories of accretion-powered X-ray pulsars are modeled yielding a torque noise strength S(in) and the average secular spin-up term [OMEGA]. We find that Her X-1, Cen X-3, A0535 + 26, and Vela X-1 can be modeled with white torque-noise leading to random walks in pulse frequency; for the remaining sources the random walk model is also acceptable. Using this model we calculate the noise strengths in the frequency derivative and estimate the ...
An advanced boundary element method (BEM) implementation for the forward problem of electromagnetic source imaging Akahn-Acar, Z; Gençer, Nevzat Güneri (IOP Publishing, 2004-11-07) The forward problem of electromagnetic source imaging has two components: a numerical model to solve the related integral equations and a model of the head geometry. This study is on the boundary element method (BEM) implementation for numerical solutions and realistic head modelling. The use of second-order (quadratic) isoparametric elements and the recursive integration technique increase the accuracy in the solutions. Two new formulations are developed for the calculation of the transfer matrices to obta...
Extended dynamical symmetries of Landau levels in higher dimensions Kürkcüoğlu, Seçkin; YURDUŞEN, İSMET (Springer Science and Business Media LLC, 2020-02-14) Continuum models for time-reversal (TR) invariant topological insulators (Tis) in d >= 3 dimensions are provided by harmonic oscillators coupled to certain SO(d) gauge fields. These models are equivalent to the presence of spin-orbit (SO) interaction in the oscillator Hamiltonians at a critical coupling strength (equivalent to the harmonic oscillator frequency) and leads to flat Landau Level (LL) spectra and therefore to infinite degeneracy of either the positive or the negative helicity states depending on...
A computational model for partially plastic stress analysis of orthotropic variable thickness disks subjected to external pressure Eraslan, Ahmet Nedim; Yedekçi, Buşra (2014-04-01) A computational model is developed to predict the states of stressand deformation in partially plastic, orthotropic, variable thickness, nonisothermal, stationary annular disks under external pressure. Assuming a state ofplane stress and using basic equations of mechanics of a disk, Maxwell relation,Hill’s quadratic yield condition, and a Swift type nonlinear hardening law, asingle governing differential equation describing the elastic and partially plasticresponse of an orthotropic, variable thickness, non...
A NEW METHOD FOR HARMONIC RESPONSE OF NONPROPORTIONALLY DAMPED STRUCTURES USING UNDAMPED MODAL DATA Özgüven, Hasan Nevzat (Elsevier BV, 1987-09-08) A method of calculating the receptances of a non-proportionally damped structure from the undamped modal data and the damping matrix of the system is presented. The method developed is an exact method. It gives exact results when exact undamped receptances are employed in the computation. Inaccuracies are due to the truncations made in the calculation of undamped receptances. Numerical examples, demonstrating the accuracy and speed of the method when truncated receptance series are used are also presented. ...

Citation Formats

M. B. Özer, “A numerically efficient frequency domain method for analysis of non Linear multi degree of freedom systems,” Chicago, IL, USA, 2012, p. 537, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/72411.