آناليز مودال سيستم هاي خطي متغير با زمان پريوديك و كاربرد آن بر روي يك تير با جرم متحرك

چكيده انگليسي :

Modal Analysis of Linear Time Periodic Systems with Application to Beam Moving Mass Systems Esmaeil Ghorbani esghorbani@gmail com march 05 2012 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language FarsiSupervisor s Name and Email Address Dr Mehdi Keshmiri Associate Professor mehdik@cc iut ac irAbstractSimilar to linear time invariant systems modal analysis methods for linear time varying systems have beendeveloped both in frequency and time domains However due to the variable nature of these systems withtime use of time frequency identification methods have been also considered in the recent years Many well developed concepts and analytic methods of linear time invariant systems cannot be applied to linear timevarying systems and these system have been often dealt on a case by case basis In this thesis first accordingto the modal analysis methods for linear time invariant systems a time domain method for extracting modalparameters of linear time varying systems is presented and after introducing the procedure the modalparameters of a beam with moving mass have been extracted and the results are examined Generally mathematical theory of the time domain modal analysis methods is complex and difficult to implement Themethod presented in this thesis is no exception In order to introduce an easier approach with higherconvergence criteria Hilbert Hong transform is presented Hilbert Hong transform is a comparative methodand in contrast to other time frequency methods such as wavelet method is simpler and more capable Afterintroducing a Hilberrt Hong based method completely modal parameters of a vibration system are extractedusing free and forced vibration response of the system Empirical mode decomposition is the key point ofHilbert Huang that extract several intrinsic mode functions from a multi frequency vibration signal Manylinear structural dynamic systems such as wind turbines helicopter blades turbo machinery and a variety ofnonlinear structures linearized about a periodic limit cycle are modeled with time periodic coefficients Linear time periodic systems such as these may exhibit parametric resonance where the damping in thesystem is negative at certain rotational frequencies leading to catastrophic failure Therefore modal analysisof these LTP systems has been a main concern for researchers and engineers A method for extracting modalparameters of linear time periodic systems in the frequency domain are introduced too It has been showedthat the frequency response function and the assumptions used to determine the frequency response functionof linear time invariant systems can not be used for linear time periodic systems However using a newfrequency space a frequency response function for a linear time periodic system is introduced and it is shownthat with a combination of this function and frequency domain modal analysis methods for linear timeinvariant systems modal parameters of a linear time varying periodic system can be extracted At the end avery preliminary approach is presented to extract the time invariant modal natural frequency of a bridge frommodal analysis of the bridge response in the presence of moving vehicles To perform this analysis amodified homotopy perturbation method is used to relate the natural frequencies of the LTI and LTPresponses Key WordsBeam with Moving Mass Modal Analysis of Linear Time Varying Systems HankelMatrix Hilbert Huang Transform Modified Homotopy Perturbation Method

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آناليز مودال سيستم هاي خطي متغير با زمان پريوديك و كاربرد آن بر روي يك تير با جرم متحرك

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