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Normalization of Complex Mode Shapes by Truncation of the Alpha-Polynomial

Niranjan, Adityanarayan C
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1448037029

Abstract Details

2015, MS, University of Cincinnati, Engineering and Applied Science: Mechanical Engineering.
Finite element (FE) models are created to correctly predict the dynamic characteristics of any system without the need to test the system. This is a viable solution to test the system in situations and environments which might be either physically unfeasible or exorbitantly expensive. These FE models however need to be validated with the data obtained from actual tests to affirm that the model's predictions are indeed correct. One parameter that is needed to validate analytical model is the mode shape. The mode shapes obtained from F.E. models are always real-valued due to the proportional nature of the assumed damping. The mode shapes obtained through experimental techniques, however, are more often than not complex-valued (complex modes) in nature. In order to validate the F.E. models, the complex mode shapes obtained from experimental data needs to be normalized. In this thesis, two such normalization techniques have been proposed. Over the years, several post-processing techniques have been suggested which are discussed briefly in Chapter (2). In this thesis, of the two proposed techniques, the first method is a pre-processing normalization technique based on truncating the alpha-polynomial obtained from the Unified Matrix Polynomial Approach (UMPA) method of modal parameter estimation. The proposed concept was tested on data obtained from a circular plate using frequency domain based high order algorithm Rational Fraction Polynomial (RFP). The proposed technique eliminated the damping and normalized the complex modal vectors effectively in low order polynomial based algorithms like Polyreference Frequency Domain - 2 (PFD - 2). The undamped natural frequencies, however, deviated from that of the actual system in case of polynomials with order higher than two. These digressions are explained with the help of 2 and 4 degree of freedom (DOF) analytical models. The second normalization method proposed is a post-processing technique based on the partial fraction method of residue synthesis. This technique was tested on data obtained from a rectangular plate. The technique successfully normalized the complex modal vectors with a very good correlation with the actual (complex) mode shapes giving a very high modal assurance criterion (MAC) value.
Randall Allemang, Ph.D. (Committee Chair)
David L. Brown, Ph.D. (Committee Member)
Allyn Phillips, Ph.D. (Committee Member)
104 p.
Mechanics
Normalization; Truncation of the alpha-polynomial; Complex mode shapes; Damping distribution

Recommended Citations

Citations

  • Niranjan, A. C. (2015). Normalization of Complex Mode Shapes by Truncation of the Alpha-Polynomial [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1448037029

    APA Style (7th edition)

  • Niranjan, Adityanarayan . Normalization of Complex Mode Shapes by Truncation of the Alpha-Polynomial. 2015. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1448037029.

    MLA Style (8th edition)

  • Niranjan, Adityanarayan . "Normalization of Complex Mode Shapes by Truncation of the Alpha-Polynomial." Master's thesis, University of Cincinnati, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1448037029

    Chicago Manual of Style (17th edition)

ucin1448037029
1,948
© 2015, some rights reserved.Creative Commons License Normalization of Complex Mode Shapes by Truncation of the Alpha-Polynomial by Adityanarayan C Niranjan is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by University of Cincinnati and OhioLINK.