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Volume 4, Issue 3
A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems

Rongming Lin

DOI: 10.4208/aamm.10-m11102

Adv. Appl. Math. Mech., 4 (2012), pp. 325-339.

Published online: 2012-04

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  • Abstract

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems. This paper presents a novel perturbative iteration (PI) algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems. Mathematical formulations of the proposed method are developed and based on these formulations, a computer algorithm is devised. Extensive numerical case examples are given to demonstrate the practicality of the proposed method. When all modes are included, the method is exact and when only a subset of modes are used, very accurate results are obtained.

  • Keywords

Frequency dependent eigenvalue problem, structural vibration, computer algorithm, damped structural vibration, perturbative iteration, eigenvalue and eigenvector sensitivity.

  • AMS Subject Headings

34L15, 34L16, 35P15, 35P30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{AAMM-4-325, author = {Lin , Rongming}, title = {A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {3}, pages = {325--339}, abstract = {

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems. This paper presents a novel perturbative iteration (PI) algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems. Mathematical formulations of the proposed method are developed and based on these formulations, a computer algorithm is devised. Extensive numerical case examples are given to demonstrate the practicality of the proposed method. When all modes are included, the method is exact and when only a subset of modes are used, very accurate results are obtained.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m11102}, url = {http://global-sci.org/intro/article_detail/aamm/122.html} }
TY - JOUR T1 - A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems AU - Lin , Rongming JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 325 EP - 339 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m11102 UR - https://global-sci.org/intro/article_detail/aamm/122.html KW - Frequency dependent eigenvalue problem, structural vibration, computer algorithm, damped structural vibration, perturbative iteration, eigenvalue and eigenvector sensitivity. AB -

Many engineering structures exhibit frequency dependent characteristics and analyses of these structures lead to frequency dependent eigenvalue problems. This paper presents a novel perturbative iteration (PI) algorithm which can be used to effectively and efficiently solve frequency dependent eigenvalue problems of general frequency dependent systems. Mathematical formulations of the proposed method are developed and based on these formulations, a computer algorithm is devised. Extensive numerical case examples are given to demonstrate the practicality of the proposed method. When all modes are included, the method is exact and when only a subset of modes are used, very accurate results are obtained.

Rongming Lin. (1970). A Novel Perturbative Iteration Algorithm for Effective and Efficient Solution of Frequency-Dependent Eigenvalue Problems. Advances in Applied Mathematics and Mechanics. 4 (3). 325-339. doi:10.4208/aamm.10-m11102
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