A modified transfer matrix method to reduce the calculation time: A case study on beam vibration

The transfer matrix method is an analytical method for investigating the vibrations in many structures such as beams, sheets, and shells. In this method, the inverse of “zero matrices” should be calculated to determine the transfer matrix. The calculation of the inverse matrix increases the computat...

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Bibliographic Details
Published in:Applied mathematics and computation 2020-08, Vol.378, p.125238, Article 125238
Main Authors: Feyzollahzadeh, Mahdi, Bamdad, Mahdi
Format: Article
Language:English
Subjects:
Calculations time
Natural frequency
Rotary beam
Transfer matrix method
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Summary:The transfer matrix method is an analytical method for investigating the vibrations in many structures such as beams, sheets, and shells. In this method, the inverse of “zero matrices” should be calculated to determine the transfer matrix. The calculation of the inverse matrix increases the computational cost in computer programming. In this paper, a method is presented to reduce the order of the inverse matrix from 2n to n order. For this purpose, the rows of the state vector and constant coefficients vector are changed, therefore the transfer matrix becomes a block diagonal matrix which is more efficient in the computation of inverse matrix. It is performed for vibration analyzing of a rotating beam as a case study. Then the impact of computation time and accuracy characteristics upon the proposed modification on TMM is discussed.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2020.125238