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A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods
Joint Authors
El-Sayed, Tamer Ahmed
Farghaly, Said Hamed
Source
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-23, 23 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-11-28
Country of Publication
Egypt
No. of Pages
23
Main Subjects
Abstract EN
The exact solution for multistepped Timoshenko beam is derived using a set of fundamental solutions.
This set of solutions is derived to normalize the solution at the origin of the coordinates.
The start, end, and intermediate boundary conditions involve concentrated masses and linear and rotational elastic supports.
The beam start, end, and intermediate equations are assembled using the present normalized transfer matrix (NTM).
The advantage of this method is that it is quicker than the standard method because the size of the complete system coefficient matrix is 4 × 4.
In addition, during the assembly of this matrix, there are no inverse matrix steps required.
The validity of this method is tested by comparing the results of the current method with the literature.
Then the validity of the exact stepped analysis is checked using experimental and FE(3D) methods.
The experimental results for stepped beams with single step and two steps, for sixteen different test samples, are in excellent agreement with those of the three-dimensional finite element FE(3D).
The comparison between the NTM method and the finite element method results shows that the modal percentage deviation is increased when a beam step location coincides with a peak point in the mode shape.
Meanwhile, the deviation decreases when a beam step location coincides with a straight portion in the mode shape.
American Psychological Association (APA)
El-Sayed, Tamer Ahmed& Farghaly, Said Hamed. 2017. A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods. Shock and Vibration،Vol. 2017, no. 2017, pp.1-23.
https://search.emarefa.net/detail/BIM-1205075
Modern Language Association (MLA)
El-Sayed, Tamer Ahmed& Farghaly, Said Hamed. A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods. Shock and Vibration No. 2017 (2017), pp.1-23.
https://search.emarefa.net/detail/BIM-1205075
American Medical Association (AMA)
El-Sayed, Tamer Ahmed& Farghaly, Said Hamed. A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods. Shock and Vibration. 2017. Vol. 2017, no. 2017, pp.1-23.
https://search.emarefa.net/detail/BIM-1205075
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1205075