An Alternative Series Solution for Free Vibration Analysis of Asymmetric L-Shaped Membranes

This study revisits the freely vibrating problem of asymmetric L-shaped membranes using a three-segmented domain decomposition (3-SDD) strategy. Motivated by the need for more accurate and flexible methods, the 3-SDD strategy is compared with the previously proposed two-segmented domain decompositio...

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Bibliographic Details
Published inApplied sciences Vol. 14; no. 16; p. 7156
Main Authors Chang, Kao-Hao, Kuo, Wen-Ten
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2024
Subjects
Boundary conditions
Comparative analysis
Decomposition
domain decomposition
eigenvalue
free vibration
membrane
Membranes
Microelectromechanical systems
region matching
Sensors
series solution
Vibration
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Summary:This study revisits the freely vibrating problem of asymmetric L-shaped membranes using a three-segmented domain decomposition (3-SDD) strategy. Motivated by the need for more accurate and flexible methods, the 3-SDD strategy is compared with the previously proposed two-segmented domain decomposition (2-SDD) strategy. The region-matching technique is used to derive an alternative series solution, and the eigenvalues obtained are compared with those in existing research. The convergence behavior and sensitivity analyses reveal that the 3-SDD strategy offers improved accuracy and stability, particularly for higher truncation terms. Detailed comparisons of the first four eigenvalue squares show strong agreement between the 3-SDD and 2-SDD strategies, confirming the reliability of both methods. This research establishes a foundation for the vibration analysis of complex membrane structures, emphasizing the benefits of the 3-SDD approach for upcoming engineering applications and showcasing its potential for broader applicability in practical scenarios. The findings underscore the importance of utilizing multi-segmented decomposition strategies to enhance the accuracy and flexibility of free vibration analysis.
ISSN:2076-3417
2076-3417
DOI:10.3390/app14167156