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Continuum-based free vibration of circular trigonal and isotropic plates
Paul R Heyliger1, Ward Johnson
1Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado 80523, USA.
The Journal of the Acoustical Society of America
|August 10, 2013
Summary
This study explores free vibration in circular plates, comparing trigonal symmetry to isotropic materials. It validates the accuracy of 3D elasticity theory against simplified thin plate theories for vibration analysis.
Area of Science:
- Solid Mechanics
- Vibrational Analysis
- Continuum Mechanics
Background:
- Understanding the free vibration of elastic plates is crucial for structural integrity and design.
- Existing simplified theories may not fully capture the complexities of anisotropic materials.
- Trigonal material symmetry introduces unique behaviors not present in isotropic materials.
Purpose of the Study:
- To investigate the influence of trigonal material symmetry on the free vibration modes of circular plates.
- To assess the accuracy of thin plate theory compared to three-dimensional elasticity theory for these plates.
- To provide quantitative insights into the vibrational behavior of such structures.
Main Methods:
- Employed approximate continuum solutions based on the three-dimensional theory of linear elasticity.
- Utilized the weak form of the equations of motion and the Ritz method in cylindrical coordinates.
- Applied group-theoretical symmetry analysis to decompose the eigenvalue problem.
Main Results:
- Calculated resonant frequencies for unrestrained elastic circular plates.
- Demonstrated the distinct impact of trigonal material symmetry on vibration modes.
- Provided a quantitative comparison between 3D elasticity and thin plate theory predictions.
Conclusions:
- Trigonal material symmetry significantly affects the free vibration characteristics of circular plates.
- Three-dimensional elasticity theory offers a more accurate representation than thin plate theory for these cases.
- The employed methodology effectively analyzes complex vibrational behaviors and provides valuable quantitative data.
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