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Vibration of elliptic cylindrical shells: higher order shell theory
Sabih I Hayek1, Jeffrey E Boisvert
1Department of Engineering Science and Mechanics, Penn State University, University Park, Pennsylvania 16802-6812, USA.
The Journal of the Acoustical Society of America
|September 7, 2010
Summary
This study analyzes the free vibration of elliptic cylindrical shells using advanced shell theory. Results reveal a seven-branch frequency-wavenumber spectrum, crucial for understanding shell dynamics.
Area of Science:
- Solid Mechanics
- Structural Dynamics
- Acoustics
Background:
- Free vibration analysis is crucial for understanding the dynamic behavior of shells.
- Elliptic cylindrical shells exhibit complex vibrational modes due to their geometry.
- Higher-order shell theories are necessary to capture intricate deformation effects.
Purpose of the Study:
- To derive and analyze the free vibration characteristics of a finite, constant-thickness elliptic cylindrical shell.
- To incorporate shear deformation, rotary inertia, and thickness stretch effects in the analysis.
- To investigate the influence of shell geometry and boundary conditions on natural frequencies.
Main Methods:
- Employed the Ritz approach for deriving the governing equations.
- Utilized a higher-order shell theory accounting for shear, rotary inertia, and thickness stretch.
- Expanded modal solutions using doubly infinite series of circular functions.
Main Results:
- Developed a frequency-wavenumber spectrum with seven distinct branches (flexural, extensional, torsional, thickness shear, thickness stretch).
- Obtained symmetric and positive definite coupled algebraic equations for natural frequencies.
- Presented numerical results for natural frequencies across various elliptic shapes and shell parameters, including a cylindrical limit.
Conclusions:
- The derived model accurately captures the complex vibration modes of elliptic cylindrical shells.
- The study provides a comprehensive understanding of the vibrational behavior influenced by geometry and material properties.
- The findings are applicable to the design and analysis of shell structures in various engineering applications.
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