While several numerical approaches exist for the vibration analysis of thin shells, there is a lack of analytical approaches to address this problem. This is due to complications that arise from coupling between the midsurface and normal coordinates in the transverse differential equation of motion (TDEM) of the shell. In this research, an Uncoupling Theorem for solving the TDEM of doubly curved, thin shells with equivalent radii is introduced. The use of the uncoupling theorem leads to the development of an uncoupled transverse differential of motion for the shells under consideration. Solution of the uncoupled spatial equation results in a general expression for the eigenfrequencies of these shells. The theorem is applied to four shell geometries, and numerical examples are used to demonstrate the influence of material and geometric parameters on the eigenfrequencies of these shells.
Skip Nav Destination
Article navigation
June 2018
Research-Article
Free Vibration of Doubly Curved Thin Shells
April Bryan
April Bryan
Mem. ASME
No. 7 Jack Trace, Enterprise,
Chaguanas 500234, Trinidad and Tobago
e-mail: aprilbr@gmail.com
No. 7 Jack Trace, Enterprise,
Chaguanas 500234, Trinidad and Tobago
e-mail: aprilbr@gmail.com
Search for other works by this author on:
April Bryan
Mem. ASME
No. 7 Jack Trace, Enterprise,
Chaguanas 500234, Trinidad and Tobago
e-mail: aprilbr@gmail.com
No. 7 Jack Trace, Enterprise,
Chaguanas 500234, Trinidad and Tobago
e-mail: aprilbr@gmail.com
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 12, 2017; final manuscript received November 3, 2017; published online December 20, 2017. Assoc. Editor: Stefano Lenci.
J. Vib. Acoust. Jun 2018, 140(3): 031003 (11 pages)
Published Online: December 20, 2017
Article history
Received:
August 12, 2017
Revised:
November 3, 2017
Citation
Bryan, A. (December 20, 2017). "Free Vibration of Doubly Curved Thin Shells." ASME. J. Vib. Acoust. June 2018; 140(3): 031003. https://doi.org/10.1115/1.4038578
Download citation file:
Get Email Alerts
Cited By
Primary Resonance in a Weakly Forced Oscillator With Both Parametric Damping and Stiffness
J. Vib. Acoust (February 2024)
Reduced-Order Modeling in Rotordynamics and Its Robustness to Random Matrix Perturbation
J. Vib. Acoust (February 2024)
Reviewer's Recognition
J. Vib. Acoust (February 2024)
Related Articles
Axisymmetrical Vibrations of Underwater Hemispherical Shells
J. Eng. Ind (August,1976)
Stress Analysis of Thin Elasto-Plastic Shells
J. Eng. Ind (August,1971)
Classical Versus Improved Thin Shell Theories: A Theoretical Argument or a Design Concern?
J. Pressure Vessel Technol (February,1997)
Small-Scale Yielding at the Tip of a Through-Crack in a Shell
J. Pressure Vessel Technol (May,1980)
Related Proceedings Papers
Related Chapters
Stress in Shells of Revolution Due to Axisymmetric Loads
Stress in ASME Pressure Vessels, Boilers, and Nuclear Components
Introduction to Analysis Tools
Dynamics of Particles and Rigid Bodies: A Self-Learning Approach
Spherical Shells, Heads, and Transition Sections
Guidebook for the Design of ASME Section VIII Pressure Vessels