Free Vibration of Doubly Curved Thin Shells

[+] Author and Article Information
April Bryan

No. 7 Jack Trace, Enterprise, Chaguanas, Trinidad and Tobago

1Corresponding author.

ASME doi:10.1115/1.4038578 History: Received August 12, 2017; Revised November 03, 2017


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 mid-surface and normal coordinates in the transverse differential equation of motion of the shell. In this research, an Uncoupling Theorem for solving the transverse differential equation of motion of doubly curved, thin shells with equivalent radii is introduced. 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.

Copyright (c) 2017 by ASME
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