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.
Free Vibration of Doubly Curved Thin Shells
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.
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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
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