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Vibrations of singly curved thin shells: Numerical results

: Aoki, Yohko; Maysenhölder, Waldemar

European Acoustics Association -EAA-; Danish Acoustical Society -DAS-:
Forum Acusticum 2011. Proceedings. CD-ROM : 27 June - 01 July, Aalborg, Denmark
Madrid: Spanish Acoustical Society, 2011
ISBN: 978-84-694-1520-7
Forum Acusticum <6, 2011, Aalborg>
European Congress on Acoustics <6, 2011, Aalborg>
Conference Paper
Fraunhofer IBP ()

This is the sequel to the previous paper by Maysenhölder & Aoki, which introduced differential equations in curvilinear coordinates for singly curved shells. The present paper provides numerical results and visualizations of time-harmonic vibrations of thin shells, such as cylinders with various cross-sections, and one-dimensionally periodic shapes. First, the transformation between Cartesian and curvilinear coordinates and the spatial variation of curvature are illustrated for parabolic and sinusoidal shapes. Then the dynamic behavior of finite shells is numerically predicted either by direct solution of the system of three partial differential equations or by solution of the equivalent eighth-order ordinary differential equation for the normal displacement component. Natural frequencies predicted by the two methods are identical, and they agree with the ones listed in references. The dynamic behavior of infinite shells is deduced from solutions of the corresponding sixth-order ordinary differential equation. Numerical results for infinite sinusoidal shapes reveal that the underlying differential equations have a problem with the rigid-body motion.