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Title: Coupled out of plane vibrations of spiral beams
Authors: Karami, M. A.
Yardımoğlu, Bülent
Inman, Daniel J.
Keywords: Perturbation techniques
Vibration problem
Spiral beams
Curved beams
Exponential solutions
Issue Date: 2009
Publisher: American Institute of Aeronautics and Astronautics Inc. (AIAA)
Source: Karami, M. A., Yardımoğlu, B., and Inman, D. J. (2009, May 4-7). Coupled out of plane vibrations of spiral beams. Paper presented at the 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Palm Springs, CA, United States.
Abstract: An analytical method is proposed to calculate the natural frequencies and corresponding mode shape functions of an Archimedean spiral beam. The deflection of the beam is due to both bending and torsion, which makes the problem coupled in nature. The governing partial differential equation and the boundary conditions are derived using Hamilton's principle. The vibration problem of a constant radius curved beam is solved using a general exponential solution with complex coefficients. Two factors make the vibrations of spirals different from oscillations of constant radius arcs. The first is the presence of terms with derivatives of the radius in the governing equations of spirals and the second is the fact that variations of radius of the beam causes the coefficients of the differential equations to be variable. It is demonstrated, using perturbation techniques that the R′ terms have negligible effect on the structure's dynamics. The spiral is then approximated with many merging constant-radius curved sections joint together to consider the slow change of radius along the spiral. The natural frequencies and mode shapes of two spiral structures have been calculated for illustration.
Description: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
ISBN: 9781563479731
ISSN: 0273-4508
Appears in Collections:Mechanical Engineering / Makina Mühendisliği
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection

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