Vibration analysis of pretwisted beams for the design of hybrid axial-torsional transducers

Liu, K, Friend, J and Yeo, L 2007, 'Vibration analysis of pretwisted beams for the design of hybrid axial-torsional transducers', in Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Honolulu, Hawaii, United States, 23-26 April 2007, pp. 6974-6993.


Document type: Conference Paper
Collection: Conference Papers

Title Vibration analysis of pretwisted beams for the design of hybrid axial-torsional transducers
Author(s) Liu, K
Friend, J
Yeo, L
Year 2007
Conference name 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
Conference location Honolulu, Hawaii, United States
Conference dates 23-26 April 2007
Proceedings title Proceedings of the 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
Publisher American Institute of Aeronautics and Astronautics, Inc
Place of publication USA
Start page 6974
End page 6993
Total pages 20
Abstract A new design for hybrid axial-torsional transducers using pretwisted beams requires the resonance frequencies of the torsional and axial vibration modes to be matched. To aid in designing such transducers, the effects of increasing pretwist and changing the cross-section geometry on the resonance frequencies are investigated analytically. The governing equations and boundary conditions for extension, torsion, and cross-sectional warping are derived using the semi-inverse method and Hamilton's principle. A general set of differential equations for the cross-sectional warping of pretwisted beams is derived. Through scaling, the warping function is shown to be locally similar to the Saint-Venant warping function when the beam is slender, low in pretwist, and torsional deformation is dominant. Using this approach, geometric and material limitations in the use of the Saint-Venant's warping function are illustrated, beyond which the simpler form may no longer be used. The simplified equations of motion are solved under the free-free boundary condition for resonance frequencies and mode shapes, and a comparison with finite element analysis illustrates the limitations
Subjects Fluid Physics
Acoustics and Acoustical Devices; Waves
Interdisciplinary Engineering not elsewhere classified
Medical Devices
DOI - identifier 10.2514/6.2007-2278
Copyright notice © 2007 AIAA
ISBN 9781563478925
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