Transverse vibrations of tapered materially inhomogeneous axially loaded shafts
 Arnaldo J. Mazzei Jr.,
 Richard A. Scott
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Abstract
Shafts loaded by axial compressive constant forces constitute an area of considerable technical importance. The transverse vibration of such shafts is the subject of the current work. Occasionally the shafts are tapered and of interest is the effect of employing functionally graded materials (FGM), with properties varying in the axial direction, on the buckling load and lowest natural frequency. The shaft cross section is circular and two types of taper are treated, namely, linear and sinusoidal. All shafts have the same volume and length and are subjected to a constant axial force below the static buckling load. EulerBernoulli theory is used with the axial force handled by a buckling type model. The problems that arise are computationally challenging but an efficient strategy employing MAPLE®’s twopoint boundary value solver has been developed. Typical results for a linear tapered pinpin shaft where one end radius is twice the other, and the FGM model varies in a power law fashion with material properties increasing in the direction of increasing area, include doubling of the buckling load and first bending frequency increase of approximately 43%, when compared to a homogeneous tapered shaft. For the same material and boundary conditions, a sinusoidal shaft, with midradius twice the value of the end ones, increases the buckling load by about 118% and the first frequency by 26%, when compared to a homogeneous sinusoidal shaft.
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 Title
 Transverse vibrations of tapered materially inhomogeneous axially loaded shafts
 Book Title
 Rotating Machinery, Structural Health Monitoring, Shock and Vibration, Volume 5
 Book Subtitle
 Proceedings of the 29th IMAC, A Conference on Structural Dynamics, 2011
 Pages
 pp 2536
 Copyright
 2011
 DOI
 10.1007/9781441994288_3
 Print ISBN
 9781441994271
 Online ISBN
 9781441994288
 Series Title
 Conference Proceedings of the Society for Experimental Mechanics Series
 Series ISSN
 21915644
 Publisher
 Springer New York
 Copyright Holder
 The Society for Experimental Mechanics, Inc.
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 Editors

 Tom Proulx ^{(ID1)}
 Editor Affiliations

 ID1. Society for Experimental Mechanics
 Authors

 Arnaldo J. Mazzei Jr. ^{(1)}
 Richard A. Scott ^{(2)}
 Author Affiliations

 1. Department of Mechanical Engineering, C. S. Mott Engineering and Science Center Kettering University, 1700 University Avenue, Flint, MI, 48504, USA
 2. Department of Mechanical Engineering G044 W. E. Lay Automotive Laboratory, University of Michigan, 1231 Beal Avenue, Ann Arbor, MI, 48109, USA
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