Free Axial Vibrations of Non-Uniform Rods

Shu Qi Guo; Shao Pu Yang

doi:10.4028/www.scientific.net/AEF.2-3.882

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HomeAdvanced Engineering ForumAdvanced Engineering Forum Vols. 2-3Free Axial Vibrations of Non-Uniform Rods

Free Axial Vibrations of Non-Uniform Rods

Abstract:

Free axial vibrations of non-uniform rods are investigated by a proposed method, which results in a series solution. In a special case, with the proposed method an exact solution with a concise form can be obtained, which imply four types of proﬁles with variation in geometry or material properties. However, the WKB (Wentzel-Kramers-Brillouin) method leads to a series solution, which is a Taylor expansion of the results of the pro-posed method. For the arbitrary non-uniform rods, the comparison indicates that the WKB method is simpler, but the convergent speed of the series solution resulting from the proposed method is faster than that of the WKB method, which is also validated numerically using an exact solution of a kind of non-uniform rods with Kummer functions.

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Periodical:

Advanced Engineering Forum (Volumes 2-3)

Pages:

882-889

DOI:

https://doi.org/10.4028/www.scientific.net/AEF.2-3.882

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Online since:

December 2011

Authors:

Shu Qi Guo, Shao Pu Yang

Keywords:

Axial Vibration, Non-Uniform Rod, Series Solution, WKB Method

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