In this paper, the coupling effects among three elastic wave modes, flexural, tangential, and radial shear, on the dynamics of a planar curved beam are assessed. Two sets of equations of motion governing the in-plane motion of a curved beam are derived, in a consistent manner, based on the theory of elasticity and Hamilton’s principle. The first set of equations retains all resulting linear coupling terms that includes both static and dynamic coupling among the three wave modes. In the derivation of the second set of equations, the effects of Coriolis acceleration and high-order elastic coupling terms are neglected, which leads to a set of equations without dynamic coupling terms between the tangential and shear wave modes. This second set of equations of motion is the one most commonly used in studies on thick curved beams that include the effects of centerline extensibility, rotary inertia, and shear deformation. The assessment is carried out by comparing the dynamic behavior predicted by each curved beam model in terms of the dispersion relations, frequency spectra, cutoff frequencies, natural frequencies and mode shapes, and frequency responses. In order to ensure the comparison is based on accurate results, the wave propagation technique is applied to obtain exact wave solutions. The results suggest that the contributions of the dynamic and high-order elastic coupling terms to the response of a thick curved beam are quite significant and that these coupling terms should not be neglected for an accurate analysis of a thick curved beam with a large curvature parameter.
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e-mail: kang@engr.ipfw.edu
e-mail: riedel@ltu.edu
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February 2012
Research Papers
Coupling of In-Plane Flexural, Tangential, and Shear Wave Modes of a Curved Beam
B. Kang,
B. Kang
Mechanical Engineering Department,
e-mail: kang@engr.ipfw.edu
Indiana University - Purdue University Fort Wayne
, Fort Wayne, IN 46805-1499
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C. H. Riedel
C. H. Riedel
Mechanical Engineering Department,
e-mail: riedel@ltu.edu
Lawrence Technological University
, Southfield, MI 48075-1058
Search for other works by this author on:
B. Kang
Mechanical Engineering Department,
Indiana University - Purdue University Fort Wayne
, Fort Wayne, IN 46805-1499e-mail: kang@engr.ipfw.edu
C. H. Riedel
Mechanical Engineering Department,
Lawrence Technological University
, Southfield, MI 48075-1058e-mail: riedel@ltu.edu
J. Vib. Acoust. Feb 2012, 134(1): 011001 (13 pages)
Published Online: December 22, 2011
Article history
Received:
August 17, 2010
Revised:
May 12, 2011
Online:
December 22, 2011
Published:
December 22, 2011
Citation
Kang, B., and Riedel, C. H. (December 22, 2011). "Coupling of In-Plane Flexural, Tangential, and Shear Wave Modes of a Curved Beam." ASME. J. Vib. Acoust. February 2012; 134(1): 011001. https://doi.org/10.1115/1.4004676
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