Abstract
A finite thin circular beam element for the out-of-plane vibration analysis of curved beams is presented in this paper. Its stiffness matrix and mass matrix are derived, respectively, from the strain energy and the kinetic energy by using the natural shape functions derived from an integration of the differential equations in static equilibrium. The matrices are formulated with respect to the local polar coordinate system or to the global Cartesian coordinate system in consideration of the effects of shear deformation and rotary inertias. Some numerical examples are analyzed to confirm the validity of the element. It is shown that this kind of finite element can describe quite efficiently and accurately the out-of-plane motion of thin curved beams.
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This paper was recommended for publication in revised form by Associate Editor Seockhyun Kim
Chang-Boo Kim received his B.S. degree in Mechanical Engineering from Seoul University, Korea in 1973. He then received his D.E.A., Dr.-Ing. and Dr.-es-Science degrees from Nantes University, France in 1979, 1981 and 1984, respectively. Dr. Kim is currently a Professor at the School of Mechanical Engineering at Inha University in Incheon, Korea. His research interests are in the area of vibrations, structural dynamics, and MEMS.
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Kim, B.Y., Kim, CB., Song, S.G. et al. A finite thin circular beam element for out-of-plane vibration analysis of curved beams. J Mech Sci Technol 23, 1396–1405 (2009). https://doi.org/10.1007/s12206-008-1213-2
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DOI: https://doi.org/10.1007/s12206-008-1213-2