Exact Out-of-Plane Natural Frequencies of Curved Timoshenko Beams
Publication: Journal of Engineering Mechanics
Volume 125, Issue 1
Abstract
A powerful and efficient method is presented for finding exact out-of-plane natural frequencies of plane structures composed of curved Timoshenko beams. Initially, exact dynamic stiffnesses are derived from the governing differential equations of motion in a form that can be used directly in the stiffness method of analysis. This enables any appropriate structure to be modeled according to standard techniques, which, in this case, yield a transcendental eigenvalue problem. Then it is shown how any desired natural frequency may be obtained with certainty by employing a modification to a well-established algorithm, which ensures that no natural frequencies can be missed and avoids the usual approximations associated with traditional finite elements. Finally, comparisons are made with published results and an example shows how the natural frequencies of a continuous curved beam are altered when the effects of shear deflection and rotary inertia are considered.
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References
1.
Anderson, M. S., and Williams, F. W. ( 1986). “BUNVIS-RG: An exact buckling and vibration program for lattice structures with repetitive geometry and substructuring options.” 27th AIAA/ASME/ASCE/AHS Structs., Struct. Dyn. and Mat. Conf., Part 2, American Institute of Aeronautics and Astronautics, New York, 211–220.
2.
Bickford, W. B., and Strom, B. T. ( 1975). “Vibration of plane curved beams.” J. Sound Vib., 39(2), 135–146.
3.
Burton, D. M. ( 1985). “The history of mathematics: An introduction.” Allyn and Bacon, Boston.
4.
Davis, R., Henshell, R. D., and Warburton, G. B. ( 1972). “Curved beam finite elements for coupled bending and torsional vibration.” Earthquake Engrg. and Struct. Dynamics, 1, 165–175.
5.
Gupta, A. K., and Howson, W. P. ( 1994). “Exact natural frequencies of plane structures composed of slender elastic curved members.” J. Sound Vib., 175(2), 145–157.
6.
Howson, W. P. ( 1979). “A compact method for computing the eigenvalues and eigenvectors of plane frames.” Advances in Engrg. Software, 1(4), 181–190.
7.
Howson, W. P., Jemah, A. K., and Zhou, J. Q. ( 1995). “Exact natural frequencies for out-of-plane motion of plane structures composed of curved beam members.” Comp. and Struct., 55(6), 989–995.
8.
Howson, W. P., and Williams, F. W. ( 1973). “Natural frequencies of frames with axially loaded Timoshenko members.” J. Sound Vib., 26(4), 503–515.
9.
Irie, T., Yamada, G., and Tanaka, K. ( 1982). “Natural frequencies of out-of-plane vibration of arcs.” Trans. of the Am. Soc. of Mech. Engrs. J. of Appl. Mech., 49, 910–913.
10.
Kang, K., Bert, C. W., and Striz, A. G. ( 1995). “Vibration analysis of shear deformable circular arches by the differential quadrature method.” J. Sound Vib., 183(2), 353–360.
11.
Oden, J. T. ( 1967). “Mechanics of elastic structures.” McGraw-Hill, London.
12.
Volterra, V., and Gaines, J. H. ( 1971). “Advanced strength of materials.” Prentice-Hall, Englewood Cliffs, N.J.
13.
Wittrick, W. H., and Williams, F. W. ( 1971). “A general algorithm for computing natural frequencies of elastic structures.” Quarterly J. Mech. Appl. Math., 24(3), 263–284.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 125 • Issue 1 • January 1999
Pages: 19 - 25
History
Received: Jan 26, 1998
Published online: Jan 1, 1999
Published in print: Jan 1999
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