Analytical formulation and evaluation for free vibration of naturally curved and twisted beams

Journal of Sound and Vibration - Tập 329 - Trang 1376-1389 - 2010
A.M. Yu1, C.J. Yang2, G.H. Nie1
1School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, PR China
2School of Urban Railway Transportation, Soochow University, Suzhou 215021, PR China

Tài liệu tham khảo

Washizu, 1964, Some considerations on a naturally curved and twisted slender beam, Journal of Mathematical Physics, 43, 111, 10.1002/sapm1964431111

Yu, 2002, Theoretical research on naturally curved and twisted beams under complicated loads, Computers and Structures, 80, 2529, 10.1016/S0045-7949(02)00329-2

Yu, 2006, Generalized coordinate for warping of naturally curved and twisted beams with general cross-sectional shapes, International Journal of Solids and Structures, 43, 2853, 10.1016/j.ijsolstr.2005.05.045

Sanchez-Hubert, 1999, Statics of curved rods on account of torsion and flexion, European Journal of Mechanics, A/Solids, 18, 365, 10.1016/S0997-7538(99)00132-1

Ignat, 2002, A model of a general elastic curved rod, Mathematical Methods in the Applied Sciences, 25, 835, 10.1002/mma.315

Wittrick, 1966, On elastic wave propagation in helical springs, International Journal of Mechanical Sciences, 8, 25, 10.1016/0020-7403(66)90061-0

Sazonov, 1977, Wave propagation in curved rods of variable cross section, Soviet Physics, Acoustics (English Translation of Akusticheskii Zhurnal), 23, 163

Tabarrok, 1988, On the dynamics of spatially curved and twisted rods-a finite element formulation, Journal of Sound and Vibration, 123, 315, 10.1016/S0022-460X(88)80114-7

Karami, 1990, Free vibrations of spatial rods. A finite-element analysis, Communications in Applied Numerical Methods, 6, 417, 10.1002/cnm.1630060602

Benedetti, 1996, Simple and effective equilibrium models for vibration analysis of curved rods, Journal of Engineering Mechanics Division—ASCE, 122, 291, 10.1061/(ASCE)0733-9399(1996)122:4(291)

Farshad, 1980, Wave propagation in prestressed curved rods, Journal of Engineering Mechanics Division—ASCE, 106, 395, 10.1061/JMCEA3.0002591

Shih., 2005, Natural vibration of arbitrary spatially curved rectangular rods with pretwisted angles, Journal of Sound and Vibration, 285, 925, 10.1016/j.jsv.2004.09.005

Yildirim, 1997, Natural frequencies of helical springs of arbitrary shape, Journal of Sound and Vibration, 204, 311, 10.1006/jsvi.1997.0940

Shorr, 1966, Fundamentals of the theory of twisted blades with a curved axis, Prochnost i Dinamika Aviatsionnykh Dvigatelei, 3, 188

Greben, 1967, On the theory of thin bars, Mekhanika Tverdogo Tela, 67

Song, 1993, Free vibration of anisotropic composite thin-walled beams of closed cross-section contour, Journal of Sound and Vibration, 167, 129, 10.1006/jsvi.1993.1325

Brancheriau, 2006, Influence of cross section dimensions on Timoshenko's shear factor application to wooden beams in free-free flexural vibration, Annals of Forest Science, 63, 319, 10.1051/forest:2006011

Timoshenko, 1921, On the correction for shear of the differential equation for transverse vibrations of prismatic bars, Philosophical Magazine Series 6, 41, 744, 10.1080/14786442108636264

Yildirim, 1996, Investigation of parameters affecting free vibration frequency of helical springs, International Journal for Numerical Methods in Engineering, 39, 99, 10.1002/(SICI)1097-0207(19960115)39:1<99::AID-NME850>3.0.CO;2-M

Wahl, 1963

V. Haktanir, E. Kiral, Determination of free vibration frequencies of helical springs by the Myklestad method, Proceedings of the Fourth National Symposium on Machinery Theory, Istanbul, September, 1990, pp. 479–488 (in Turkish).