×

Out-of-plane dynamic stability analysis of curved beams subjected to uniformly distributed radial loading. (English. Ukrainian original) Zbl 1272.74314

Int. Appl. Mech. 46, No. 11, 1327-1337 (2011); translation from Prikl. Mekh., Kiev 46, No. 11, 133-144 (2010).
Summary: In this study, out-of-plane stability analysis of tapered cross-sectioned thin curved beams under uniformly distributed radial loading is performed by using the finite-element method. Solutions referred to as Bolotin’s approach are analysed for dynamic stability, and the first unstable regions are examined. Out-of-plane vibration and out-of-plane buckling analyses are also studied. In addition, the results obtained in this study are compared with the published results of other researchers for the fundamental frequency and critical lateral buckling load. The effects of subtended angle, variations of cross-section, and dynamic load parameter on the stability regions are shown in graphics.

MSC:

74H55 Stability of dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S05 Finite element methods applied to problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] M. R. Banan, G. Karami, and M. Farshad, ”Finite element stability analysis of curved beams on elastic foundation,” Math. Comp. Model., 14, 863–867 (1990). · Zbl 0729.73234 · doi:10.1016/0895-7177(90)90304-6
[2] Z. P. Bazant and L. Cedolin, Stability of Structures, Oxford Univ. Press, New York (1991).
[3] H. T. Belek, Vibration Characteristics of Shrouded Blades on Rigid and Flexible Disks, Ph D. Thesis, University of Surrey, England (1977).
[4] V. V. Bolotin, Dynamic Stability of Elastic Systems, Holden Day, San Francisco (1964). · Zbl 0125.15301
[5] N. Fukuchi and T. Tanaka, ”Non-periodic motions and fractals of a circular arch under follower forces with small disturbances,” Steel Compos. Struct., 6, No. 2, 87–101 (2006). · doi:10.12989/scs.2006.6.2.087
[6] C. S. Huang, Y. P. Tseng, and S. H. Chang, ”Out-of-plane dynamic response of non circular curved beams by numerical Laplace transform,” J. Sound Vibr., 215, No. 3, 40–424 (1998).
[7] K. J. Kang, C. W. Bert, and A. G. Striz, ”Vibration and buckling analysis of circular arches using DQM,” Comp. Struct., 60, No. 1, 49–57 (1995). · Zbl 0918.73354 · doi:10.1016/0045-7949(95)00375-4
[8] M. Kawakami, T. Sakiyama, H. Matsuda, and C. Morita, ”In-plane and out-of-plane free vibrations of curved beams with variable cross sections,” J. Sound Vibr., 187, No. 3, 381–401 (1995). · doi:10.1006/jsvi.1995.0531
[9] N. I. Kim and M. Y. Kim, ”Free vibration and elastic analysis of shear-deformable non-symmetric thin-walled curved beams: A centroid-shear center formulation,” Struct. Eng. Mech., 21, No. 1, 19–33 (2005). · doi:10.12989/sem.2005.21.1.019
[10] S. Y. Lee and J. C. Chao, ”Out-of-plane vibrations of curved non-uniform beams of constant radius,” J. Sound Vibr., 238, No. 3, 443–458 (2000). · doi:10.1006/jsvi.2000.3084
[11] S. Y. Lee and J. C. Chao, ”Exact solutions for out-of-plane vibration of curved nonuniform beams,” Trans. ASME, J. Appl. Mech., 68, No. 2, 186–191 (2001). · Zbl 1110.74541 · doi:10.1115/1.1346679
[12] S. Nair, V. K. Garg, and Y. S. Lai, ”Dynamic stability of a curved rail under a moving load,” Appl. Math. Model., 9, 220–224 (1985). · doi:10.1016/0307-904X(85)90011-3
[13] I. U. Ojalvo and M. Newman, ”Natural frequencies of clamped ring segments,” Machine Design, 21, 219–220 (1964).
[14] H. Ozturk, I. Yesilyurt, and M. Sabuncu, ”In plane analysis of non-uniform cross-sectioned curved beams,” J. Sound Vib., 296, No. 1–2, 277–291 (2006). · doi:10.1016/j.jsv.2006.03.002
[15] J. P. Papangelis and N. S. Trahair, ”Flexural-torsional buckling of arches,” J. Struct Eng., 113, No. 4, 889–906 (1987). · doi:10.1061/(ASCE)0733-9445(1987)113:4(889)
[16] M. Petyt and C. C. Fleischer, ”Free vibration of curved beam,” J. Sound Vibr., 18, No. 1, 17–30 (1971). · Zbl 0233.73153 · doi:10.1016/0022-460X(71)90627-4
[17] A. B. Sabir and D. G. Ashwell, ”A comparasion of curved beam finite elements when used in vibration problem,” J. Sound Vibr., 18, 555–563 (1971). · doi:10.1016/0022-460X(71)90106-4
[18] M. Sabuncu, Vibration Characteristics of Rotating Aerofoil Cross-Section Bladed-Disc Assembly, PhD Thesis, University of Surrey, England (1978).
[19] J. M. Silva and P. V. Urgueira, ”Out of plane dynamic response of curved beams an analytical model,” Int. J. Solids Struct., 24, No. 3, 271–284 (1988). · Zbl 0629.73042 · doi:10.1016/0020-7683(88)90033-9
[20] J. Thomas and B. A. H. Abbas, ”Dynamic stability of Timoshenko beam by finite element method,” Trans. ASME, J. Eng. Ind., 98, 1145–1151 (1976). · doi:10.1115/1.3439069
[21] S. P. Timoshenko and J. M. Gere, Theory of Elastic Stability, McGraw-Hill, New York (1961).
[22] E. Tüfekci and A. Arpaci, ”Analytical solutions of in-plane static problems for non-uniform curved beams including axial and shear deformations,” Struct. Eng. Mech., 22, No. 2, 131–150 (2006). · doi:10.12989/sem.2006.22.2.131
[23] R. T. Wang and Y. L. Sang, ”Out-of-plane vibration of multi-span curved beam due to moving loads,” Struct. Eng. Mech., 7, No. 4, 361–375 (1999). · doi:10.12989/sem.1999.7.4.361
[24] J. S. Wu and L. K. Chiang, ”Free vibration analysis of arches using curved beam elements,” Int. J. Numer. Meth. Eng., 58, 1907–1936 (2003). · Zbl 1032.74689 · doi:10.1002/nme.837
[25] F. Yang, R. Sedaghati, and E. Esmailzadeh, ”Free in-plane vibration of general curved beams using finite element method,” J. Sound Vibr., 318, No. 4–5, 850–867 (2008). · doi:10.1016/j.jsv.2008.04.041
[26] V. Yýldýrým, ”A computer program for the free vibration analysis of elastic arcs,” Comput. Struct., 62, No. 3, 475–485 (1996).
[27] C. H. Yoo, Y. J. Kang, and J. S. Davidson, ”Buckling analysis of curved beams by finite element discretization,” J. Eng. Mech. ASCE, 122, No. 8, 762–770 (1996). · doi:10.1061/(ASCE)0733-9399(1996)122:8(762)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.