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Meccanica
Erschienen in: Meccanica 4/2014

01.04.2014

Analysis of curved beams using a new differential transformation based curved beam element

verfasst von: S. Rajasekaran

Erschienen in: Meccanica | Ausgabe 4/2014

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Abstract

Differential transformation method is used to obtain the shape functions for nodal variables of an arbitrarily non-uniform curved beam element including the effects of shear deformation considering axially functionally graded material. The proposed shape functions depend on the variations in cross-sectional area, moment of inertia, curvature and material properties along the axis of the curved beam element. The static and free vibration of axially functionally graded tapered curved beams including shear deformation and rotary inertia are studied through solving several examples. Numerical results are presented for circular, parabolic, catenary, elliptic and sinusoidal beams (both forms—prime and quadratic) with hinged-hinged, hinged-clamped and clamped-clamped and clamped-free end restraints. Three general taper types (depth taper, breadth taper and square taper) for rectangular cross section are studied. Out of plane vibration is studied and the lowest natural frequencies are calculated and compared with the published results. Out of plane buckling is investigated for circular beams due to radial load.
Vorheriger Artikel Kinematical analysis of overconstrained and underconstrained mechanisms by means of computational algebraic geometry
Nächster Artikel Three-dimensional thermoelastic analysis of finite length laminated cylindrical panels with functionally graded layers

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Literatur
1.
Michell JH (1890) The small deformation of curves and surfaces with application to the vibrations of helix and circular ring. In: Messenger of mathematics, 1968
2.
3.
Love AEH (1944) A treatise on the mathematical theory of elasticity, 4th edn. Dover, New York MATH
4.
Volterra F, Morell JD (1961) Lowest natural frequency of elastic arc for vibrations outside the plans of initial curvature. J Appl Mech 28:624–627 CrossRefMathSciNet
5.
Ojalvo IU, Newman N (1964) Natural frequencies of clamped ring segments. Mach Des 21:219–220
6.
Rao SS (1971) Effects of transverse shear and rotary inertia on the coupled twist-bending vibrations of circular rings. J Sound Vib 16(4):551–566 ADSCrossRefMATH
7.
8.
Davis R, Henshell RD, Warburton GB (1972) Curved beam finite elements for coupled bending and torsional vibrations. Earthq Eng Struct Dyn 1:165–175 CrossRef
9.
Markus S, Nanasi T (1981) Vibration of curved beams. Shock Vib Dig 13:3–14 CrossRef
10.
Laura PAA, Maurizi MJ (1987) Recent research on vibrations of arch type structures. Shock Vib Dig 19:6–9 CrossRef
11.
Chidamparam P, Leissa AW (1993) Vibrations of planar curved beams, rings and arches. Appl Mech Rev 46:467–483 ADSCrossRef
12.
Auciello NM, De Rosa MA (1994) Free vibrations of circular arches: a review. J Sound Vib 174:433–458 ADSCrossRef
13.
Wagner H, Ramamurti V (1977) Beam vibrations—a review. Shock Vib Dig 9:17–24 CrossRef
14.
Wang TM, Laskey A, Ahmad M (1984) Natural frequencies for out-of-plane vibrations of continuous curved beams considering shear and rotary inertia. Int J Solids Struct 20:257–265 CrossRefMATH
15.
Kawakami M, Sakiyama T, Matsuda H, Morita C (1995) In plane and out-of-plane free vibrations of curved beams with variable sections. J Sound Vib 187:381–401 ADSCrossRef
16.
Xiong Y, Tabarrok BA (1992) A finite element model for the vibration of spatial rods under various applied loads. Int J Mech Sci 34:41–51 CrossRefMATH
17.
Rajasekaran S (2013) Buckling and vibration of axially functionally graded non-uniform beams using differential transformation based dynamic stiffness approach. Meccanica 48(50):1053–1070 CrossRefMathSciNet
18.
Bambill DV, Rossit CA, Rossi RE, Felix DH (2013) Transverse free vibration of non-uniform rotating Timoshenko beams with elastically clamped boundary conditions. Meccanica 48(6):1289–1311 CrossRefMathSciNet
19.
Yildirim V (1996) Investigation of parameters affecting free vibration frequency of helical springs. Int J Numer Methods Eng 39:99–114 CrossRefMATH
20.
Wu JS, Chiang LK (2004) Free vibrations of a circularly curved Timoshenko beam normal to its initial plane using finite curved beam element. Comput Struct 82:25–40 CrossRef
21.
Wu JS, Chiang LK (2004) A new approach for free vibration analysis of arches with effect of shear deformation and rotary inertia considered. J Sound Vib 277:49–71 ADSCrossRef
22.
Tufekci E, Arpaci A (1998) Exact solution of in-plane vibrations of circular arches with account taken of axial extension, transverse shear and rotary inertia effects. J Sound Vib 209:845–856 ADSCrossRef
23.
Tufekci E, Dogruer Y (2006) Out-of-plane free vibration of a circular arch with uniform cross section: exact solution. J Sound Vib 291:525–538 ADSCrossRef
24.
Irie T, Yamada AG, Takahashi I (1982) Natural frequencies of out-of-plane vibrations of arcs. J Appl Mech 49:910–913 CrossRefMATH
25.
Kang K, Bert CW, Stritz AG (1995) Vibration analysis for shear deformable circular arches by the differentia quadrature method. J Sound Vib 181:353–360 ADSCrossRef
26.
Huang CS, Tseng YP, Chang SH, Hung CI (2000) Out-of-plane dynamic analysis of beams with arbitrarily curvature and cross section by dynamic stiffness matrix method. Int J Solids Struct 37:495–513 CrossRefMATH
27.
Chen CN (2008) DQEM analysis of out-of-plane vibration of non-prismatic curved beam structures considering the effects of shear deformation. Adv Eng Softw 39:466–472 CrossRef
28.
Wang TM, Nettleton RH, Kerta B (1980) Natural frequencies for out-of-plane vibrations of continuous curved beams. J Sound Vib 68:427–436 ADSCrossRefMATH
29.
Snyder JM, Wilson JF (1992) Free vibrations of continuous horizontally curved beam. J Sound Vib 157:340–355 ADSCrossRef
30.
Piovan MT, Cortinez H, Rossi RE (2000) Out of plane vibrations of shear deformable continuous horizontally curved thin-walled beam. J Sound Vib 237:101–118 ADSCrossRef
31.
Wang TM, Brannen WF (1982) Natural frequencies of out of plane vibrations of curved beams on elastic foundations. J Sound Vib 84:241–246 ADSCrossRef
32.
Issa MS, Nasr ME, Naiem NA (1990) Free vibrations of curved Timoshenko beams on Pasternak foundation. Int J Solids Struct 26:1243–1252 CrossRef
33.
Lee BK, Oh SJ, Park KK (2002) Free vibrations of shear deformable circular curved beams resting on an elastic foundation. Int J Struct Stab Dyn dy(2):77–97 CrossRef
34.
Sabuncu M, Ozturk H, Cimer S (2011) Out of plane dynamic stability analysis of curved beam subjected to uniformly distributed radial loading. Int J Appl Mech 46(11):1327–1337 CrossRefMATH
35.
Silva KM, Urgueira PV (1988) Out of plane dynamic response of curved beams an analytical model. Int J Solids Struct 24(3):271–284 CrossRefMATH
36.
Yang F, Sedaghati R, Esmailzadeh E (2008) Free in-plane vibration of general curved beams using finite element method. J Sound Vib 318(4–5):850–867 ADSCrossRef
37.
Choi JK, Lim JK (1993) Simple curved shear beam elements. Commun Numer Methods Eng 9(8):659–669 CrossRefMATH
38.
Koziey BL, Mirza FA (1994) Consistent curved beam element. Comput Struct 51(6):643–654 CrossRefMATH
39.
Litewka P, Rakowski J (1997) Efficient curved finite element. Int J Numer Methods Eng 40(14):2629–2652 CrossRefMATH
40.
Sabir AB, Djoudi MS, Sfendji A (1994) The effect of shear deformation on the vibration of circular arches by the finite element method. Thin-Walled Struct 18:47–66 CrossRef
41.
Lee SY, Chao JC (2000) Out of plane vibrations of curved non-uniform beams of constant radius. J Sound Vib 238(3):443–458 ADSCrossRefMathSciNet
42.
Yousefi A, Rastgoo A (2011) Free vibrations of functionally graded spatial curved beams. Comput Struct 93:3048–3056 CrossRef
43.
Lee BK, Oh SJ, Mo JM, Lee TE (2008) Out-of-plane free vibrations of curved beams with variable curvature. J Sound Vib 318:227–246 ADSCrossRef
44.
45.
Lawrence JD (1972) A catalog of special plane curves. Dover, New York MATH
46.
Oh SJ, Lee BK, Lee IW (1998) Free vibrations of circular arches with variable cross-section considering shear deformations and rotatory inertia. In: Fifth pacific structural steel conference, Seoul, Korea, October 13–16
47.
Oh SJ, Lee BK, Lee IW, Park MH (1998) Free vibrations of noncircular arches considering rotatory inertia and shear deformation. In: Comput mech, Barcelona, Spain
48.
Rajasekaran S (2013) Free vibration of tapered arches made of axially functionally graded materials. Struct Eng Mech 45(4):565–590
49.
Leontovich V (1959) Frames and arches. Mc-Graw-Hill, New York
50.
Wakashima K, Hirano T, Nino M (1990) Space applications of advanced structural materials. ESA SP 303:97–102
51.
Nakamura T, Wang T, Sampath S (2000) Determination of properties of graded materials by inverse analysis and instrumented indentation. Acta Mater 48:4293–4306 CrossRef
52.
Zhou JK (1980) Differential transform and its application for electrical circuits. Huazhong University Press, China
53.
Ozdemir O, Kaya MO (2006) Flap wise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method. J Sound Vib 289:413–420 ADSCrossRef
54.
Mei C (2008) Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam. Comput Struct 86:1280–1284 CrossRef
55.
Chen CK, Ho SH (1996) Application of differential transformation to eigenvalue problem. Appl Comput Math 79:504–510 CrossRefMathSciNet
56.
57.
Schilling RL, Harris SL (2000) Applied numerical methods for engineers using Matlab and C. Brooks/Cole/Thomson Learning, New York
58.
Papangelis JP, Trahair NS (1987) Flexural torsional buckling of arches. J Struct Eng 113(4):889–906 CrossRef
59.
Wilson EL (2002) Three dimensional static and dynamic analysis of structures. In: Computers and structures, Berkeley, USA
60.
Pilkey WD (2005) Formula for stress, strain and structural matrices, 2nd edn. Wiley, New York
61.
Rajasekaran S, Padmanabhan S (1989) Equations of curved beams. J Eng Mech Div 115(5):1094–1111 CrossRef
Metadaten
Titel
Analysis of curved beams using a new differential transformation based curved beam element
verfasst von
S. Rajasekaran
Publikationsdatum
01.04.2014
Verlag
Springer Netherlands
Erschienen in
Meccanica / Ausgabe 4/2014
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-013-9835-3

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