References
- Bellman, R. and Casti, J. (1971), "Differential quadrature and Long term Integration", J. Math. Anal. Appl., 34, 235-238. https://doi.org/10.1016/0022-247X(71)90110-7
- Bert, C.W., Wang, X. and Striz, A.G. (1993), "Differential quadrature for static and free vibration analysis of anisotropic plates", Int. J. Solids. Struct., 30(13), 1737-1744. https://doi.org/10.1016/0020-7683(93)90230-5
- Bert, C.W., Wang, X. and Striz, A.G. (1994), "Static and free vibration analysis of beams and plates by differential quadrature method", Acta. Mech., 102, 11-24. https://doi.org/10.1007/BF01178514
- Borg, S.F. and Gennaro, J.J. (1959), Advanced Structural Analysis, Van Nostrand, Princeton, NJ.
- Boresi, A.P., Sidebottom, O.M., Seely, F.B. and Smith, J.O, (1978), Advanced Mechanics of Materials, John Wiley and sons, New York.
- Chidamparam, P. and Leissa, A.W. (1993), "Vibration of planar curved beams, rings and arches", Appl. Mech. Rev., 46 (9), 467-483. https://doi.org/10.1115/1.3120374
- Den Hartog, J.P. (1928), "The lowest natural frequencies of circular arcs", Philos. Mag., 75, 400-408.
- Friedman, Z. and Kosmatka, J.B, (1998), "An accurate two-node Finite Element for shear deformable curved beams", Int. J. Numer. Methods Eng, 41,473-498. https://doi.org/10.1002/(SICI)1097-0207(19980215)41:3<473::AID-NME294>3.0.CO;2-Q
- Gupta, A.K. (1985), "Vibration of tapered beams", J. Struct. Eng., ASCE, 111,19-36. https://doi.org/10.1061/(ASCE)0733-9445(1985)111:1(19)
- Gutierrez, R.H., Laura, P.A.A., Rossi, R.E., Bertero, R. and Villaggi, A. (1989), "In-plane vibrations of noncircular arcs of non-uniform cross-section", J. Sound. Vib, 129, 181-200. https://doi.org/10.1016/0022-460X(89)90577-4
- Henrych, J. (1989), The dynamics of arches and frames, Elsevier, New York.
- Huang, C.S., Tseng, Y.P., Leissa, A.W. and Nieh, A.Y. (1998), "An exact solution for in plane vibrations of an arch having variable curvature and cross section", Int. J. Mech. Sci., 40(11), 1159-1173. https://doi.org/10.1016/S0020-7403(98)00020-4
- Irie, T., Yamada, G. and Tanaka, K. (1983), "Natural frequencies of in-plane vibration of arcs", J. Appl. Mech., 50(2), 449-452. https://doi.org/10.1115/1.3167058
- Kang, K., Bert, C.W. and Striz, A.G. (1995), "Vibration analysis of shear deformable circular arches by differential quadrature method", J. Sound. Vib., 183, 353-360. https://doi.org/10.1006/jsvi.1995.0258
- Kawakami, M., Sakiyama, T., Matsuda, H. and Morita, C. (1995), "In-plane and out-of-plane free vibrations of curved beams with variable sections", J. Sound Vib., 187, 381-401. https://doi.org/10.1006/jsvi.1995.0531
- Kim, J.G. and Lee, J.K. (2008), "Free vibration Analysis of arches based on the hybrid mixed formulation with consistent quadratic stress functions", Comput. Struct., 86(15-16), 1672-1681. https://doi.org/10.1016/j.compstruc.2007.07.002
- Koizumi, M. (1993), "The concept of FGM", Ceram. Trans, Functionally Graded Materials, 34, 3-10.
- Koizumi, M. (1997), "FGM activities in Japan", Composites: part B, 28,1-4.
- Laura, P.A.A., Verniere De Irassar, P.L., Carnicer, R. and Bertero, R. (1988), "A Note on vibrations of a circumferential arch with thickness varying in a discontinuous fashion", J. Sound. Vib., 120, 95-105 https://doi.org/10.1016/0022-460X(88)90336-7
- Lawrence, J.D. (1972), A Catalog of special plane curves, Dover publishers.
- Lee, B.K. and Wilson, J.F. (1989), "Free vibration of arches with variable curvature", J. Sound Vib., 136, 75-89.
- Leontovich, V. (1959), Frames and Arches, Mc-Graw-Hill.
- Lockwood, E.H. (1961), A book of curves, Cambridge University Press.
- Malekzadeh, P. (2009), "Two dimensional in-plane free vibration of functionally graded circular arches with temperature dependent properties", Compos. Struct., 91(1), 38-47. https://doi.org/10.1016/j.compstruct.2009.04.034
- Malekzadeh, P. and Setoodeh, A.R. (2009), "DQM in-plane free vibration of laminated moderately thick circular deep arches", Adv. Eng. Softw., 40(9), 798-803. https://doi.org/10.1016/j.advengsoft.2009.01.011
- Malekzadeh, P., Atashi, M.M. and Karami, G. (2009), "In-plane free vibration of functionally graded circular arches with temperature dependent properties under thermal environment", J. Sound.Vib., 326(3- 5), 837-851. https://doi.org/10.1016/j.jsv.2009.05.016
- Malekzadeh, P., Golbahar, M.R. and Atashi, M.M. (2010), "Out of plane free vibration of functionally graded circular curved beams in thermal environment", Compos. Struct., 92(2),541-552. https://doi.org/10.1016/j.compstruct.2009.08.040
- Malekzadeh, P. (2010), "Out-of-plane Free vibration Analysis of Functionally graded Circular curved beams supported on elastic foundation", Int. J. App. Mech, 2(3), 635-657. https://doi.org/10.1142/S175882511000069X
- Maurizi, M.J., Rossi, R.E. and Belles, P.M. (1991), "Lowest natural frequency of clamped circular arcs of linearly tapered width", J. Sound. Vib,, 144,357-361. https://doi.org/10.1016/0022-460X(91)90755-9
- Maurizi, M.J., Belles, P.M., Rossi, R.E. and De Rosa, M.A. (1993), "Free vibration of a three-centred arc clamped at the ends", J. Sound. Vib., 161,187-189. https://doi.org/10.1016/0022-460X(93)90478-T
- Oh, S.J., Lee, B.K. and Lee, I.W. (1998a), "Free vibrations of circular arches with variable cross-section considering shear deformations and rotatory inertia", Fifth Pacific Structural Steel Conference, Seoul, Korea, October.
- Oh, S.J., Lee. B.K., Lee, I.W. and Park, M.H. (1998b), "Free vibrations of noncircular arches considering rotatory inertia and shear deformation", Comput. Mech., Barcelona, Spain.
- Oh, S.J., Lee, B.K. and Lee, I.W. (2000), "Free vibrations of non-circular arches with non-uniform crosssection", Int. J. Solids. Struct., 37(36) , 4871-4891. https://doi.org/10.1016/S0020-7683(99)00194-8
- Piovan, M.T., Domini, S. and Ramirez, J.M. (2012), "In-plane and out-of-plane dynamics and buckling of functionally graded circular curved beam", Compos. Struct., 94, 3194-3206. https://doi.org/10.1016/j.compstruct.2012.04.032
- Rajasekaran, S. (2007), "Symbolic computation and differential quadrature method- A boon to engineering analysis", Struct. Eng. Mech., 27(6), 713-739. https://doi.org/10.12989/sem.2007.27.6.713
- Rajasekaran, S. (2008), "Buckling of fully and partially embedded non-prismatic columns using differential quadrature and differential transformation methods", Struct. Eng. Mech., 28(2), 221-238. https://doi.org/10.12989/sem.2008.28.2.221
- Romanelli, E. and Laura, P.A. (1972), "Fundamental frequencies of non-circular, elastic, hinged arcs", J. Sound. Vib., 24, 17-22. https://doi.org/10.1016/0022-460X(72)90118-6
- Schilling, R.L. and Harris, S.L. (2000), Applied Numerical Methods for Engineers using Matlab and C, Brooks/Cole, Thomson Learning.
- Shafiee, H., Naei, M. and Eslami, M. (2006), "In-plane and out-of -plane buckling of arches made of functionally graded material", Int. J. Mech. Sci, 48, 907-915. https://doi.org/10.1016/j.ijmecsci.2006.01.001
- Shahba, A., Attarnejad, R., Tavanaie Marvi, M. and Hajilar, S. (2011), "Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions", Composites-part-B-Eng., 42(4), 801-808..
- Shahba, A. and Rajasekaran, S. (2012), "Free vibration and stability of tapered Euler-Bernoulli Beam made of axially Functionally graded material", Appl. Math. Model., 36, 3094-3111. https://doi.org/10.1016/j.apm.2011.09.073
- Shahba, A., Attarnejad, R., Jandaghi Semnani, S. and Honarvar Gheitanbaf, H. (2012), "New shape functions for non uniform curved Timoshenko beam with arbitrarily varying curvature using basic displacement functions", Meccanica, DOI, 10.1007/s 11012-012-9591-9.
- Shu, C. (2000), Differential Quadrature and its application in Engineering, Springer, Berlin.
- Tufekci, E. and Arpaci, A. (1998), "Exact Solution of in-plane vibrations of circular arches with account taken of axial extension, transverse shear and rotatory inertia effects", J. Sound. Vib., 209(5), 845-856. https://doi.org/10.1006/jsvi.1997.1290
- Tufekci, E. and Dogruer, O.Y. (2006), "Out-of-plane free vibration of a circular arch with uniform cross section: Exact solution", J. Sound. Vib., 291(3-5),525-538. https://doi.org/10.1016/j.jsv.2005.06.008
- Valetsos, A.S., Austin, W.J., Pereia, C.A.L. and Wung, S.J. (1972), "Free in-plane vibration of Circular Arches", J. Eng. Mech-ASCE., 98 (2), 311-329.
- Volterra, E. and Morell, J.D. (1960), "A Note on the lowest natural frequency of elastic arcs", J. Appl. Mech., 27, 744-746. https://doi.org/10.1115/1.3644096
- Wang, T.M. (1975), "Effect of variable curvature on fundamental frequency of clamped parabolic arcs", J. Sound. Vib., 41,247-251. https://doi.org/10.1016/S0022-460X(75)80100-3
- Wilson, E.L. (2002), Three Dimensional Static and Dynamic Analysis of Structures, Computers and Structures Inc., Berleley, California.
- Wilson, J.F., Lee, B.K. and Oh, S.J. (1994), "Free vibrations of circular arches with variable cross-section", Struct. Eng. Mech, 2(4), 345-357. https://doi.org/10.12989/sem.1994.2.4.345
- Wolf. Jr., J.A. (1971), "Natural Frequencies of Circular Arches", J. Struct. Eng-ASCE., 97(9), 2337-2350.
- Yousefi, A. and Rastgoo, A. (2011), "Free vibration of functionally graded spatial curved beams", Compos. Struct., 93(11), 3048-3056. https://doi.org/10.1016/j.compstruct.2011.04.024
- Zhao, Y. and Kang, H. (2008), "In-plane free vibration analysis of cable-arch structure", J. Sound. Vib., 312(3), 363-379. https://doi.org/10.1016/j.jsv.2007.04.038
Cited by
- Static, stability and free vibration analysis of arches using a new differential transformation-based arch element vol.77, 2013, https://doi.org/10.1016/j.ijmecsci.2013.09.012
- Nonlocal static analysis of a functionally graded material curved nanobeam 2018, https://doi.org/10.1080/15376494.2017.1285463
- Vertical seismic response analysis of straight girder bridges considering effects of support structures vol.8, pp.6, 2015, https://doi.org/10.12989/eas.2015.8.6.1481
- Study of complex nonlinear vibrations by means of accurate analytical approach vol.17, pp.5, 2014, https://doi.org/10.12989/scs.2014.17.5.721
- High conservative nonlinear vibration equations by means of energy balance method vol.11, pp.1, 2016, https://doi.org/10.12989/eas.2016.11.1.129
- Nonlinear vibration analysis of a type of tapered cantilever beams by using an analytical approximate method vol.59, pp.1, 2016, https://doi.org/10.12989/sem.2016.59.1.001
- Bending, buckling and vibration of small-scale tapered beams vol.120, 2017, https://doi.org/10.1016/j.ijengsci.2017.08.005
- Analytical study of nonlinear vibration of oscillators with damping vol.9, pp.1, 2015, https://doi.org/10.12989/eas.2015.9.1.221
- Analysis of curved beams using a new differential transformation based curved beam element vol.49, pp.4, 2014, https://doi.org/10.1007/s11012-013-9835-3
- A novel approximate solution for nonlinear problems of vibratory systems vol.57, pp.6, 2016, https://doi.org/10.12989/sem.2016.57.6.1039
- Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM vol.57, pp.2, 2016, https://doi.org/10.12989/sem.2016.57.2.221
- Vibration of sandwich plates considering elastic foundation, temperature change and FGM faces vol.70, pp.5, 2013, https://doi.org/10.12989/sem.2019.70.5.601
- In-Plane Free Vibration of Uniform Circular Arches Made of Axially Functionally Graded Materials vol.19, pp.8, 2013, https://doi.org/10.1142/s0219455419500846
- Free Vibrations of Symmetric Arch: Boundary Conditions of Stress Resultants Revisited vol.20, pp.9, 2013, https://doi.org/10.1142/s021945542071008x
- Free Vibration of AFG Circular Arch with Symmetric and Anti-symmetric Boundary Conditions at Mid-Arc vol.12, pp.3, 2013, https://doi.org/10.3390/sym12030417