How to cite this paper
Kim, G., Oh, S., Lee, T & Lee, B. (2021). Free vibrations of axially functionally graded horseshoe arch.Engineering Solid Mechanics, 9(3), 251-262.
Refrences
Borg, S.F. & Gennaro, J.J. (1959). Advanced structural analysis. Van Nostrand Reinhold Company, New York, NY, USA.
Burden, R.L. & Faires, D.J. & Burden, A.M. (2016). Numerical analysis. Cengage Learning, Boston, MA, USA.
Chandran, G. & Rajendran, M.G. (2014). Study on buckling of column made of functionally graded material. International Journal of Mechanical and Production Engineering, 2(2), 52-54.
Horibe, T. & Mori, K. (2018). Large deflections of tapered cantilever beams made of axially functionally graded materials. Mechanical Engineering Journal, Japan Society of Mechanical Engineers, 5, 1-10.
Joo, S.M., Park, K.K., Lee, B.K. & Hwang, H.J. (1985). Free vibration analysis of fixed ended parabolic arches. Journal of Korean Society of Civil Engineers, 5(3), 31-38 (in Korean).
Lee, B.K., Oh, S.J. & Lee, T.E. (2014). In-plane free vibrations of horseshoe circular arch. Journal of the Korean Society of Civil Engineers, 34(4), 1043-1052 (in Korean).
Lee, B.K., Park, K.K., Oh, S.J. & Lee, T.E. (2016). Planar free vibrations of horseshoe elliptic arch. KSCE Journal of Civil Engineering, 20 (4), 1411-1418.
Lee, J.K. & Lee, B.K. (2019). Free vibration and buckling of tapered columns made of axially functionally graded materials. Applied Mathematical Modelling, 75, 73-87.
Lee, J.K. & Lee, B.K. (2020). Free vibration of AFG circular arch with symmetric and anti-symmetric boundary conditions at mid-arc. Symmetry-Basel, 12, 417 (14 pages).
Li, X. (2008). A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Bernoulli-Euler beam. Journal of Sound and Vibration, 318, 1211-1229.
Lü, Q. & Lü, C.F. (2009). Exact two-dimensional solutions for in-plane natural frequencies of laminated circular arches. Journal of Sound and Vibrations, 318(4-5), 982-920.
Malekzadeh, P., Setoodeh, A.R. & Barmshouri, E. (2008). A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches. Journal of Sound and Vibration, 315 (1-2), 212-225.
Nieh, K.Y., Huang, C.S. & Tseng, Y.P. (2003). An analytical solution for in-plane free vibration and stability of loaded elliptic arches. Computers & Structures, 81(13), 1311-1327.
Noori, A.R., Aslan, T.A. & Temel, B. (2018). An efficient approach for in-plane free and forced vibrations of axially functionally graded parabolic arches with nonuniform cross section. Composite Structures, 200, 701-710.
Perkins, N.C. (1990). Planar vibration of an elastica arch: Theory and Practice. Journal of Vibration and Acoustics, 112, 374-379.
Ranganathan, S., Abed, F. & Aldadah, M.G. (2016). Buckling of slender columns with functionally graded micro-structures. Mechanics of Advanced Materials and Structures, 23, 1360-1367.
Rao, S.S. (2007). Vibration of continuous system. John Wiley & Sons, Inc., Hoboken, NJ, USA.
Riedel, C.H. & Kang, B.S. (2006). Free vibration of elastically coupled dual-span curved beams. Journal of Sound and Vibration, 290(3-5), 820-838.
Shin, Y.J., Kwon, K.M. & Yun, J.H. (2008). Vibration analysis of a circular arch with variable cross-section using differential transformation and generalized differential quadrature. Journal of Sound and Vibration, 309(1-2), 9-19.
Tufekci, E. & Ozdemir, O. (2006). Exact solution of free in-plane vibration of a stepped circular arch. Journal of Sound and Vibration, 295(3-5), 725-738.
Weaver, W., Timoshenko, S.P. & Young, D.H. (1990). Vibration problems in engineering. John Wiley & Sons, Inc., Hoboken, NJ, USA.
Wilson, J.F. & Lee, B.K. (1995). In-plane free vibrations of catenary arches with unsymmetric axes. Structural Engineering and Mechanics, 3(3), 511-525.
Burden, R.L. & Faires, D.J. & Burden, A.M. (2016). Numerical analysis. Cengage Learning, Boston, MA, USA.
Chandran, G. & Rajendran, M.G. (2014). Study on buckling of column made of functionally graded material. International Journal of Mechanical and Production Engineering, 2(2), 52-54.
Horibe, T. & Mori, K. (2018). Large deflections of tapered cantilever beams made of axially functionally graded materials. Mechanical Engineering Journal, Japan Society of Mechanical Engineers, 5, 1-10.
Joo, S.M., Park, K.K., Lee, B.K. & Hwang, H.J. (1985). Free vibration analysis of fixed ended parabolic arches. Journal of Korean Society of Civil Engineers, 5(3), 31-38 (in Korean).
Lee, B.K., Oh, S.J. & Lee, T.E. (2014). In-plane free vibrations of horseshoe circular arch. Journal of the Korean Society of Civil Engineers, 34(4), 1043-1052 (in Korean).
Lee, B.K., Park, K.K., Oh, S.J. & Lee, T.E. (2016). Planar free vibrations of horseshoe elliptic arch. KSCE Journal of Civil Engineering, 20 (4), 1411-1418.
Lee, J.K. & Lee, B.K. (2019). Free vibration and buckling of tapered columns made of axially functionally graded materials. Applied Mathematical Modelling, 75, 73-87.
Lee, J.K. & Lee, B.K. (2020). Free vibration of AFG circular arch with symmetric and anti-symmetric boundary conditions at mid-arc. Symmetry-Basel, 12, 417 (14 pages).
Li, X. (2008). A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Bernoulli-Euler beam. Journal of Sound and Vibration, 318, 1211-1229.
Lü, Q. & Lü, C.F. (2009). Exact two-dimensional solutions for in-plane natural frequencies of laminated circular arches. Journal of Sound and Vibrations, 318(4-5), 982-920.
Malekzadeh, P., Setoodeh, A.R. & Barmshouri, E. (2008). A hybrid layerwise and differential quadrature method for in-plane free vibration of laminated thick circular arches. Journal of Sound and Vibration, 315 (1-2), 212-225.
Nieh, K.Y., Huang, C.S. & Tseng, Y.P. (2003). An analytical solution for in-plane free vibration and stability of loaded elliptic arches. Computers & Structures, 81(13), 1311-1327.
Noori, A.R., Aslan, T.A. & Temel, B. (2018). An efficient approach for in-plane free and forced vibrations of axially functionally graded parabolic arches with nonuniform cross section. Composite Structures, 200, 701-710.
Perkins, N.C. (1990). Planar vibration of an elastica arch: Theory and Practice. Journal of Vibration and Acoustics, 112, 374-379.
Ranganathan, S., Abed, F. & Aldadah, M.G. (2016). Buckling of slender columns with functionally graded micro-structures. Mechanics of Advanced Materials and Structures, 23, 1360-1367.
Rao, S.S. (2007). Vibration of continuous system. John Wiley & Sons, Inc., Hoboken, NJ, USA.
Riedel, C.H. & Kang, B.S. (2006). Free vibration of elastically coupled dual-span curved beams. Journal of Sound and Vibration, 290(3-5), 820-838.
Shin, Y.J., Kwon, K.M. & Yun, J.H. (2008). Vibration analysis of a circular arch with variable cross-section using differential transformation and generalized differential quadrature. Journal of Sound and Vibration, 309(1-2), 9-19.
Tufekci, E. & Ozdemir, O. (2006). Exact solution of free in-plane vibration of a stepped circular arch. Journal of Sound and Vibration, 295(3-5), 725-738.
Weaver, W., Timoshenko, S.P. & Young, D.H. (1990). Vibration problems in engineering. John Wiley & Sons, Inc., Hoboken, NJ, USA.
Wilson, J.F. & Lee, B.K. (1995). In-plane free vibrations of catenary arches with unsymmetric axes. Structural Engineering and Mechanics, 3(3), 511-525.