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Year 2018, Volume: 31 Issue: 4, 1093 - 1105, 01.12.2018

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References

  • [10] Yamada, Y., Nakagiri, S., Takatsuka, K., “Elastic-plastic analysis of Saint-Venant torsion problem by a hybrid stress model”, International Journal for Numerical Methods in Engineering, 5(2):193-207, (1972).
  • [11] Noor, A.K., Andersen, C.M., “Mixed isoparametric elements for Saint-Venant torsion”, Computer Methods Applied Mechanics and Engineering, 6:195-218, (1975).
  • [12] Xiao, Q., Karihaloo, B., Li, Z., Williams, F., “An improved hybrid-stress element approach to torsion of shafts”, Computers & Structures, 71:535-563, (1999).
  • [13] Nouri, T., Gay, D., “Shear stresses in orthotropic composite beams”, International Journal of Engineering Science, 32:1647-1667, (1994).
  • [14] Sapountzakis, E.J., “Nonuniform torsion of multi-material composite bars by the boundary element method”, Computers & Structures, 79:2805-2816, (2001).
  • [15] Sapountzakis, E.J., Mokos, V.G., “Warping shear stresses in nonuniform torsion of composite bars by BEM”, Computer Methods in Applied Mechanics and Engineering, 192:4337-4353, (2003).
  • [16] Sapountzakis, E.J., Mokos, V.G., “Nonuniform torsion of bars variable cross section”, Computers & Structures, 82:703-715, (2004).
  • [17] Katsikadelis, J.T., Sapountzakis, E.J., “Torsion of composite bars by boundary element method”, Journal of the Engineering Mechanics Division, 111:1197-1210, (1985).
  • [18] Chou, S.I., Mohr, J.A., “Boundary integral method for torsion of composite shafts”, Res Mechanica: International Journal of Mechanical and Materials Engineering, 29:41-56, (1990).
  • [19] Dumir, P.C., Kumar, R., “Complex variable boundary element method for torsion of anisotropic bars”, Applied Mathematical Modelling, 17:80-88, (1993).
  • [1] Herrmann, L.R., “Elastic torsional analysis of irregular shapes”, Journal of the Engineering Mechanics Division, 91:11-19, (1965).
  • [20] Friedman, Z., Kosmatka, J.B., “Torsion and flexure of a prismatic isotropic beam using the boundary element method”, Computers & Structures, 74:479-494, (2000).
  • [21] Gaspari, D., Aristodemo, M., “Torsion and flexure analysis of orthotropic beams by a boundary element model”, Engineering Analysis with Boundary Elements, 29:850-858, (2005).
  • [22] Wang, C.T., “Applied Elasticity”, McGraw-Hill, (1953).
  • [23] Ely, J.F., Zienkiewicz, O.C., “Torsion of compound bars-a relaxation solution”, International Journal of Mechanical Sciences, 1:356-365, (1960).
  • [24] Darılmaz, K., Orakdöğen, E., Girgin, K., “Saint-Venant torsion of arbitrarily shaped orthotropic composite or FGM sections by a hybrid finite element approach”, Acta Mechanica, https://doi.org/10.1007/s00707-017-2067-1, (2017).
  • [25] Volterra, E., “Bending of a circular beam resting on an elastic foundation”, ASME Journal of Applied Mechanics, 19:1-4, (1952).
  • [26] Volterra, E., “Deflection of circular beams resting on elastic foundation obtained by the methods of harmonic analysis”, ASME Journal of Applied Mechanics, 20:227-232, (1953).
  • [27] Dasgupta, S., Sengupta, D., “Horizontally curved isoparametric beam element with or without elastic foundation including effect of shear deformation”, Computers & Structures, 29(6):967-973, (1988).
  • [28] Banan, M.R., Karami, G., Farshad, M., “Finite element analysis of curved beams on elastic foundation”, Computers & Structures, 32(1):45-53, (1989).
  • [29] Shenoi, R.A., Wang, W., “Flexural behaviour of a curved orthotropic beam on an elastic foundation”, The Journal of Strain Analysis for Engineering Design, 36(1):1-15, (2001).
  • [2] Krahula, J.L., Lauterbach, G.F., “A finite element solution for Saint-Venant torsion”, AIAA Journal, 7:2200-2203, (1969).
  • [30] Arici, M., Granata, M.F., “Generalized curved beam on elastic foundation solved by transfer matrix method”, Structural Engineering and Mechanics, 40(2):279-295, (2011).
  • [31] Çalım, F.F., Akkurt, F.G., “Static and free vibration analysis of straight and circular beams on elastic foundation”, Mechanics Research Communications, 38:89-94, (2011).
  • [32] Arici, M., Granata, M.F., Margiotta, P., “Hamiltonian structural analysis of curved beams with or without generalized two-parameter foundation”, Archive of Applied Mechanics, 83:1695-1714, (2013).
  • [33] Panayotounakos, D.E., Theocaris, P.S., “The dynamically loaded circular beam on an elastic foundation”, Journal of Applied Mechanics, 47:139-144, (1980).
  • [34] Wang, T.M., Brannen, W.F., “Natural frequencies for out-of-plane vibrations of curved beams on elastic foundations”, Journal of Sound and Vibration, 84(2):241-246, (1982).
  • [35] Issa, M.S., “Natural frequencies of continuous curved beams on Winkler-type foundation”, Journal of Sound and Vibration, 127(2):291-301, (1988).
  • [36] Issa, M.S., Nasr, M.E., Naiem, M.A., “Free vibrations of curved Timoshenko beams on Pasternak foundations”, International Journal of Solids and Structures, 26(11):1243-1252, (1990).
  • [37] Lee, B.K., Oh, S.J., Park, K.K., “Free vibrations of shear deformable circular curved beams resting on elastic foundations”, International Journal of Structural Stability and Dynamics, 2(1):77-97, (2002).
  • [38] Wu, X., Parker, R.G., “Vibration of rings on a general elastic foundation”, Journal of Sound and Vibration, 295:194–213, (2006).
  • [39] Kim, N., Fu, C.C., Kim, M.Y., “Dynamic stiffness matrix of non-symmetric thin-walled curved beam on Winkler and Pasternak type foundations”, Advances in Engineering Software, 38:158-171, (2007).
  • [3] Lamancusa, J.S., Saravanos, D.A., “The torsional analysis of bars with hollow square cross-sections”, Finite Element in Analysis and Design, 6:71-79, (1989).
  • [40] Malekzadeh, P., Haghighi, M.R.G., Atashi, M.M., “Out-of-plane free vibration analysis of functionally graded circular curved beams supported on elastic foundation”, International Journal of Applied Mechanics, 2(3):635-652, (2010).
  • [41] Celep, Z., “In-plane vibrations of circular rings on a tensionless foundation”, Journal of Sound and Vibration, 143(3):461-471, (1990).
  • [42] Kutlu, A., Ermis, M., Eratlı, N., Omurtag, M.H., “Forced vibration of a planar curved beam on Pasternak foundation, 19th International Conference on Structural and Construction Engineering, Istanbul, 2640-2644, (2017).
  • [43] Çalım, F.F., “Forced vibration of curved beams on two-parameter elastic foundation”, Applied Mathematical Modelling, 36:964-973, (2012).
  • [44] Çalım, F.F., “Dynamic response of curved Timoshenko beams resting on viscoelastic foundation”, Structural Engineering and Mechanics, 59(4):761-774, (2016).
  • [45] Eratlı, N., Argeso, H., Çalım. F.F., Temel. B., Omurtag. M.H., “Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM” Journal of Sound and Vibration, 333(16): 3671-3690, (2014).
  • [46] Ermis, M., Eratlı, N., Argeso, H., Kutlu, A., Omurtag, M.H., “Parametric Analysis of Viscoelastic Hyperboloidal Helical Rod”, Advances in Structural Engineering, 19(9):1420-1434, (2016).
  • [47] Bhimaraddi, A., Chandrashekhara, K., “Some Observations on The Modelling of Laminated Composite Beams with General Lay-ups”, Composite Structures, 19: 371380, (1991).
  • [48] Yıldırım, V., “Governing Equations of Initially Twisted Elastic Space Rods Made of Laminated Composite Materials”, International Journal of Engineering Science, 37(8):1007-1035, (1999).
  • [49] Doğruoğlu, A.N., Omurtag, M.H., “Stability analysis of composite-plate foundation interaction by mixed FEM”, Journal of Engineering Mechanics, ASCE, 126(9):928-936, (2000).
  • [4] Li, Z., Ko, J.M., Ni, Y.Q., “Torsional rigidity of reinforced concrete bars with arbitrary sectional shape”, Finite Elements in Analysis and Design, 35:349-361, (2000).
  • [50] Orakdöğen, E., Küçükarslan, S., Sofiyev, A., Omurtag, M.H., “Finite element analysis of functionally graded plates for coupling effect of extension and bending”, Meccanica, 45(1):63-72, (2010).
  • [51] Omurtag, M.H., Aköz, A.Y., “Hyperbolic paraboloid shell analysis via mixed finite element formulation”, International Journal for Numerical Methods in Engineering, 37(18):3037-3056, (1994).
  • [52] Aköz, A.Y., Omurtag, M.H., Doğruoğlu, A.N., “The mixed finite element formulation for three - dimensional bars”, International Journal of Solids Structures, 28(2):225-234, (1991).
  • [53] Omurtag, M.H., Aköz, A.Y., “The mixed finite element solution of helical beams with variable cross-section under arbitrary loading”, Computers & Structures, 43(2):325-331, (1992).
  • [54] Arıbas, U., Kutlu, A., Omurtag, M.H., “Static analysis of moderately thick, composite, circular rods via mixed FEM”, Proceedings of the World Congress on Engineering 2016, WCE 2016, London, 2, (2016).
  • [55] Arıbas, U., Eratlı, N., Omurtag, M.H., “Free vibration analysis of moderately thick, sandwich, circular beams”, Proceedings of the World Congress on Engineering 2016, WCE 2016, London, 2, (2016).
  • [56] Ermis, M., Arıbas, U.N., Eratlı, N., Omurtag, M.H., “Static and free vibration analysis of composite straight beams on the Pasternak foundation”, 10th International Conference on Finite Differences, Finite Elements, Finite Volumes, Boundary Elements, Barcelona, 12:113-122, (2017).
  • [57] Arıbas, U.N., Yılmaz, M., Eratlı, N., Omurtag, M.H., “Static and free vibration analysis of planar curved composite beams on elastic foundation”, 8th International Conference on Theoretical and Applied Mechanics, Brasov, 2:35-42, (2017).
  • [58] Dubner, H., Abate, J., “Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform”, Journal of the Association for Computing Machinery, 15(1):115-123, (1968).
  • [59] Durbin, F., “Numerical inversion of Laplace transforms: An efficient improvement to Dubner and Abate′s method”, Computer Journal, 17:371-376, (1974).
  • [5] Darılmaz, K., Orakdogen, E., Girgin, K., Küçükarslan, S., “Torsional rigidity of arbitrarily shaped composite sections by hybrid finite element approach”, Steel and Composite Structures, 7:241-251, (2007).
  • [60] Narayanan, G.V., “Numerical Operational Methods in Structural Dynamics”, Ph.D. Thesis, University of Minnesota, Minneapolis, America, (1979).
  • [6] Eratlı, N., Yılmaz, M., Darılmaz, K., Omurtag, M.H., “Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM”, Structural Engineering and Mechanics, 57:221-238, (2016).
  • [7] Zienkiewicz, O.C., Cheung, Y.K., “Finite elements in the solution of field problems”, The Engineer, 220:507-510, (1965).
  • [8] Moan, T., “Finite element stress field solution of the problem of Saint-Venant torsion”, International Journal for Numerical Methods in Engineering, 5:455-458, (1973).
  • [9] Valliappan, S., Pulmano, V.A., “Torsion of nonhomogeneous anisotropic bars”, Journal of the Structural Division, 100:286-295, (1974).

Forced vibration analysis of warping considered curved composite beams resting on viscoelastic foundation

Year 2018, Volume: 31 Issue: 4, 1093 - 1105, 01.12.2018

Abstract

The forced vibration analysis of warping
considered curved composite Timoshenko beams resting on viscoelastic foundation
is investigated via the mixed finite element method. Rocking is considered both
for Winkler and Pasternak viscoelastic foundations. Two nodded curved element
has 12 degrees of freedom. Problems are solved in frequency domain via Laplace
transform and modified Durbin’s algorithm is used for back transformation to
time domain. Warping considered average torsional rigidities of the composite
cross-sections are calculated numerically by ANSYS and verified by the
literature. After the verification of the algorithms, as benchmark examples,
curved composite beams on rocking considered viscoelastic Pasternak foundation
are solved.

References

  • [10] Yamada, Y., Nakagiri, S., Takatsuka, K., “Elastic-plastic analysis of Saint-Venant torsion problem by a hybrid stress model”, International Journal for Numerical Methods in Engineering, 5(2):193-207, (1972).
  • [11] Noor, A.K., Andersen, C.M., “Mixed isoparametric elements for Saint-Venant torsion”, Computer Methods Applied Mechanics and Engineering, 6:195-218, (1975).
  • [12] Xiao, Q., Karihaloo, B., Li, Z., Williams, F., “An improved hybrid-stress element approach to torsion of shafts”, Computers & Structures, 71:535-563, (1999).
  • [13] Nouri, T., Gay, D., “Shear stresses in orthotropic composite beams”, International Journal of Engineering Science, 32:1647-1667, (1994).
  • [14] Sapountzakis, E.J., “Nonuniform torsion of multi-material composite bars by the boundary element method”, Computers & Structures, 79:2805-2816, (2001).
  • [15] Sapountzakis, E.J., Mokos, V.G., “Warping shear stresses in nonuniform torsion of composite bars by BEM”, Computer Methods in Applied Mechanics and Engineering, 192:4337-4353, (2003).
  • [16] Sapountzakis, E.J., Mokos, V.G., “Nonuniform torsion of bars variable cross section”, Computers & Structures, 82:703-715, (2004).
  • [17] Katsikadelis, J.T., Sapountzakis, E.J., “Torsion of composite bars by boundary element method”, Journal of the Engineering Mechanics Division, 111:1197-1210, (1985).
  • [18] Chou, S.I., Mohr, J.A., “Boundary integral method for torsion of composite shafts”, Res Mechanica: International Journal of Mechanical and Materials Engineering, 29:41-56, (1990).
  • [19] Dumir, P.C., Kumar, R., “Complex variable boundary element method for torsion of anisotropic bars”, Applied Mathematical Modelling, 17:80-88, (1993).
  • [1] Herrmann, L.R., “Elastic torsional analysis of irregular shapes”, Journal of the Engineering Mechanics Division, 91:11-19, (1965).
  • [20] Friedman, Z., Kosmatka, J.B., “Torsion and flexure of a prismatic isotropic beam using the boundary element method”, Computers & Structures, 74:479-494, (2000).
  • [21] Gaspari, D., Aristodemo, M., “Torsion and flexure analysis of orthotropic beams by a boundary element model”, Engineering Analysis with Boundary Elements, 29:850-858, (2005).
  • [22] Wang, C.T., “Applied Elasticity”, McGraw-Hill, (1953).
  • [23] Ely, J.F., Zienkiewicz, O.C., “Torsion of compound bars-a relaxation solution”, International Journal of Mechanical Sciences, 1:356-365, (1960).
  • [24] Darılmaz, K., Orakdöğen, E., Girgin, K., “Saint-Venant torsion of arbitrarily shaped orthotropic composite or FGM sections by a hybrid finite element approach”, Acta Mechanica, https://doi.org/10.1007/s00707-017-2067-1, (2017).
  • [25] Volterra, E., “Bending of a circular beam resting on an elastic foundation”, ASME Journal of Applied Mechanics, 19:1-4, (1952).
  • [26] Volterra, E., “Deflection of circular beams resting on elastic foundation obtained by the methods of harmonic analysis”, ASME Journal of Applied Mechanics, 20:227-232, (1953).
  • [27] Dasgupta, S., Sengupta, D., “Horizontally curved isoparametric beam element with or without elastic foundation including effect of shear deformation”, Computers & Structures, 29(6):967-973, (1988).
  • [28] Banan, M.R., Karami, G., Farshad, M., “Finite element analysis of curved beams on elastic foundation”, Computers & Structures, 32(1):45-53, (1989).
  • [29] Shenoi, R.A., Wang, W., “Flexural behaviour of a curved orthotropic beam on an elastic foundation”, The Journal of Strain Analysis for Engineering Design, 36(1):1-15, (2001).
  • [2] Krahula, J.L., Lauterbach, G.F., “A finite element solution for Saint-Venant torsion”, AIAA Journal, 7:2200-2203, (1969).
  • [30] Arici, M., Granata, M.F., “Generalized curved beam on elastic foundation solved by transfer matrix method”, Structural Engineering and Mechanics, 40(2):279-295, (2011).
  • [31] Çalım, F.F., Akkurt, F.G., “Static and free vibration analysis of straight and circular beams on elastic foundation”, Mechanics Research Communications, 38:89-94, (2011).
  • [32] Arici, M., Granata, M.F., Margiotta, P., “Hamiltonian structural analysis of curved beams with or without generalized two-parameter foundation”, Archive of Applied Mechanics, 83:1695-1714, (2013).
  • [33] Panayotounakos, D.E., Theocaris, P.S., “The dynamically loaded circular beam on an elastic foundation”, Journal of Applied Mechanics, 47:139-144, (1980).
  • [34] Wang, T.M., Brannen, W.F., “Natural frequencies for out-of-plane vibrations of curved beams on elastic foundations”, Journal of Sound and Vibration, 84(2):241-246, (1982).
  • [35] Issa, M.S., “Natural frequencies of continuous curved beams on Winkler-type foundation”, Journal of Sound and Vibration, 127(2):291-301, (1988).
  • [36] Issa, M.S., Nasr, M.E., Naiem, M.A., “Free vibrations of curved Timoshenko beams on Pasternak foundations”, International Journal of Solids and Structures, 26(11):1243-1252, (1990).
  • [37] Lee, B.K., Oh, S.J., Park, K.K., “Free vibrations of shear deformable circular curved beams resting on elastic foundations”, International Journal of Structural Stability and Dynamics, 2(1):77-97, (2002).
  • [38] Wu, X., Parker, R.G., “Vibration of rings on a general elastic foundation”, Journal of Sound and Vibration, 295:194–213, (2006).
  • [39] Kim, N., Fu, C.C., Kim, M.Y., “Dynamic stiffness matrix of non-symmetric thin-walled curved beam on Winkler and Pasternak type foundations”, Advances in Engineering Software, 38:158-171, (2007).
  • [3] Lamancusa, J.S., Saravanos, D.A., “The torsional analysis of bars with hollow square cross-sections”, Finite Element in Analysis and Design, 6:71-79, (1989).
  • [40] Malekzadeh, P., Haghighi, M.R.G., Atashi, M.M., “Out-of-plane free vibration analysis of functionally graded circular curved beams supported on elastic foundation”, International Journal of Applied Mechanics, 2(3):635-652, (2010).
  • [41] Celep, Z., “In-plane vibrations of circular rings on a tensionless foundation”, Journal of Sound and Vibration, 143(3):461-471, (1990).
  • [42] Kutlu, A., Ermis, M., Eratlı, N., Omurtag, M.H., “Forced vibration of a planar curved beam on Pasternak foundation, 19th International Conference on Structural and Construction Engineering, Istanbul, 2640-2644, (2017).
  • [43] Çalım, F.F., “Forced vibration of curved beams on two-parameter elastic foundation”, Applied Mathematical Modelling, 36:964-973, (2012).
  • [44] Çalım, F.F., “Dynamic response of curved Timoshenko beams resting on viscoelastic foundation”, Structural Engineering and Mechanics, 59(4):761-774, (2016).
  • [45] Eratlı, N., Argeso, H., Çalım. F.F., Temel. B., Omurtag. M.H., “Dynamic analysis of linear viscoelastic cylindrical and conical helicoidal rods using the mixed FEM” Journal of Sound and Vibration, 333(16): 3671-3690, (2014).
  • [46] Ermis, M., Eratlı, N., Argeso, H., Kutlu, A., Omurtag, M.H., “Parametric Analysis of Viscoelastic Hyperboloidal Helical Rod”, Advances in Structural Engineering, 19(9):1420-1434, (2016).
  • [47] Bhimaraddi, A., Chandrashekhara, K., “Some Observations on The Modelling of Laminated Composite Beams with General Lay-ups”, Composite Structures, 19: 371380, (1991).
  • [48] Yıldırım, V., “Governing Equations of Initially Twisted Elastic Space Rods Made of Laminated Composite Materials”, International Journal of Engineering Science, 37(8):1007-1035, (1999).
  • [49] Doğruoğlu, A.N., Omurtag, M.H., “Stability analysis of composite-plate foundation interaction by mixed FEM”, Journal of Engineering Mechanics, ASCE, 126(9):928-936, (2000).
  • [4] Li, Z., Ko, J.M., Ni, Y.Q., “Torsional rigidity of reinforced concrete bars with arbitrary sectional shape”, Finite Elements in Analysis and Design, 35:349-361, (2000).
  • [50] Orakdöğen, E., Küçükarslan, S., Sofiyev, A., Omurtag, M.H., “Finite element analysis of functionally graded plates for coupling effect of extension and bending”, Meccanica, 45(1):63-72, (2010).
  • [51] Omurtag, M.H., Aköz, A.Y., “Hyperbolic paraboloid shell analysis via mixed finite element formulation”, International Journal for Numerical Methods in Engineering, 37(18):3037-3056, (1994).
  • [52] Aköz, A.Y., Omurtag, M.H., Doğruoğlu, A.N., “The mixed finite element formulation for three - dimensional bars”, International Journal of Solids Structures, 28(2):225-234, (1991).
  • [53] Omurtag, M.H., Aköz, A.Y., “The mixed finite element solution of helical beams with variable cross-section under arbitrary loading”, Computers & Structures, 43(2):325-331, (1992).
  • [54] Arıbas, U., Kutlu, A., Omurtag, M.H., “Static analysis of moderately thick, composite, circular rods via mixed FEM”, Proceedings of the World Congress on Engineering 2016, WCE 2016, London, 2, (2016).
  • [55] Arıbas, U., Eratlı, N., Omurtag, M.H., “Free vibration analysis of moderately thick, sandwich, circular beams”, Proceedings of the World Congress on Engineering 2016, WCE 2016, London, 2, (2016).
  • [56] Ermis, M., Arıbas, U.N., Eratlı, N., Omurtag, M.H., “Static and free vibration analysis of composite straight beams on the Pasternak foundation”, 10th International Conference on Finite Differences, Finite Elements, Finite Volumes, Boundary Elements, Barcelona, 12:113-122, (2017).
  • [57] Arıbas, U.N., Yılmaz, M., Eratlı, N., Omurtag, M.H., “Static and free vibration analysis of planar curved composite beams on elastic foundation”, 8th International Conference on Theoretical and Applied Mechanics, Brasov, 2:35-42, (2017).
  • [58] Dubner, H., Abate, J., “Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform”, Journal of the Association for Computing Machinery, 15(1):115-123, (1968).
  • [59] Durbin, F., “Numerical inversion of Laplace transforms: An efficient improvement to Dubner and Abate′s method”, Computer Journal, 17:371-376, (1974).
  • [5] Darılmaz, K., Orakdogen, E., Girgin, K., Küçükarslan, S., “Torsional rigidity of arbitrarily shaped composite sections by hybrid finite element approach”, Steel and Composite Structures, 7:241-251, (2007).
  • [60] Narayanan, G.V., “Numerical Operational Methods in Structural Dynamics”, Ph.D. Thesis, University of Minnesota, Minneapolis, America, (1979).
  • [6] Eratlı, N., Yılmaz, M., Darılmaz, K., Omurtag, M.H., “Dynamic analysis of helicoidal bars with non-circular cross-sections via mixed FEM”, Structural Engineering and Mechanics, 57:221-238, (2016).
  • [7] Zienkiewicz, O.C., Cheung, Y.K., “Finite elements in the solution of field problems”, The Engineer, 220:507-510, (1965).
  • [8] Moan, T., “Finite element stress field solution of the problem of Saint-Venant torsion”, International Journal for Numerical Methods in Engineering, 5:455-458, (1973).
  • [9] Valliappan, S., Pulmano, V.A., “Torsion of nonhomogeneous anisotropic bars”, Journal of the Structural Division, 100:286-295, (1974).
There are 60 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Civil Engineering
Authors

Umit Necmettin Arıbas

Merve Ermıs This is me

Akif Kutlu

Nihal Eratlı

Mehmet Hakkı Omurtag

Publication Date December 1, 2018
Published in Issue Year 2018 Volume: 31 Issue: 4

Cite

APA Arıbas, U. N., Ermıs, M., Kutlu, A., Eratlı, N., et al. (2018). Forced vibration analysis of warping considered curved composite beams resting on viscoelastic foundation. Gazi University Journal of Science, 31(4), 1093-1105.
AMA Arıbas UN, Ermıs M, Kutlu A, Eratlı N, Omurtag MH. Forced vibration analysis of warping considered curved composite beams resting on viscoelastic foundation. Gazi University Journal of Science. December 2018;31(4):1093-1105.
Chicago Arıbas, Umit Necmettin, Merve Ermıs, Akif Kutlu, Nihal Eratlı, and Mehmet Hakkı Omurtag. “Forced Vibration Analysis of Warping Considered Curved Composite Beams Resting on Viscoelastic Foundation”. Gazi University Journal of Science 31, no. 4 (December 2018): 1093-1105.
EndNote Arıbas UN, Ermıs M, Kutlu A, Eratlı N, Omurtag MH (December 1, 2018) Forced vibration analysis of warping considered curved composite beams resting on viscoelastic foundation. Gazi University Journal of Science 31 4 1093–1105.
IEEE U. N. Arıbas, M. Ermıs, A. Kutlu, N. Eratlı, and M. H. Omurtag, “Forced vibration analysis of warping considered curved composite beams resting on viscoelastic foundation”, Gazi University Journal of Science, vol. 31, no. 4, pp. 1093–1105, 2018.
ISNAD Arıbas, Umit Necmettin et al. “Forced Vibration Analysis of Warping Considered Curved Composite Beams Resting on Viscoelastic Foundation”. Gazi University Journal of Science 31/4 (December 2018), 1093-1105.
JAMA Arıbas UN, Ermıs M, Kutlu A, Eratlı N, Omurtag MH. Forced vibration analysis of warping considered curved composite beams resting on viscoelastic foundation. Gazi University Journal of Science. 2018;31:1093–1105.
MLA Arıbas, Umit Necmettin et al. “Forced Vibration Analysis of Warping Considered Curved Composite Beams Resting on Viscoelastic Foundation”. Gazi University Journal of Science, vol. 31, no. 4, 2018, pp. 1093-05.
Vancouver Arıbas UN, Ermıs M, Kutlu A, Eratlı N, Omurtag MH. Forced vibration analysis of warping considered curved composite beams resting on viscoelastic foundation. Gazi University Journal of Science. 2018;31(4):1093-105.