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http://dx.doi.org/10.12989/scs.2015.19.3.635

Vibration analysis of a pre-stressed laminated composite curved beam  

Ozturk, Hasan (Dokuz Eylul University, Department of Mechanical Engineering)
Publication Information
Steel and Composite Structures / v.19, no.3, 2015 , pp. 635-659 More about this Journal
Abstract
In this study, natural frequency analysis of a large deflected cantilever laminated composite beam fixed at both ends, which forms the case of a pre-stressed curved beam, is investigated. The laminated beam is considered to have symmetric and asymmetric lay-ups and the effective flexural modulus of the beam is used in the analysis. In order to obtain the pre-stressed composite curved beam case, an external vertical concentrated load is applied at the free end of a cantilever laminated composite beam and then the loading point of the deflected beam is fixed. The non-linear deflection curve of the flexible beam undergoing large deflection is obtained by the Reversion Method. The curved laminated composite beam is modeled by using the Finite Element Method with a straight-beam element approach. The effects of orientation angle and vertical load on the natural frequency parameter for the first four modes are examined and the results obtained are given in graphics. It has been found that the effect of the load parameter, which forms the curved laminated beam, on the natural frequency parameter, almost disappears after a certain value of the load parameter. This certain value differs for each laminated curved beam and each vibration mode.
Keywords
large deflection; laminated curved beam; vibration; non-linear deflection; finite element method;
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Times Cited By KSCI : 2  (Citation Analysis)
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1 Addessi, D., Lacarbonara, W. and Paolone, A. (2005), "On the linear normal modes of planar pre-stressed curved beams", J. Sound Vib., 284(3-5), 1075-1097.   DOI
2 Agarwal, S., Chakraborty, A. and Gopalakrishnan, S. (2006), "Large deformation analysis for anisotropic and inhomogeneous beams using exact linear static solutions", Compos. Struct., 72(1), 91-104.   DOI
3 Ang, M.H., Wei, W. and Teck-Seng, L. (1993), "On the estimation of the large deflection of a cantilever beam", Proceedings of the IECON '93 International Conference on Industrial Electronics, Control, and Instrumentation, Maui, HI, USA, November.
4 Bauchau, O.A. and Hong, C.H. (1988), "Nonlinear composite beam theory", J. Appl. Mech.-T. Asme, 55(1), 156-163.   DOI
5 Bayat, M., Pakar, I. and Bayat, M. (2013), "On the large amplitude free vibrations of axially loaded Euler-Bernoulli beams", Steel Compos. Struct., Int. J., 14(1), 73-83.   DOI
6 Belendez, T., Neipp, C. and Belendez, A. (2002), "Large and small deflections of a cantilever beam", Eur. J. Phys., 23(3), 371-379.   DOI
7 Belendez, T., Neipp, C. and Belendez, A. (2003), "Numerical and experimental analysis of a cantilever beam: a laboratory project to introduce geometric nonlinearity in mechanics of materials", Int. J. Eng. Educ., 19(6), 885-892.
8 Bisshopp, K.E. and Drucker, D.C. (1945), "Large deflection of cantilever beams", Q. Appl, Math., 3, 272-275.   DOI
9 Chen, J.K. and Sun, C.T. (1985), "Dynamic large deflection response of composite laminates subjected to impact", Compos. Struct., 4(1), 59-73.   DOI
10 Chen, L. (2010), "An integral approach for large deflection cantilever beams", Int. J. Nonlin. Mech., 45(3), 301-305.   DOI
11 Cornil, M.B., Capolungo, L., Qu, J. and Jairazbhoy, V.A. (2007), "Free vibration of a beam subjected to large static deflection", J. Sound Vib., 303(3-5), 723-740.   DOI
12 Gay, D., Hoa, S.V. and Tsai, S.W. (2003), Composite Materials Design and Applications, CRC press, New York, NY, USA.
13 Hadji, L., Daouadji, T.H., Tounsi, A. and Bedia, E.A. (2014), "A higher order shear deformation theory for static and free vibration of FGM beam", Steel Compos. Struct., Int. J., 16(5), 507-519.   DOI
14 Hajianmaleki, M. and Qatu, M.S. (2013), "Vibrations of straight and curved composite beams: A review", Compos. Struct., 100, 218-232.   DOI
15 Holden, J.T. (1972), "On the finite deflections of thin beams", Int. J. Solids Struct., 8(8), 1051-1055.   DOI
16 Holland, D.B., Virgin, L.N. and Plaut, R.H. (2008), "Large deflections and vibration of a tapered cantilever pulled at its tip by a cable", J. Sound Vib., 310(1-2), 433-441.   DOI
17 Jeon, S.M., Cho, M.H. and Lee, I. (1995), "Static and dynamic analysis of composite box beams using large deflection theory", Comput. Struct., 57(4), 635-642.   DOI
18 Jones, R.M. (1999), Mechanical of Composite Materials, (2nd Edition), Taylor & Francis Inc, USA.
19 Karaagac, C., Ozturk, H. and Sabuncu, M. (2013), "Effects of an edge crack on the free vibration and lateral buckling of a cantilever laminated composite slender beam", J. Vib. Control, 19(16), 2506-2522.   DOI
20 Kant, T. and Kommineni, J.R. (1994), "Large amplitude free vibration analysis of cross-ply composite and sandwich laminates with a refined theory and C0 finite elements", Comput. Struct., 50(1), 123-134.   DOI
21 Khdeir, A.A. and Reddy, J.N. (1994), "Free vibration of cross-ply laminated beams with arbitrary boundary conditions", Int. J. Eng. Sci., 32(12), 1971-1980.   DOI
22 Kien, N.D. (2013), "Large displacement response of tapered cantilever beams made of axially functionally graded material", Compos. Part B, 55, 298-305.   DOI
23 Lee, K. (2002), "Large deflections of cantilever beams of non-linear elastic material under a combined loading", Int. J. Nonlin. Mech., 37(3), 439-443.   DOI
24 Murty, A.V.K. and Shimpi, R.P. (1974), "Vibration of laminated beams", J. Sound Vib., 36(2), 273-284.   DOI
25 Nallathambi, A.K., Rao, C.L. and Srinivasan, S.M. (2010), "Large deflection of constant curvature cantilever beam under follower load", Int. J. Mech. Sci., 52(3), 440-445.   DOI
26 Ozturk, H. (2011), "In-plane free vibration of a pre-stressed curved beam obtained from a large deflected cantilever beam", Finite Elem. Anal. Des., 47(3), 229-236.   DOI
27 Ozturk, H. and Sabuncu, M. (2005) "Stability analysis of a cantilever composite beam on elastics supports", Compos. Sci. Technol., 65(13), 1982-1995.   DOI
28 Rao, K.M., Desai, Y.M. and Chitnis, M.R. (2001), "Free vibrations of laminated beams using mixed theory", Compos. Struct., 52(2), 149-160.   DOI
29 Pulngern, T., Chucheepsakul, S. and Halling, M.W. (2005), "Analytical and experimental studies on the large amplitude free vibrations of variable-arc-length beams", J. Vib. Control, 11(7), 923-947.   DOI
30 Rao, B.N. and Rao, G.V. (1986), "On the large deflection of cantilever beams with end rotational load", ZAMM-Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 66(10), 507-509.   DOI
31 Reddy, J.N. (1997), Mechanics of Laminated Composite Plates Theory and Analysis, CRS Press, New York, NY, USA.
32 Rikards, R., Chate, A. and Barkanov, E. (1993), "Finite element analysis of damping the vibrations of laminated composites", Compos. Struct., 47(6), 1005-1015.   DOI
33 Schmidt, W.F. (1978), "Nonlinear bending of beams using the finite element method", Comput. Struct., 8(1), 153-158.   DOI
34 Silva, V.D.D. (2006), Mechanics and Strength of Materials, Springer, Berlin, Heidelberg, Germany.
35 Stemple, A.D. and Lee, S.W. (1989), "A finite element model for composite beams undergoing large deflection with arbitrary cross- sectional warping", Int. J. Numer. Meth. Eng., 28(9), 2143-2160.   DOI
36 Sun, C.T. and Chin, H. (1988), "On large deflection effects in unsymmetric cross-ply composite laminates", J. Compos. Mater., 22(11), 1045-1059.   DOI
37 Thomas, D.L. and Wilson, R.R. (1973), "The use of straight beam finite elements for analysis of vibrations of curved beams", J. Sound Vib., 26(1), 155-158.   DOI
38 Wang, T.M. (1968), "Non-linear bending of beams with concentrated loads", J. Franklin Inst., 285(5), 386-390.   DOI
39 Tseng, Y.P., Huang, C.S. and Kao, M.S. (2000), "In-plane vibration of laminated curved beams with variable curvature by dynamic stiffness analysis", Compos. Struct., 50(2), 103-114.   DOI
40 Upadhyay, P.C. and Lyons, J.S. (2000), "Effect of hygrothermal environment on the bending of PMC laminates under large deflection", J. Reinf. Plast. Compos., 19(6), 465-491.   DOI
41 Wang, T.M. (1969), "Non-linear bending of beams with uniformly distributed loads", Int. J. Nonlin. Mech., 4(4), 389-395.   DOI
42 Yang, T.Y. (1973), "Matrix displacement solution to elastica problems of beams and frames", Int. J. Solids Struct., 9(7), 829-842.   DOI
43 Yang, Y.B., Kuo, S.R. and Yau, J.D. (1991), "Use of straight-beam approach to study buckling of curved beams", J. Struct. Eng.-ASCE., 117(7), 1963-1978.   DOI
44 Zhang, Y., Wang, S. and Petersson, B. (2003), "Large deflection analysis of composite laminates", J. Mater. Process. Technol., 138(1-3), 34-40.   DOI