Free Vibrations of Continuous Grading Fiber Orientation Beams on Variable Elastic Foundations
محورهای موضوعی : EngineeringS Kamarian 1 , M.H Yas 2 , A Pourasghar 3
1 - Department of Mechanical Engineering, Razi University
2 - Department of Mechanical Engineering, Razi University
3 - Department of Mechanical Engineering, Razi University
کلید واژه: Elastic foundation, Free vibrations, Beam, Continuous grading fiber orientation, GDQ Method,
چکیده مقاله :
Free vibration characteristics of continuous grading fiber orientation (CGFO) beams resting on variable Winkler and two-parameter elastic foundations have been studied. The beam is under different boundary conditions and assumed to have arbitrary variations of fiber orientation in the thickness direction. The governing differential equations for beam vibration are being solved using Generalized Differential Quadrature (GDQ) method. Numerical results are presented for a beam with arbitrary variation of fiber orientation in the beam thickness and compared with similar discrete laminate beam. The main contribution of this work is to present useful results for continuous grading of fiber orientation through thickness of a beam on variable elastic foundation and its comparison with similar discrete laminate composite beam. The results show the type of elastic foundation plays very important role on the natural frequency parameter of a CGFO beam. According to the numerical results, frequency characteristics of the CGFO beam resting on a constant Winkler elastic foundation is almost the same as of a composite beam with different fiber orientations for large values of Winkler elastic modulus, and fiber orientations has less effect on the natural frequency parameter. The interesting results show that normalized natural frequency of the CGFO beam is smaller than that of a similar discrete laminate beam and tends to the discrete laminated beam with increasing layers. It is believed that new results are presented for vibrational behavior of CGFO beams are of interest to the scientific and engineering community in the area of engineering design.
[1] Suresh S., Moretensen A., 1998, Fundamentals of functionally graded materials, IOM communications limited, London.
[2] Pradhan SC., Loy CT., Lam KY., Reddy J.N., 2000, Vibration characteristic of functionally graded cylindrical shells under various boundary conditions, Applied Acoustics 61:119-129.
[3] Zhou Ding., 1993, A general solution to vibrations of beams on variable Winkler elastic foundation, Computers & structures 47: 83-90.
[4] Thambiratnam D., Zhuge Y., 1996, Free vibration analysis of beams on elastic foundation, Computers & Structures 60: 971–980.
[5] Matsunaga H., 1999, Vibration and buckling of deep beam–columns on two-parameter elastic foundations, Journal of Sound and Vibration 228(2): 359–376.
[6] Ying J., Lu C.F., Chen W.Q., 2008, Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations, Composite Structures 84: 209–219.
[7] Yas M. H., Kamarian S., Eskandari J., Pourasghar A., 2011, Optimization of functionally graded beams resting on elastic foundations, Journal of Solid Mechanic 3(4):365-378.
[8] Bellman R., Kashef B.G., Casti J., 1972, Differential quadrature: a technique for a rapid solution of non linear partial differential equations, Journal of Computational Physics 10: 40–52.
[9] Shu C., 2000, Differential quadrature and its application in engineering, Springer, Berlin.
[10] Chen WQ., Bian ZG., 2003, Elasticity solution for free vibration of laminated beam, Composite Structures 62:75-82.
[11] Chen WQ., 3D, 2005, free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported, Composite Structures 69:77-87.
[12] Khalili S.M.R., Jafari A.A., 2010, Eftekhari S.A., A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads, Composite Structures 92:2497-2511.
[13] Pradhan S.C., Murmu T., 2009, Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method, Journal of Sound and Vibration 321: 342-362.
[14] Sobhani Aragh B., Yas M.H., 2010, Three-Dimensional free vibration of functionally graded fiber orientation and volume fraction cylindrical panels, Materials & Design 31: 4543-4552.
[15] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells, CRC Press, Boca Raton, FL, Second Edition.
[16] Shu C., Richards B.E., 1992, Application of differential quadrature to solve two-dimensional incompressible Navier-stokes equations, International Journal for Numerical Methods in Fluids 15:791-798.
[17] Bert CW., Malik M., 1996, Differential quadrature method in computational mechanics, Applied Mechanics Reviews 49:1-28.
