Effect of the Multi Vibration Absorbers on the Nonlinear FG Beam Under Periodic Load with Various Boundary Conditions
محورهای موضوعی : Mechanical Engineering
H Ahmadi
1
(Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran)
K Foroutan
2
(Faculty of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran)
کلید واژه: Periodic load, Vibration response, Functionally graded beam, Vibration absorbers,
چکیده مقاله :
A semi-analytical method is used to study the effects of the multi vibration absorbers on the nonlinear functionally graded (FG) Euler-Bernoulli beam subjected to periodic load. The material properties of the beam are assumed to be continuously graded in the thickness direction. The governing equations of functionally graded beam are obtained based on the Hamilton's principle and these equations are solved by using the Rayleigh-Ritz method. To validate the results, comparisons are made with the available solutions for the natural frequencies of isotropic beam. The effects of the multi vibration absorbers and material parameters on the vibration response of functionally graded beamare investigated. For case study the effect of two symmetrical vibration absorbers is considered, these absorbers are applicable in some of the mechanic systems. In those systems, two absorbers are used close to the beginning and end of the structures instead of using them in the middle of these structures. By considering the industrial applications, it is shown that using the two symmetrical vibration absorbers with lower mass is close to the end of functionally graded beam is better than the middle of one. Also, the effect of different numbers of the vibration absorbers on the nonlinear functionally graded beam with simply supported boundary condition is considered. The results shown that increasing the number of vibration absorbers leads to decreasing the maximum deflection.
[1] Mao Q., Pietrzko S., 2010, Free vibration analysis of stepped beams by using adomian decomposition method, Applied Mathematics and Computation 217: 3429-3441.
[2] Hsu J.C., Lai H.Y., Chen C.K., 2008, Free vibration of non-uniform euler-bernoulli beams with general elastically end constraints using adomain modified decomposition method, Journal of Sound and Vibration 318: 965-981.
[3] Aydogdu M., Taskin V., 2007, Free vibration analysis of functionally graded beams with simply supported edges, Material Design 28: 1651-1656.
[4] Sina S.A., Navazi H.M., Haddadpour H., 2009, An analytical method for free vibration analysis of functionally graded beams, Material Design 30: 741-747.
[5] Kapuria S., Bhattacharyya M., Kumar A.N., 2008, Bending and free vibration response of layered functionally graded beams: A theoretical model and its experimental validation, Composite Structures 82: 390-402.
[6] Kitipornchai S., Ke L.L., Yang J., Xiang Y., 2009, Nonlinear vibration of edge cracked functionally graded timoshenko beams, Journal of Sound and Vibration 324: 962-982.
[7] Alshorbagy Amal E., Eltaher M.A., Mahmoud F.F., 2011, Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling 35: 412-425.
[8] Wattanasakulpong N., Prusty B.G., Kelly D.W., Hoffman M., 2010, A theoretical investigation on the free vibration of functionally graded beams, Proceedings of the 10th International Conference on Computational Structures Technology, Valencia.
[9] Yang J., Chen Y., 2008, Free vibration and buckling analysis of functionally graded beams with edge cracks, Composite Structures 83: 48-60.
[10] Sahraee S., Saidi A.R., 2009, Free vibration and buckling analysis of functionally graded deep beam-columns on two-parameter elastic foundations using the differential quadrature method, Journal of Mechanical Engineering Science 223: 1273-1284.
[11] Rahimi G.H., Gazor M.S., Hemmatnezhad M., Toorani H., 2013, On the postbuckling and free vibrations of FG Timoshenko beams, Composite Structures 95: 247-253.
[12] Kojima H., Saito H., 1983, Forced vibration of a beam with a non-linear dynamic vibration absorber, Journal of Sound and Vibration 88: 559-568.
[13] Huang Y.M., Chen C.C., 2000, Optimal design of dynamic absorbers on vibration and noise control of the fuselage, Composite Structures 76: 691-702.
[14] Yamaguchi H., 1985, Vibrations of a beam with an absorber consisting of a viscoelastic beam and a spring-viscous damper, Journal of Sound and Vibration 103: 417-425.
[15] Juang J.N., 1984, Optimal design of a passive vibration absorber for a truss beam, Journal of Guidance Control and Dynamics 7: 733-739.
[16] Najafi M., Ashory M.R., Jamshidi E., 2009, Optimal design of beam vibration absorbers under point harmonic excitation, Society for Experimental Mechanics, Orlando, Florida USA.
[17] Bonsel J.H., Fey R.H.B., Nijmeijer H., 2004, Application of a dynamic vibration absorber to a piecewise linear beam system, Nonlinear Dynamic 37: 227-243.
[18] Esmailzadeh E., Jalilj N., 1998, Optimum design of vibration absorbers for structurally damped Timoshenko Beams, Journal of Vibration and Acoustics 120: 833-841.
[19] Wong W.O., Tang S.L., Cheung Y.L., Cheng L., 2007, Design of a dynamic vibration absorber for vibration isolation of beams under point or distributed loading, Journal of Sound and Vibration 301: 898-908.
[20] Kang Y.K., Park C.h., Kim J., Choi S.B., 2002, Interaction of active and passive vibration control of laminated composite beams with piezoceramic sensors/actuators, Material Design 23: 277-286.
[21] Khorshidi M.A., Shariati M., 2016, Free vibration analysis of sigmoid functionally graded nanobeams based on a modified couple stress theory with general shear deformation theory, Journal of the Brazilian Society of Mechanical Sciences and Engineering 38: 2607-2619.
[22] Volmir A.S., 1972, Non-Linear Dynamics of Plates and Shells, Science Edition M, USSR.
[23] Majkut L., 2009, Free and forced vibration of Timoshenko beams described by single difference equation, Journal of Theoretical and Applied Mechanics 47: 193-210.
