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http://dx.doi.org/10.12989/sss.2018.21.3.349

Vibration suppression of a double-beam system by a two-degree-of-freedom mass-spring system  

Rezaiee-Pajand, Mohammad (Department of Civil Engineering, Ferdowsi University of Mashhad)
Sani, Ahmad Aftabi (Department of Civil Engineering, Ferdowsi University of Mashhad)
Hozhabrossadati, Seyed Mojtaba (Department of Civil Engineering, Ferdowsi University of Mashhad)
Publication Information
Smart Structures and Systems / v.21, no.3, 2018 , pp. 349-358 More about this Journal
Abstract
This paper investigates the free vibration analysis of double-beam system coupled by a two-degree-of-freedom mass-spring system. In order to generalize the model, the main beams are assumed to be elastically restrained against translation and rotation at one end and free at the other. Furthermore, the mass-spring system is elastically connected to the beams at adjustable positions by means of four translational and rotational springs. The governing differential equations of the beams and the mass-spring system are derived and analytically solved by using the Fourier transform method. Moreover, as a second way, a finite element solution is derived. The frequency parameters and mode shapes of some diverse cases are obtained using both methods. Comparison of obtained results by two methods shows the accuracy of both solutions. The influence of system parameters on the free vibration response of the studied mechanical system is examined.
Keywords
double-beam; two-degree-of-freedom mass-spring system; vibration suppression; elastic supports; Fourier transform; free vibration; exact solution; finite element method;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
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1 Abu-Hilal, M. (2006), "Dynamic response of a double Euler-Bernoulli beam due to a moving constant load", J. Sound Vib., 297(3-5), 477-491.   DOI
2 Ariaei, A, Ziaei-Rad, S. and Ghayour, M. (2011), "Transverse vibration of a multiple-Timoshenko beam system with intermediate elastic connections due to a moving load", Arch. Appl. Mech., 81(3), 263-281.   DOI
3 Banerjee, J.R. (2003), "Dynamic stiffness formulation and its application for a combined beam and a two degree-of-freedom system", J. Vib. Acoust., 125(3), 351-358.   DOI
4 Cha, P.D. and Chan, M. (2009), "Mitigating vibration along an arbitrarily supported elastic structure using multiple two-degree-of-freedom oscillators", J. Vib. Acoust., 131, 0310081-03100810.
5 Cha, P.D. and Zhou, X. (2008), "Frequency response of a combined structure using a modified finite element method", AIAA J., 46(10), 2408-2415.   DOI
6 Chang, T.P. and Chang, C.Y. (1998), "Vibration analysis of beams with a two-degree-of-freedom spring-mass system", Int. J. Solids Struct., 35(5-6), 383-401.   DOI
7 Chen, D.W. (2006), "The exact solution for free vibration of uniform beams carrying multiple two-degree-of-freedom spring-mass system", J. Sound Vib., 295(1-2), 342-361.   DOI
8 De Rosa, M.A. and Lippiello, M. (2007), "Non-classical boundary conditions and DQM for double beams", Mech. Res. Commun., 34(7-8), 538-544.   DOI
9 Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's nonlocal elasticity theory for vibration analysis rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857.   DOI
10 El-Sayed, T.A. and Farghaly, S.H. (2016), "Exact vibration of Timoshenko beam combined with multiple mass spring sub-system", Struct. Eng. Mech., 57(6), 989-1014.   DOI
11 Giunta, G., Koutsawa, Y., Belouettar S. and Calvi, A (2014), "A dynamic analysis of three-dimensional functionally graded beams by hierarchical models", Smart Struct. Syst., 13(4), 637-657.   DOI
12 Gurgoze, M. and Erol, H. (2004), "On laterally vibrating beams carrying tip masses, coupled by several double spring-mass systems", J. Sound Vib., 269, 431-438.   DOI
13 Gurgoze, M., Erdogan, G. and Inceoglu, S. (2001), "Bending vibrations of beams coupled by a double spring-mass system", J. Sound Vib., 243, 361-369.
14 Hozhabrossadati, S.M., Aftabi Sani, A. and Mofid, M. (2016), "Free vibration analysis of a beam with an intermediate sliding connection joined by a mass-spring system", J. Vib. Control, 22(4), 955-964.   DOI
15 Hozhabrossadati, S.M., Aftabi Sani, A., Mofid, M. and Mehri, B. (2015), "Green's function for uniform Euler-Bernoulli beams at resonant condition: Introduction of Fredholm Alternative Theorem", Appl. Math. Model., 39(12), 3366-3379.   DOI
16 Hozhabrossadati, S.M., Aftabi Sani, A. and Mofid, M. (2015), "Vibration of beam with elastically restrained ends and rotational spring -lumped rotary inertia system at mid-span", Int. J. Struct. Stab. Dynam., 15(2), 1450040.   DOI
17 Jun, L. and Hongxing, H. (2008), "Dynamic Stiffness vibration analysis of an elastically connected three-beam system", Appl. Acoust., 69(7), 591-600.   DOI
18 Hussein, M.F.M. and Hunt, H.E.M. (2006), "Modelling of flouting-slab tracks with continuous slabs under oscillating moving loads", J. Sound Vib., 297(1-2), 37-54.   DOI
19 Inceoglu, S. and Gurgoze, M. (2001), "Bending vibrations of beams coupled by several double spring-mass system", J. Sound Vib., 243, 370-379.
20 Jen, M.U. and Magrab, E.B. (1993), "Natural frequencies and mode shapes of beams carrying a two degree-of-freedom spring-mass system", J. Vib. Acoust., 115(2), 202-209.   DOI
21 Kukla, S. (1994), "Free vibration of the system of two beams connected by many translational springs", J. Sound Vib., 172, 130-135.   DOI
22 Laura, P.A.A., Susemihl, E.A., Pombo, J.L., Luisoni, L.E. and Gelos, R. (1977), "On the dynamic behavior of structural elements carrying elastically mounted concentrated masses", Appl. Acoust., 10(2), 121-145.   DOI
23 Lee, K.T. (2009), "Vibration of two cantilever beams clamped at one end and connected by a rigid body at the other", J. Mech. Sci. Technol., 23(2), 358-371.   DOI
24 Li, J. and Hua, H. (2007), "Spectral finite element analysis of elastically connected double-beam system", Finite Elem. Anal. Des., 43(15), 1155-1168.   DOI
25 Lin, H.P. and Yang, D. (2013), "Dynamic responses of two beams connected by a spring-mass device", J. Mech., 29(1), 143-155.   DOI
26 Rezaiee-Pajand, M. and Hozhabrossadati, S.M. (2016), "Analytical and numerical method for free vibration of double-axially functionally graded beams", Compos. Struct., 152, 488-498.   DOI
27 Magrab, E.B. (2007), "Natural frequencies and mode shapes of Timoshenko beams with attachments", J. Vib. Control, 13(7), 905-934.   DOI
28 Mao, O. and Wattanasakulpong, N. (2015), "Vibration and stability of a double-beam system interconnected by an elastic foundation under conservative and nonconservative axial load", Int. J. Mech. Sci., 93, 1-7.   DOI
29 Oniszczuk, Z. (2003), "Forced transverse vibrations of an elastically connected complex simply supported double beam systems", J. Sound Vib., 264(2), 273-286.   DOI
30 Rajabi, R., Kargarnovin, M.H. and Gharini, M. (2013), "Dynamic analysis of a simply supported Euler-Bernoulli beam subjected to a moving oscillator", Acta Mechanica, 224(2), 425-446.   DOI
31 Simsek, M. and Cansiz, S. (2012), "Dynamics of elastically connected double-functionally graded beam systems with different boundary conditions under action of a moving harmonic load", Compos. Struct., 94(9), 2861-2878.   DOI
32 Stojanovic, V. and. Kozic, P. (2012), "Forced transverse vibration of Rayleigh and Timoshenko double-beam system with effect of compressive axial load", Int. J. Mech. Sci., 60(1), 59-71.   DOI
33 Stojanovic, V., Kozic, P. and Pavlovic, R. (2011), "Effect of rotary inertia and shear on vibration and buckling of a double beam system under compressive axial loading", Arch. Appl. Mech., 81(12), 1993-2005.   DOI
34 Zhang, Y.Q., Lu, Y., Wang, S.L. and Liu, X. (2008), "Vibration and buckling of a double beam system under compressive axial loading", J. Sound Vib., 318(1-2), 341-352.   DOI
35 Vu, H.V., Ordonez, A.M. and Karnopp, B.H. (2000), "Vibration of a double-beam system", J. Sound Vib., 229(4), 807-822.   DOI
36 Wu, J.J. (2002), "Alternative approach for free vibration of beams carrying a number of two-degree of freedom spring-mass systems", J. Struct. Eng., 128(12), 604-1616.
37 Wu, J.J. (2005), "Use of equivalent-damper method for free vibration analysis of a beam carrying multiple two-degree-of-freedom spring-mass-damper systems", J. Sound Vib., 281(1-2), 275-293.   DOI
38 Yang, Y.B., Li, Y.C. and Chang, K.C. (2012), "Using two connected vehicles to measure the frequencies of bridges with rough surface: a theoretical study", Acta Mechanica, 223(8), 1851-1861.   DOI
39 Zhang, Y.Q., Lu, Y. and. Ma, G.W. (2008), "Effect of compressive axial load on forced transverse vibration of a double-beam system", Int. J. Mech. Sci., 50(2), 299-305.   DOI