Vibration of Conducting Two-Layer Sandwich Homogeneous Elastic Beams in Transverse Magnetic Fields
Publication: Journal of Aerospace Engineering
Volume 27, Issue 3
Abstract
A theory governing the flexural vibration of a conducting two-layer sandwich homogeneous elastic beam in a transverse magnetic field is presented. The physics driving this problem derives from an energy dissipation mechanism through press-fit joints in structural laminates. Recent advances made in the mechanics of sandwich-layered structures have shown that by simulating an environment of nonuniform interface pressure, structural vibration can be attenuated significantly. Equations of mathematical physics governing the stresses and the structural vibration are derived via a laminated beam theory employing the Newtonian form of Cauchy’s stress equations. By restricting mathematical analysis to the case of cantilever architecture, a closed-form polynomial expression is derived for the system response. In particular, the effects of magnetoelasticity, material conductivity, and interfacial pressure gradient on the response characteristics are demonstrated for design analysis and engineering applications. It is shown via integral transforms that each mode of vibration is governed by a two-dimensional family of natural frequency. For special and limit cases, recent theoretical and experimental results are validated from the theory reported in this paper.
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References
Brown, W. F. (1966). “Magnetoelastic interaction.” Tracts in natural philosophy, Vol. 9, Springer, Berlin.
Dai, H. L., and Wang, X. (2004). “Dynamic responses of piezoelectric hollow cylinders in an axial magnetic field.” Int. J. Solids Struct., 41(18–19), 5231–5246.
Damisa, O. (2003). “Slip damping of Timoshenko beam close to resonance.” J. Eng. Res., 11(1–2), 13–26.
Damisa, O., Olunloyo, V. O. S., Osheku, C. A., and Oyediran, A. A. (2007). “Static analysis of slip damping with clamped laminated beams.” Eur. J. Sci. Res., 17(4), 455–476.
Damisa, O., Olunloyo, V. O. S., Osheku, C. A., and Oyediran, A. A. (2008). “Dynamic analysis of slip damping in clamped layered beams with non-uniform pressure distribution at the interface.” J. Sound Vib., 309(3–5), 349–374.
Goodman, L. E., and Klumpp, J. H. (1956). “Analysis of slip damping with reference to turbine blade vibration.” J. Appl. Mech., 23(3), 421–429.
Hansen, S. W., and Spies, R. (1997). “Structural damping in laminated beams due to interfacial slip.” J. Sound Vib., 204(2), 183–202.
Hasanyan, D. J., Librescu, L., and Ambur, D. R. (2004). “A few results on the foundation of the theory and behavior of nonlinear magnetoelastic plates carrying an electrical current.” Int. J. Eng. Sci., 42(15–16), 1547–1572.
Lee, J. S. (1992). “Destabilizing effect of magnetic damping in plate strip.” J. Eng. Mech., 161–173.
Lee, J. S. (1996). “Dynamic stability of conducting beam-plates in transverse magnetic fields.” J. Eng. Mech., 89–94.
Librescu, L., Hasanyan, D., Qin, Z., and Ambur, D. R. (2003). “Nonlinear magneto-thermo-elasticity of anisotropic plates immersed in a magnetic field.” J. Therm. Stresses, 26(11–12), 1277–1305.
Miya, K., Tagaki, T., and Ando, Y. (1980). “Finite element analysis of magnetoelastic buckling of a ferromagnetic beam-plate.” J. Appl. Mech., 47(2), 377–382.
Moon, F. C., and Pao, Y.-H. (1968). “Magnetoelastic buckling of a thin plate.” J. Appl. Mech., 35(1), 53–58.
Moon, F. C., and Pao, Y.-H. (1969). “Vibration and dynamic instability of a beam-plate in a transverse magnetic field.” J. Appl. Mech., 36(1), 92–100.
Nanda, B. K. (2006). “Study of the effect of bolt diameter and washer on damping in layered and jointed structures.” J. Sound Vib., 290(3–5), 1290–1314.
Nanda, B. K. (2011). “Damping of layered cantilever beams of various materials with uniform intensity of pressure distribution at the interfaces.” Int. J. Struct. Eng., 2(4), 315–333.
Nanda, B. K., and Behera, A. K. (1999). “Study on damping in layered and jointed structures with uniform pressure distribution at the interfaces.” J. Sound Vib., 226(4), 607–624.
Olunloyo, V. O., Damisa, O., and Osheku, C. A. (2008). “Vibration damping in structures with layered viscoelastic beam-plate.” J. Vib. Acoust., 130(6), 061002.
Olunloyo, V. O. S., Damisa, O., Osheku, C. A., and Oyediran, A. A. (2010). “Analysis of the effects of laminate depth and materials on the damping associated with layered structures in a pressurized environment.” Trans. Can. Soc. Mech. Eng., 34(2), 165–196.
Peach, M. O., Christopherson, N. S., Dalrymple, J. M., and Viegelahn, G. L. (1988). “Magnetoelastic buckling: Why theory and experiment disagree.” Exp. Mech., 28(1), 65–69.
Singh, B., and Nanda, B. K. (2012). “Slip damping mechanism in welded structures using response surface methodology.” Exp. Mech., 52(7), 771–791.
Takagi, T., Tani, J., Matsubara, Y., Mogi, I., and Miya, K., eds. (1993). “Electromagneto-mechanics coupling effects for non-ferromagnetic and ferromagnetic structures.” Proc., 2nd Int. Workshop on Electromagnetic Forces and Related Effects on Blankets and other Structures Surrounding Fusion Plasma Torus, Tokai, Japan, 81–90.
Thatoi, D. N., Mohanty, R. C., Acharya, A. K., and Nanda, B. K. (2012). “Damping improvement in layered and jointed beams by finite element analysis.” Adv. Mater. Res., 505, 501–505.
Tiersten, H. F. (1964). “Coupled magnetomechanical equations for magnetically saturated insulators.” J. Math. Phys., 5, 1298.
Wallerstein, D. V., and Peach, M. O. (1972). “Magnetoelastic buckling of beams and thin plates of magnetically soft materials.” J. Appl. Mech., 39(2), 451–455.
Wang, X., and Dai, H. L. (2004). “Magnetothermodynamic stress and perturbation of magnetic field vector in an orthotropic thermoelastic cylinder.” Int. J. Eng. Sci., 42(5–6), 539–556.
Wang, X., and Lee, J. S. (2006). “Dynamic stability of ferromagnetic beam-plates with magnetoelastic interaction and magnetic damping in transverse magnetic fields.” J. Eng. Mech., 422–428.
Wang, X., Lee, J. S., and Zheng, X. J. (2003). “Magneto-thermo-elastic instability of ferromagnetic plates in thermal and magnetic fields.” Int. J. Solids Struct., 40(22), 6125–6142.
Wang, X., Lu, G., and Guillow, S. R. (2002). “Magnetothermodynamic stress and pertubation of magnetic field vector in a solid cylinder.” J. Therm. Stresses, 25(10), 909–926.
Zheng, X. J., Zhou, Y. H., Wang, X. Z., and Lee, J. S. (1999). “Bending and buckling of ferroelastic plates.” J. Eng. Mech., 180–185.
Zhou, Y.-H., and Miya, K. (1998). “A theoretical prediction of natural frequency of a ferromagnetic beam-plate with low susceptibility in an in-plane magnetic field.” J. Appl. Mech., 65(1), 121–126.
Zhou, Y.-H., and Zheng, X. (1997). “A general expression of magnetic force for soft ferromagnetic plates in complex magnetic fields.” Int. J. Eng. Sci., 35(15), 1405–1417.
Zhou, Y.-H., Zheng, X.-J., and Miya, K. (1995). “Magnetoelastic bending and snapping of ferromagnetic plates in oblique magnetic field.” Fusion Eng. Des., 30(4), 325–337.
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© 2014 American Society of Civil Engineers.
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Received: Jan 13, 2011
Accepted: Nov 16, 2012
Published online: Nov 20, 2012
Published in print: May 1, 2014
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