Abstract
The vibration suppression analysis of a simply-supported laminated composite beam with magnetostrictive layers resting on visco-Pasternak’s foundation is presented. The constant gain distributed controller of the velocity feedback is utilized for the purpose of vibration damping. The formulation of displacement field is proposed according to Euler-Bernoulli’s classical beam theory (ECBT), Timoshenko’s first-order beam theory (TFBT), Reddy’s third-order shear deformation beam theory, and the simple sinusoidal shear deformation beam theory. Hamilton’s principle is utilized to give the equations of motion and then to describe the vibration of the current beam. Based on Navier’s approach, the solution of the dynamic system is obtained. The effects of the material properties, the modes, the thickness ratios, the lamination schemes, the magnitudes of the feedback coefficient, the position of magnetostrictive layers at the structure, and the foundation modules are extensively studied and discussed.
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References
REDDY, J. N. Mechanics of Laminated Composite Plates: Theory and Analysis, CRC Press, Boca Raton (1997)
SUMAN, S. D., HIRWANI, C. K., CHATURVEDI, A., and PANDA, S. K. Effect of magnetostrictive material layer on the stress and deformation behaviour of laminated structure. IOP Conference Series: Materials Science and Engineering, 178, 012026 (2017)
KRISHNA, M. A. V., ANJANAPPA, M., and WU, Y. F. The use of magnetostrictive particle actuators for vibration attenuation of flexible beams. Journal of Sound and Vibration, 206(2), 133–149 (1997)
KRISHNA, M. A. V., ANJANAPPA, M., WU, Y. F., BHATTACHARYA, B., and BHAT, M. S. Vibration suppression of laminated composite beam using embedded magnetostrictive layers. Journal of the Institution of Engineers: Aerospace Engineers Journal, 78, 38–44 (1998)
REDDY, J. N. and BARBOSA, J. I. On vibration suppression of magnetostrictive beams. Smart Materials and Structures, 9(1), 49–58 (2000)
PRADHAN, S. C., NG, T. Y., LAM, K. Y., and REDDY, J. N. Control of laminated composite plates using magnetostrictive layers. Smart Materials and Structures, 10(4), 1–11 (2001)
SUBRAMANIAN, P. Vibration suppression of symmetric laminated composite beams. Smart Materials and Structures, 11(6), 880–885 (2002)
KUMAR, J. S., GANESAN, N., SWARNAMANI, S., and PADMANABHAN, C. Active control of beam with magnetostrictive layer. Composite Structures, 81(13), 1375–1382 (2003)
KUMAR, J. S., GANESAN, N., SWARNAMANI, S., and PADMANABHAN, C. Active control of cylindrical shell with magnetostrictive layer. Journal of Sound and Vibration, 262(3), 577–589 (2003)
LEE, S. J., REDDY, J. N., and ROSTAM-ABADI, F. Transient analysis of laminated composite plates with embedded smart-material layers. Finite Elements in Analysis and Design, 40(5-6), 463–483 (2004)
KUMAR, J. S., GANESAN, N., SWARNAMANI, S., and PADMANABHAN, C. Active control of simply supported plates with a magnetostrictive layer. Smart Materials and Structures, 13(3), 487–492 (2004)
GHOSH, D. P. and GOPALAKRISHNAN, S. Coupled analysis of composite laminate with embedded magnetostrictive patches. Smart Materials and Structures, 14(6), 1462–1473 (2005)
ZHOU, H. M. and ZHOU, Y. H. Vibration suppression of laminated composite beams using actuators of giant magnetostrictive materials. Smart Materials and Structures, 16(1), 198–206 (2007)
OLABI, A. G. and GRUNWALD, A. Design and application of magnetostrictive materials. Materials & Design, 29(2), 469–483 (2008)
KARUNANIDHI, S. and SINGAPERUMAL, M. Design, analysis and simulation of magnetostrictive actuator and its application to high dynamic servo valve. Sensors and Actuators A: Physical, 157(2), 185–197 (2010)
FERREIRA, A. J. M., CARRERA, E., CINEFRA, M., ROQUE, C. M. C., and POLIT, O. Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations. Composites Part B: Engineering, 42(5), 1276–1284 (2011)
LEE, S. J. and REDDY, J. N. Non-linear response of laminated composite plates under thermomechanical loading. International Journal of Non-Linear Mechanics, 40(7), 971–985 (2005)
REDDY, J. N. On laminated composite plates with integrated sensors and actuators. Engineering Structures, 21(7), 568–593 (1999)
ZENKOUR, A. M. Torsional analysis of heterogeneous magnetic circular cylinder. Steel and Composite Structures, 17(4), 535–548 (2014)
ZHANG, Y., ZHOU, H., and ZHOU, Y. Vibration suppression of cantilever laminated composite plate with nonlinear giant magnetostrictive material layers. Acta Mechanica Solida Sinca, 28, 50–60 (2015)
DAPINO, M. J., FLATAU, A. B., and CALKINS, F. T. Statistical analysis of Terfenol-D materials properties. Smart Structures and Intelligent Systems, 3041, 256–267 (1997)
SUN, L. and ZHENG, X. Numerical simulation on coupling behavior of Terfenol-D rods. International Journal of Solids and Structures, 43(6), 1613–1623 (2006)
ANJANAPPA, M. and BI, J. Modelling, design and control of embedded Terfenol-D actuator. Smart Structures and Intelligent Systems, 1917, 908–918 (1993)
ANJANAPPA, M. and BI, J. A theoretical and experimental study of magnetostrictive mini actuators. Smart Materials and Structures, 3(2), 83–91 (1994)
ZENKOUR, A. M. and EL-SHAHRANY, H. D. Vibration suppression analysis for laminated composite beams contain actuating magnetostrictive layers. Journal Computational Applied Mechanics, 50(1), 69–75 (2019)
ZENKOUR, A. M. and EL-SHAHRANY, H. D. Vibration suppression of advanced plates embedded magnetostrictive layers via various theories. Journal of Materials Research and Technology, 9(3), 4727–4748 (2020)
KOCONIS, D. B., KOLLAR, L. P., and SPRINGER, G. S. Shape control of composite plates and shells with embedded actuators I: voltage specified. Journal of Composite Materials, 28(5), 415–458 (1994)
HONG, C. C. Transient responses of magnetostrictive plates without shear effects. International Journal of Engineering Science, 47(3), 355–362 (2009)
HONG, C. C. Transient responses of magnetostrictive plates by using the GDQ method. European Journal of Mechanics-A/Solids, 29(6), 1015–1021 (2010)
SHANKAR, G., KUMAR, S. K., and MAHATO, P. K. Vibration analysis and control of smart composite plates with delamination and under hygrothermal environment. Thin-Walled Structures, 116, 53–68 (2017)
ARANI, A. G. and MARAGHI, Z. K. A feedback control system for vibration of magnetostrictive plate subjected to follower force using sinusoidal shear deformation theory. Ain Shams Engineering Journal, 7(1), 361–369 (2016)
ARANI, A. G., MARAGHI, Z. K., and ARANI, H. K. Vibration control of magnetostrictive plate under multi- physical loads via trigonometric higher order shear deformation theory. Journal of Vibration and Control, 23(19), 3057–3070 (2017)
CHEN, Y. H., HUANG, Y. H., and SHIH, C. T. Response of an infinite Timoshenko beam on a viscoelastic foundation to a harmonic moving load. Journal of Sound and Vibration, 241(5), 809–824 (2001)
CALIM, F. F. Free and forced vibration analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation. Composites Part B: Engineering, 103, 98–112 (2016)
AREFI, M. and ZENKOUR, A. M. Wave propagation analysis of a functionally graded magnetoelectro-elastic nanobeam rest on visco-Pasternak foundation. Mechanics Research Communications, 79, 51–62 (2017)
ZENKOUR, A. M. Nonlocal elasticity and shear deformation effects on thermal buckling of a CNT embedded in a viscoelastic medium. The European Physical Journal Plus, 133, 14 (2018)
SOBHY, M. and ZENKOUR, A. M. Magnetic field effect on thermomechanical buckling and vibration of viscoelastic sandwich nanobeams with CNT reinforced face sheets on a viscoelastic substrate. Composites Part B: Engineering, 154, 492–506 (2018)
ZENKOUR, A. M. and AL-SUBHI, A. H. Thermal vibrations of a graphene sheet embedded in viscoelastic medium based on nonlocal shear deformation theory. International Journal of Acoustics and Vibration, 24(3), 485–493 (2019)
BAFERANI, A. H. and SAIDI, A. R. Effects of in-plane loads on vibration of laminated thick rectangular plates resting on elastic foundation: an exact analytical approach. European Journal of Mechanics-A/Solids, 42, 299–314 (2013)
MALEKZADEH, K., KHALILI, S. M. R., and ABBASPOUR, P. Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses. Composite Structures, 92(6), 1478–1484 (2010)
THAI, H. T., PARK, M., and CHOI, D. H. A simple refined theory for bending, buckling and vibration of thick plates resting on elastic foundation. International Journal of Mechanical Sciences, 73, 40–52 (2013)
RAZAVI, S. and SHOOSHTARI, A. Free vibration analysis of a magneto-electro-elastic doublycurved shell resting on a Pasternak-type elastic foundation. Smart Materials and Structures, 23(10), 105003 (2014)
ZAMANI, H. A., AGHDAM, M. M., and SADIGHI, M. Free vibration analysis of thick viscoelastic composite plates on visco-Pasternak foundation using higher-order theory. Composite Structures, 182(12), 25–35 (2017)
ZENKOUR, A. M. Thermal effects on the bending response of fiber-reinforced viscoelastic composite plates using a sinusoidal shear deformation theory. Acta Mechanica, 171(3-4), 171–187 (2004)
ZENKOUR, A. M. On vibration of functionally graded plates according to a refined trigonometric plate theory. International Journal of Structural Stability and Dynamics, 5(2), 279–297 (2005)
ZENKOUR, A. M. The refined sinusoidal theory for FGM plates on elastic foundations. International Journal of Mechanical Sciences, 51(11-12), 869–880 (2009)
ZENKOUR, A. M. Exact relationships between the classical and sinusoidal plate theories for FGM plates. Mechanics of Advanced Materials and Structures, 19(7), 551–567 (2012)
ZENKOUR, A. M. Hygrothermal effects on the bending of angle-ply composite plates using a sinusoidal theory. Composite Structures, 94(12), 3685–3696 (2012)
ZENKOUR, A. M. Trigonometric solution for an exponentially graded thick plate resting on elastic foundations. Archive of Mechanical Engineering, 65(2), 193–208 (2018)
LI, J., MA, Z., WANG, Z., and NARITA, Y. Random vibration control of laminated composite plates with piezoelectric fiber reinforced composites. Acta Mechanica Solida Sinca, 29(3), 316–327 (2016)
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Zenkour, A.M., El-Shahrany, H.D. Vibration suppression of magnetostrictive laminated beams resting on viscoelastic foundation. Appl. Math. Mech.-Engl. Ed. 41, 1269–1286 (2020). https://doi.org/10.1007/s10483-020-2635-7
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DOI: https://doi.org/10.1007/s10483-020-2635-7