An applied theory describing the transverse vibrations of a cantilever bimorph in an alternating magnetic field is presented. The bimorph is made of piezoactive materials, which is a multilayer composite with alternating piezoelectric and piezomagnetic layers. The mechanical and physical properties of such a composite are specified by their effective constants. This theory can serve as a model for energy harvesting devices under the action of an external alternating magnetic field. Within the framework of the theory, quadratic distributions of electric and magnetic potentials over the cantilever thickness are assumed inhomogeneous in its longitudinal direction. The stress-strain state of the bimorph, the distribution of electric and magnetic fields, and its natural frequencies are calculated. In addition, the case where the potential at one of electrodes is unknown is examined. The results of calculations in the low-frequency region are compared with those found by a finite-element model based on a system of partial differential equations built in the COMSOL Multiphysics package. A comparison showed a good agreement between the calculated field characteristics and the data of finite-element modeling in the entire area of the bimorph, except in the vicinity of the beam fixation and its free end.
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04 November 2022
A Correction to this paper has been published: https://doi.org/10.1007/s11029-022-10066-7
References
P. Gaudenzi, Smart Structures: Physical Behaviour, Mathematical Modelling and Applications, John Wiley & Sons, New York—Chichester—Brisbane—Toronto (2009).
I. N. Qader, M. Kok, F. Dagdelen, and Y. Aydogdu, “A review of smart materials: researches and applications,” El-Cezerî Journal of Science and Engineering, 6, No. 3, 755-788 (2019).
R. Janeliukstis and D. Mironovs, “Smart composite structures with embedded sensors for load and damage monitoring – a review,” Mech. Compos. Mater., 57, No. 2, 131-152 (2021).
S. V. Plotnikova and G. M. Kulikov, “Shape control of composite plates with distributed piezoelectric actuators in a three-dimensional formulation,” Mech. Compos. Mater., 56, No. 5, 557-572 (2020).
A. Kovalovs, E. Barkanov, S. Ruchevskis, and M. Wesolowski, “Modeling and design of a full-scale rotor blade with embedded piezocomposite actuators,” Mech. Compos. Mater., 53, No. 2, 179-192 (2017).
T. Amrillah, A. Hermawan, C. P. Wulandari, A. D. Muthi’Ah, and F. M. Simanjuntak, “Crafting the multiferroic BiFeO3-CoFe2O4 nanocomposite for next-generation devices: A review,” Materials and Manufacturing Processes, 36, No. 14, 1579-1596 (2021).
R. Lamouri, O. Mounkachi, E. Salmani, M. Hamedoun, A. Benyoussef, and H. Ez-Zahraouy, “Size effect on the magnetic properties of CoFe2O4 nanoparticles: a Monte Carlo study,” Ceramics International, 46, No. 6, 8092-8096 (2020).
M. Fiebig, “Revival of the magnetoelectric effect,” Journal of Physics D: Applied Physics, 38, No. 8, R123– R152 (2005).
K. V. Siva, P. Kaviraj, and A. Arockiarajan, “Improved room temperature magnetoelectric response in CoFe2O4-BaTiO3 core shell and bipolar magnetostrictive properties in CoFe2O4,” Materials Letters, 268, 127623 (2020).
K. S. Challagulla and A. V. Georgiades, “Micromechanical analysis of magneto-electro-thermo-elastic composite materials with applications to multilayered structures,” International Journal of Engineering Science, 49, No. 1, 85-104 (2011).
V. Novatskiy and V. A. Shachnev, Electromagnetic Effects in Solids [in Russian], Мir, Мoscow (1986).
V. Z. Parton and B. A. Kudryavtsev, Electromagnetoelasticity of Piezoelectric and Electroconductive Bodies [in Russian], Мoscow, Nauka (1988).
A. O. Vatul’yan and A. A. Rynkova, “Flexural vibrations of a piezoelectric bimorph with a cut internal electrode,” Journal of Applied Mechanics and Technical Physics, 42, No. 1, 164-168 (2001).
A. N. Soloviev, P. A. Oganesyan, T. G. Lupeiko, E. V. Kirillova, S. H. Chang, and C. D. Yang, in: I. A. Parinov (ed.), Advanced Materials, Ch. 46, Modeling of Non-Uniform Polarization for Multi-Layered Piezoelectric Transducer for Energy Harvesting Devices, Springer, Heidelberg, 651-658 (2016).
J. G. Wang, L. F. Chen, and S. Fang, “State vector approach to analysis of multilayered magneto-electro-elastic plates,” Int. J. Solids and Structures, 40, No. 7, 1669-1680 (2003).
E. Pan, “Exact solution for simply supported and multilayered magneto-electro-elastic plates,” J. Appl. Mech., 68, No. 4, 608-618 (2001).
A. Milazzo, C. Orlando, and A. Alaimo, “An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem,” Smart Materials and Structures, 18, No. 8, 085012 (2009).
M. O. Levi and V. V. Kalinchuk, in: 2017 Dynamics of Systems, Mechanisms and Machines (Dynamics), Some Features of the Dynamics of Electro-Magneto-Elastic Half-Space with Initial Deformations, IEEE, Omsk, 1-5 (2017).
E. Pan and P. R. Heyliger, “Free vibrations of simply supported and multilayered magneto-electro-elastic plates,” Journal of Sound and Vibration 252, No. 3, 429-442 (2002).
A. R. Annigeri, N. Ganesan, and S. Swarnamani, “Free vibration behaviour of multiphase and layered magneto-electroelastic beam,” Journal of Sound and Vibration, 299, Nos. 1-2, 44-63 (2007).
A. Milazzo, I. Benedetti, and C. Orlando, “Boundary element method for magneto electro elastic laminates,” Comput. Model. Eng. Sci., 15, 17-30 (2006).
A. N. Soloviev, V. A. Chebanenko, I. A. Parinov, and P. A. Oganesyan, “Applied theory of bending vibrations of a piezoelectric bimorph with a quadratic electric potential distribution,” Materials Physics and Mechanics, 42, No. 1, 65-73 (2019).
D. T. Binh, V. A. Chebanenko, L. V. Duong, E. Kirillova, P. M. Thang, and A. N. Soloviev, “Applied theory of bending vibration of the piezoelectric and piezomagnetic bimorph,” Journal of Advanced Dielectrics, 10, No. 3, 2050007 (2020).
N. V. Kurbatova, D. K. Nadolin, A. V. Nasedkin, P. A. Oganesyan, and A. N. Soloviev, in: H. Altenbach, E. Carrera, G. Kulikov (eds.), Analysis and Modelling of Advanced Structures and Smart Systems. Advanced Structured Materials, Finite Element Approach for Composite Magneto-Piezoelectric Materials Modeling in ACELAN-COMPOS Package, Springer, Singapore, 69-88 (2018).
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This work was carried out with the financial support of the Russian Science Foundation grant No. 21-19-00423, https://rscf.ru/project/21-19-00423/ at the Southern Federal University.
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Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 58, No. 4, pp. 675-690, July-August, 2022. Russian DOI: https://doi.org/10.22364/mkm.58.4.02.
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Soloviev, A.N., Do, B.T., Chebanenko, V.A. et al. Flexural Vibrations of a Composite Piezoactive Bimorph in an Alternating Magnetic Field: Applied Theory and Finite-Element Simulation. Mech Compos Mater 58, 471–482 (2022). https://doi.org/10.1007/s11029-022-10043-0
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DOI: https://doi.org/10.1007/s11029-022-10043-0