Geodesic
Applied theory of flexural vibrations of a piezoactive bimorph in the framework of an uncoupled boundary-value problem of thermoelectroelasticity
Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 364-374.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we consider transverse steady oscillations of a piezoactive bimorph in the formulation of a plane deformation. The problem is solved within the framework of linear thermoelectroelasticity, while the temperature problem is solved separately and the temperature distribution is taken into account in the constitutive relations of electroelasticity. On the basis the Kirchhoff–Love type hypothesis for mechanical quantities and a symmetric quadratic distribution of the electric potential, an approximate theory for calculating bimorph vibrations is constructed. Numerical experiments have been carried out for various cases of pinning and excitation of vibrations. The results of these experiments were compared with calculations made using the finite element method in the COMSOL package and showed the adequacy of the constructed theory in the low-frequency region.
Keywords: thermoelectroelasticity, bimorph, applied theory, finite element method, piezoelectric generator for collecting and storing energy.
Mots-clés : vibrations 
@article{CMFD_2023_69_2_a11,
     author = {A. N. Soloviev and V. A. Chebanenko and M. S. Germanchuk},
     title = {Applied theory of flexural vibrations of a piezoactive bimorph in the framework of an uncoupled boundary-value problem of thermoelectroelasticity},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {364--374},
     publisher = {mathdoc},
     volume = {69},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a11/}
}
TY  - JOUR
AU  - A. N. Soloviev
AU  - V. A. Chebanenko
AU  - M. S. Germanchuk
TI  - Applied theory of flexural vibrations of a piezoactive bimorph in the framework of an uncoupled boundary-value problem of thermoelectroelasticity
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2023
SP  - 364
EP  - 374
VL  - 69
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a11/
LA  - ru
ID  - CMFD_2023_69_2_a11
ER  - 
%0 Journal Article
%A A. N. Soloviev
%A V. A. Chebanenko
%A M. S. Germanchuk
%T Applied theory of flexural vibrations of a piezoactive bimorph in the framework of an uncoupled boundary-value problem of thermoelectroelasticity
%J Contemporary Mathematics. Fundamental Directions
%D 2023
%P 364-374
%V 69
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a11/
%G ru
%F CMFD_2023_69_2_a11
A. N. Soloviev; V. A. Chebanenko; M. S. Germanchuk. Applied theory of flexural vibrations of a piezoactive bimorph in the framework of an uncoupled boundary-value problem of thermoelectroelasticity. Contemporary Mathematics. Fundamental Directions, Contemporary Mathematics. Fundamental Directions, Tome 69 (2023) no. 2, pp. 364-374. http://geodesic.mathdoc.fr/item/CMFD_2023_69_2_a11/

[1] Bednarek S., “Elastic and magnetic properties of heat-shrinkable ferromagnetic composites with elastomer matrix”, Mater. Sci. Engrg. B, 77 (2000), 120–127 | DOI

[2] Binh D. T., Chebanenko V. A., Duong L. V., Kirillova E., Thang P. M., Soloviev A. N., “Applied theory of bending vibration of the piezoelectric and piezomagnetic bimorph”, J. Adv. Dielectrics, 10:3 (2020), 2050007 | DOI

[3] Du J. K., Wang J., Zhou Ya., “Thickness vibrations of a piezoelectric plate under biasing fields”, Ultrasonics, 44 (2006), 853–857

[4] Huang J., “Micromechanics determinations of thermoelectroelastic fields and effective thermoelectroelastic moduli of piezoelectric composites”, Mater. Sci. Engrg. B, 39 (1996), 163–172 | DOI

[5] Kulikov G. M., Mamontov A., Plotnikova S., “Coupled thermoelectroelastic stress analysis of piezoelectric shells”, Composite Structures, 124 (2015), 65–76 | DOI

[6] Levin V., “Exact relations between the effective thermoelectroelastic characteristics of piezoelectric composites”, Int. J. Engrg. Sci., 2013, 14–20 | DOI | MR | Zbl

[7] Levin V. M., Rakovskaja M. I., Kreher W. S., “The effective thermoelectroelastic properties of microinhomogeneous materials”, Int. J. Solids Structures, 36 (1999), 2683–2705 | DOI | Zbl

[8] Nowacki W., “Mathematical models of phenomenological piezoelectricity”, Banach Center Publ., 1, no. 15, 1985, 593–607 | DOI

[9] Pasternak I., Pasternak R., Sulym H., “A comprehensive study on Green's functions and boundary integral equations for 3D anisotropic thermomagnetoelectroelasticity”, Eng. Anal. Bound. Elem., 64 (2016), 222–229 | DOI | MR | Zbl

[10] Soloviev A. N., Chebanenko V. A., Oganesyan P. A., Chao S.-F., Liu Y.-M., “Applied theory for electro-elastic plates with non-homogeneous polarization”, Mater. Phys. Mech., 42:2 (2019), 242–255

[11] Xu K., Noor A. K., Tang Y. Y., “Three-dimensional solutions for coupled thermoelectroelastic response of multilayered plates”, Comput. Methods Appl. Mech. Engrg., 126:3-4 (1995), 355–371 | DOI

[12] Xu K., Noor A. K., Tang Y. Y., “Three-dimensional solutions for free vibrations of initially-stressed thermoelectroelastic multilayered plates”, Contemporary Research in Engineering Science, Springer, Berlin—Heidelberg, 1995, 593–612

[13] Zhang C., Cheung Y. K., Di S., Zhang N., “The exact solution of coupled thermoelectroelastic behavior of piezoelectric laminates”, Comput. Struct., 80 (2002), 1201–1212 | DOI

[14] Zhong X., Wu Y., Zhang K., “An extended dielectric crack model for fracture analysis of a thermopiezoelectric strip”, Acta Mech. Solida Sin., 33 (2020), 521–545 | DOI