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Erschienen in: Mechanics of Composite Materials 1/2022

25.03.2022

A Modal Analysis of Forced Vibration of a Piezoelectric Plate with Initial Stress by the Finite-Element Simulation

verfasst von: A. Daşdemir

Erschienen in: Mechanics of Composite Materials | Ausgabe 1/2022

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Abstract

A modal analysis of forced vibrations caused by a time-harmonic force from a piezoelectric plate standing on a rigid foundation is presented. A 3D linearized elasticity theory for solids under initial stress (TLTESIS) is used. It is assumed that a uniformly distributed normal loadings acting on the lateral surfaces of the plate yield the initial stress state. The piezoelectric plate is under the action of a time-harmonic force poled in various directions. A mathematical model is developed, and the problem is solved employing the 3D finite-element method (3D-FEM). Some numerical results illustrating the influence of changes in the poling direction and other important factors, such as the initial stress, on the dynamic behavior of the plate are presented.

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Literatur
1.
Zurück zum Zitat P. Kumar, M. Mahanty, A. Chattopadhyay and A. K. Singh, “Effect of interfacial imperfection on shear wave propagation in a piezoelectric composite structure: Wentzel–Kramers–Brillouin asymptotic approach,” J. Intell. Mater. Syst. Struct., 30, No. 18-19, 2789-2807 (2019).CrossRef P. Kumar, M. Mahanty, A. Chattopadhyay and A. K. Singh, “Effect of interfacial imperfection on shear wave propagation in a piezoelectric composite structure: Wentzel–Kramers–Brillouin asymptotic approach,” J. Intell. Mater. Syst. Struct., 30, No. 18-19, 2789-2807 (2019).CrossRef
2.
Zurück zum Zitat M. Mahanty, A. Chattopadhyay, P. Kumar and A. K. Singh, “Effect of initial stress, heterogeneity and anisotropy on the propagation of seismic surface waves,” Mech. Adv. Mater. Struc., 27, No. 3, 177-188 (2020).CrossRef M. Mahanty, A. Chattopadhyay, P. Kumar and A. K. Singh, “Effect of initial stress, heterogeneity and anisotropy on the propagation of seismic surface waves,” Mech. Adv. Mater. Struc., 27, No. 3, 177-188 (2020).CrossRef
3.
Zurück zum Zitat J. Yang, An Introduction to the Theory of Piezoelectricity, Springer, New York (2005). J. Yang, An Introduction to the Theory of Piezoelectricity, Springer, New York (2005).
4.
Zurück zum Zitat H. F. Tiersten, Linear Piezoelectric Plate Vibrations: Elements of the Linear Theory of Piezoelectricity and the Vibrations Piezoelectric Plates, Springer, New York (2013). H. F. Tiersten, Linear Piezoelectric Plate Vibrations: Elements of the Linear Theory of Piezoelectricity and the Vibrations Piezoelectric Plates, Springer, New York (2013).
5.
Zurück zum Zitat R. V. Southwell, “On the general theory of elastic stability,” Philos. Trans. Royal Soc. Ser. A, 213, 187-244 (1914). R. V. Southwell, “On the general theory of elastic stability,” Philos. Trans. Royal Soc. Ser. A, 213, 187-244 (1914).
6.
Zurück zum Zitat C. B. Biezeno and H. Hencky, “On the general theory of elastic stability,” In: Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, 31, 569-592 (1928). C. B. Biezeno and H. Hencky, “On the general theory of elastic stability,” In: Proceedings Koninklijke Nederlandse Akademie van Wetenschappen, 31, 569-592 (1928).
7.
Zurück zum Zitat M. A. Biot, “Nonlinear elasticity theory and the linearized case for a body under initial stress,” Philos. Mag. Ser., 7, No. 27, 468-489 (1939).CrossRef M. A. Biot, “Nonlinear elasticity theory and the linearized case for a body under initial stress,” Philos. Mag. Ser., 7, No. 27, 468-489 (1939).CrossRef
8.
Zurück zum Zitat H. Neuber, “Die Grundgleichungen der elastischen Stabilität in allgemeinen Koordinaten und ihre Integration,” ZAMM, 23, 321-330 (1943).CrossRef H. Neuber, “Die Grundgleichungen der elastischen Stabilität in allgemeinen Koordinaten und ihre Integration,” ZAMM, 23, 321-330 (1943).CrossRef
9.
Zurück zum Zitat E. Trefftz, “Zur Theorie der Stabilität des elastischen Gleichgewichts,” ZAMM, 12, No. 2, 160–165 (1933).CrossRef E. Trefftz, “Zur Theorie der Stabilität des elastischen Gleichgewichts,” ZAMM, 12, No. 2, 160–165 (1933).CrossRef
10.
Zurück zum Zitat A. E. Green, R. S. Rivlin, and R. T. Shield, “General theory of small deformations superposed on large elastic deformations,” Proc. Roy. Soc. A, 211, 211–292 (1952). A. E. Green, R. S. Rivlin, and R. T. Shield, “General theory of small deformations superposed on large elastic deformations,” Proc. Roy. Soc. A, 211, 211–292 (1952).
11.
Zurück zum Zitat A. N. Guz, “3D theory of elastic stability under finite subcritical deformations,” J. Appl. Mech., 8, No. 12, 25-44 (1972). A. N. Guz, “3D theory of elastic stability under finite subcritical deformations,” J. Appl. Mech., 8, No. 12, 25-44 (1972).
12.
Zurück zum Zitat L. M. Zubov, “Theory of small deformations of prestressed thin shells,” J. Appl. Math. Mech., 40, No. 1, 73-82 (1976).CrossRef L. M. Zubov, “Theory of small deformations of prestressed thin shells,” J. Appl. Math. Mech., 40, No. 1, 73-82 (1976).CrossRef
13.
Zurück zum Zitat H. F. Tiersten, “Perturbation theory for linear electroelastic equations for small fields superimposed on a bias,” J. Acoust. Soc. Am., 64, No. 3, 832-837 (1978).CrossRef H. F. Tiersten, “Perturbation theory for linear electroelastic equations for small fields superimposed on a bias,” J. Acoust. Soc. Am., 64, No. 3, 832-837 (1978).CrossRef
14.
Zurück zum Zitat R. W. Ogden, Nonlinear Elastic Deformations, Ellis Horwood/Halsted Press, New York (1984). R. W. Ogden, Nonlinear Elastic Deformations, Ellis Horwood/Halsted Press, New York (1984).
15.
Zurück zum Zitat S. D. Akbarov and A. N. Guz, Mechanics of Curved Composites, Kluwer Acad. Publ., Dordrecht-Boston-London (2000).CrossRef S. D. Akbarov and A. N. Guz, Mechanics of Curved Composites, Kluwer Acad. Publ., Dordrecht-Boston-London (2000).CrossRef
16.
Zurück zum Zitat J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press, Florida (2003). J. N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, CRC press, Florida (2003).
17.
Zurück zum Zitat A. N. Guz, Fundamentals of the 3D Theory of Stability of Deformable Bodies, Springer, New York (1999). A. N. Guz, Fundamentals of the 3D Theory of Stability of Deformable Bodies, Springer, New York (1999).
18.
Zurück zum Zitat S. D. Akbarov, Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized 3D Approach, Springer, New York (2015).CrossRef S. D. Akbarov, Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized 3D Approach, Springer, New York (2015).CrossRef
19.
Zurück zum Zitat S. D. Akbarov, A. Yildiz, and M. Eroz, “Forced vibration of the prestressed bi-layered plate-strip with finite length resting on a rigid foundation,” Appl. Math. Model., 35, No. 1, 250-256 (2011).CrossRef S. D. Akbarov, A. Yildiz, and M. Eroz, “Forced vibration of the prestressed bi-layered plate-strip with finite length resting on a rigid foundation,” Appl. Math. Model., 35, No. 1, 250-256 (2011).CrossRef
20.
Zurück zum Zitat S. Gupta, D. K. Majhi, S. Kundu, and S. K. Vishwakarma, “Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space,” Appl. Math. Comput., 218, No. 9, 5655-5664 (2012). S. Gupta, D. K. Majhi, S. Kundu, and S. K. Vishwakarma, “Propagation of torsional surface waves in a homogeneous layer of finite thickness over an initially stressed heterogeneous half-space,” Appl. Math. Comput., 218, No. 9, 5655-5664 (2012).
21.
Zurück zum Zitat W. T. Hu and W. Y. Chen, “Influence of lateral initial pressure on axisymmetric wave propagation in hollow cylinder based on first power hypo-elastic model,” J. Cent. South Univ., 21, No. 2, 753-760 (2014).CrossRef W. T. Hu and W. Y. Chen, “Influence of lateral initial pressure on axisymmetric wave propagation in hollow cylinder based on first power hypo-elastic model,” J. Cent. South Univ., 21, No. 2, 753-760 (2014).CrossRef
22.
Zurück zum Zitat X. Guo and P. Wei, “Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses,” Ultrasonics, 66, 72-85 (2016).CrossRef X. Guo and P. Wei, “Dispersion relations of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with initial stresses,” Ultrasonics, 66, 72-85 (2016).CrossRef
23.
Zurück zum Zitat U. B. Yesil, “Forced and natural vibrations of an orthotropic prestressed rectangular plate with neighboring two cylindrical cavities,” Comput. Mater. Continua., 53, No. 1, 1-22 (2017). U. B. Yesil, “Forced and natural vibrations of an orthotropic prestressed rectangular plate with neighboring two cylindrical cavities,” Comput. Mater. Continua., 53, No. 1, 1-22 (2017).
24.
Zurück zum Zitat A. Dașdemir, “Forced vibrations of prestressed sandwich plate-strip with elastic layers and piezoelectric core,” Int. Appl. Mech., 54, No. 4, 480-493 (2018).CrossRef A. Dașdemir, “Forced vibrations of prestressed sandwich plate-strip with elastic layers and piezoelectric core,” Int. Appl. Mech., 54, No. 4, 480-493 (2018).CrossRef
25.
Zurück zum Zitat A. Daşdemir, “Effect of imperfect bonding on the dynamic response of a prestressed sandwich plate-strip with elastic layers and a piezoelectric core,” Acta Mech. Solida Sin., 30, No. 6, 658-667 (2017).CrossRef A. Daşdemir, “Effect of imperfect bonding on the dynamic response of a prestressed sandwich plate-strip with elastic layers and a piezoelectric core,” Acta Mech. Solida Sin., 30, No. 6, 658-667 (2017).CrossRef
26.
Zurück zum Zitat A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23-59 (2002).CrossRef A. N. Guz, “Elastic waves in bodies with initial (residual) stresses,” Int. Appl. Mech., 38, No. 1, 23-59 (2002).CrossRef
27.
Zurück zum Zitat S. D. Akbarov, “Recent investigations on dynamic problems for an elastic body with initial (residual) stresses,” Int. Appl. Mech., 43, No. 12, 1305-1324 (2007).CrossRef S. D. Akbarov, “Recent investigations on dynamic problems for an elastic body with initial (residual) stresses,” Int. Appl. Mech., 43, No. 12, 1305-1324 (2007).CrossRef
28.
Zurück zum Zitat S. D. Akbarov, Stability Loss and Buckling Delamination. Springer, Berlin (2012). S. D. Akbarov, Stability Loss and Buckling Delamination. Springer, Berlin (2012).
29.
Zurück zum Zitat A. Daşdemir, “A mathematical model for forced vibration of prestressed piezoelectric plate-strip resting on rigid foundation,” Matematika: MJIAM, 34, No. 2, 419-431 (2018).CrossRef A. Daşdemir, “A mathematical model for forced vibration of prestressed piezoelectric plate-strip resting on rigid foundation,” Matematika: MJIAM, 34, No. 2, 419-431 (2018).CrossRef
Metadaten
Titel
A Modal Analysis of Forced Vibration of a Piezoelectric Plate with Initial Stress by the Finite-Element Simulation
verfasst von
A. Daşdemir
Publikationsdatum
25.03.2022
Verlag
Springer US
Erschienen in
Mechanics of Composite Materials / Ausgabe 1/2022
Print ISSN: 0191-5665
Elektronische ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-022-10012-7

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