Abstract
We consider the problems of natural oscillations of nanosize piezoelectric bodies taking into account surface stresses and surface electric charges. The spectral properties of the boundary-value problems are determined by the combination of approaches developed earlier for piezoelectric bodies and for elastic bodies with surface stresses. We formulate theorems on the changes of the natural frequencies under the changes of boundary conditions and material characteristics. We also discuss finite element approaches for determination of the natural frequencies, the resonance and antiresonance frequencies of nanosize piezoelectric bodies. The paper provides the results of finite element computations of the model problems that illustrate some of the observed trends for the frequency changes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Duan, H.L., Wang, J., Huang, Z.P., Karihaloo, B.L.: Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53, 1574–1596 (2005)
Duan, H.L., Wang, J., Karihaloo, B.L., Huang, Z.P.: Nanoporous materials can be made stiffer than non-porous counterparts by surface modifcation. Acta mater. 54, 2983–2990 (2006)
Jing, G.Y., Duan, H.L., Sun, X.M., et al.: Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy, Phys. Rev. B 73, 235409-1–235409-6 (2006)
Belokon, A.V., Vorovich, I.I.: Some mathematical problems of the theory of electroelastic solids, In: Current problems in the mechanics of deformable media. Izv. Dnepropetr. Gos. Univ., Dnepropetrovsk (1979)
Altenbach, H., Eremeyev, V.A., Lebedev, L.P.: On the existence of solution in the linear elasticity with surface stresses, Z. Angew. Math. Mech. 90(3), 231–240 (2010)
Altenbach, H., Eremeyev, V.A., Lebedev, L.P.: On the spectrum and stiffness of an elastic body with surface stresses, Z. Angew. Math. Mech. 91(9), 699–710 (2011)
Belokon, A.V., Nasedkin, A.V.: Some properties of the natural frequencies of electroelastic bodies of bounded dimentions. J. Appl. Math. Mech. (PMM) 60, 145–152 (1996)
Riesz, F., Szokefalvi-Nagy, B.: Functional Analysis. Dover, New York (1990)
Mikhlin, S.G.: Variational Methods in Mathematical Physics. Pergamon Press, Oxford (1964)
Bathe, K.J.: Finite Element Procedure. Prentice-Hall, Englewood Cliffs, NJ (1996)
Zienkewicz, O.C., Morgan, K.: Finite Elements and Approximation. Wiley, NY (1983)
Dieulesaint, E., Royer, D.: Ondes elastiques dans les solides. Application au Traitement du Signal. Masson, Paris (1974)
Iovane, G., Nasedkin, A.V.: Some theorems about spectrum and finite element approach for eigenvalue problems for elastic bodies with voids. Comput. Math. Appl. 53, 789–802 (2007)
Iovane, G., Nasedkin, A.V.: Modal analysis of piezoelectric bodies with voids. I. Mathematical approaches, Appl. Math. Model. 34(1), 60–71 (2010)
G. Iovane, A.V. Nasedkin, Modal analysis of piezoelectric bodies with voids. II. Finite element simulation, Appl. Math. Model. 34(1), 47–59 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Nasedkin, A.V., Eremeyev, V.A. (2013). Spectral Properties of Piezoelectric Bodies with Surface Effects. In: Altenbach, H., Morozov, N. (eds) Surface Effects in Solid Mechanics. Advanced Structured Materials, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35783-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-642-35783-1_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35782-4
Online ISBN: 978-3-642-35783-1
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)