Spectral Properties of Piezoelectric Bodies with Surface Effects

Weconsider theproblemsofnaturaloscillationsofnanosize piezoelectric bodies taking into account surface stresses and surface electric charges. The spec- tral 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 dis- cuss finite element approaches for determination of the natural frequencies, the res- onance and antiresonance frequencies of nanosize piezoelectric bodies. The paper provides the results of finite element computations of the model problems that illus- trate some of the observed trends for the frequency changes.

[1]  Andrey Nasedkin,et al.  Modal analysis of piezoelectric bodies with voids. I. Mathematical approaches , 2010 .

[2]  S. Mikhlin,et al.  Variational Methods in Mathematical Physics , 1965 .

[3]  Some properties of the natural frequencies of electroelastic bodies of bounded dimensions , 1996 .

[4]  O. Zienkiewicz,et al.  Finite elements and approximation , 1983 .

[5]  Victor A. Eremeyev,et al.  On the existence of solution in the linear elasticity with surface stresses , 2010 .

[6]  H. Saunders.  Book Reviews : NUMERICAL METHODS IN FINITE ELEMENT ANALYSIS K.-J. Bathe and E.L. Wilson Prentice-Hall, Inc, Englewood Cliffs, NJ , 1978 .

[7]  Bhushan Lal Karihaloo,et al.  Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress , 2005 .

[8]  Andrey Nasedkin,et al.  Modal analysis of piezoelectric bodies with voids. II. Finite element simulation , 2010 .

[9]  G. Iovane,et al.  Some theorems about spectrum and finite element approach for eigenvalue problems for elastic bodies with voids , 2007, Comput. Math. Appl..

[10]  E. Dieulesaint,et al.  Ondes élastiques dans les solides : application au traitement du signal , 1974 .

[11]  K. Bathe.  Finite Element Procedures , 1995 .

[12]  Victor A. Eremeyev,et al.  On the spectrum and stiffness of an elastic body with surface stresses , 2011 .

[13]  Bhushan Lal Karihaloo,et al.  Nanoporous materials can be made stiffer than non-porous counterparts by surface modification , 2006 .

[14]  Jianbin Xu,et al.  Surface effects on elastic properties of silver nanowires: Contact atomic-force microscopy , 2006 .