 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| V.A. Eremeev and A.V. Nasedkin, "Natural Vibrations of Nanodimensional Piezoelectric Bodies with Contact-Type Boundary Conditions," Mech. Solids. 50 (5), 495-507 (2015) |
| Year |
2015 |
Volume |
50 |
Number |
5 |
Pages |
495-507 |
| DOI |
10.3103/S0025654415050027 |
| Title |
Natural Vibrations of Nanodimensional Piezoelectric Bodies with Contact-Type Boundary Conditions |
| Author(s) |
V.A. Eremeev (Otto-von-Guericke Universität Magdeburg, Universitätsplatz 2, 39106 Magdeburg, Germany; South Scientific Center, Russian Academy of Sciences, ul. Chekhova 41, Rostov-on-Don, 344006 Russia; South Federal University, pr. Stachki 200/1, Rostov-on-Don, 344090 Russia)
A.V. Nasedkin (South Federal University, pr. Stachki 200/1, Rostov-on-Don, 344090 Russia, nasedkin@math.sfedu.ru) |
| Abstract |
Homogeneous problems of vibrations of nanodimensional piezoelectric bodies with surface stresses and electric charges taken into account are studied. The boundary conditions modeling the frictionless contact of a body with rigid massive punches and the body coverings by a system of open and grounded electrodes are considered. The weak statements of these problems are given. It is proved that the spectrum is real and discrete and the system of eigenfunctions is complete. Several theorems on the eigenfrequency variations are stated with the surface effects taken into account and in the case of variations in the mechanical and electrical boundary conditions and the material characteristics. The finite element approximations are used to state finite-dimensional generalized eigenvalue problems. The results of finite-element calculations of the model problem, which illustrate the influence of surface effects, are given. |
| Keywords |
electro-elasticity, piezoelectricity, nanomechanics, eigenfrequency, spectral property, surface effect |
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|
| Received |
11 February 2013 |
| Link to Fulltext |
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