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Портал Begell Электронная Бибилиотека e-Книги Журналы Справочники и Сборники статей Коллекции
International Journal of Fluid Mechanics Research
ESCI SJR: 0.206 SNIP: 0.446 CiteScore™: 0.5

ISSN Печать: 2152-5102
ISSN Онлайн: 2152-5110

Выпуски:
Том 46, 2019 Том 45, 2018 Том 44, 2017 Том 43, 2016 Том 42, 2015 Том 41, 2014 Том 40, 2013 Том 39, 2012 Том 38, 2011 Том 37, 2010 Том 36, 2009 Том 35, 2008 Том 34, 2007 Том 33, 2006 Том 32, 2005 Том 31, 2004 Том 30, 2003 Том 29, 2002 Том 28, 2001 Том 27, 2000 Том 26, 1999 Том 25, 1998 Том 24, 1997 Том 23, 1996 Том 22, 1995

International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v30.i1.40
19 pages

Parametric Vibrations of Three-Layer Piezoelectric Shells of Revolution

O. V. Karnaukhova
S.P.Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. I. Kozlov
S.P.Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A. O. Rasskazov
S.P.Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine

Краткое описание

The problem of parametric vibrations of elastic three-layer shells composed of middle orthotropic dielectric or metal layer and two piezoelectric layers is studied. On the basis of the mechanical Kirchoff - Love hypothesis and adequate assumptions for an electrical field the constitutive equations for forces and moments are obtained for varying electrode positions, type of polarization and electrical boundary conditions. It is shown how nonlinear and linearized equations describing the parametric vibrations of the arbitrary shaped shells can be obtained if the constitutive equations, universal equations of motion, kinematic equations and boundary conditions are used. The linearized equations describe a region of dynamic instability (RDI). On the boundary of RDI the harmonic motion occurs. This gives an opportunity to reduce the problem of investigations of the principal RDI to solving the eigenvalue problems and the problem of static stability. Method of finite elements is developed to solve these problems. The problem of parametric vibrations of a three-layer cylindrical piezoelectric panel is considered in detail. The analytical solution of the problem is obtained for the case of simply supported edges. Correlation of an analytical and finite-element solutions demonstrates high accuracy of the first. The problem of parametric vibrations under harmonic mechanical load is solved for the open-circuited and short-circuited conditions. The essential influence of the electric boundary conditions on the size of RDI that can be used for control of the parametric vibrations of the shells is shown. The finite-element solution of the problem of parametric vibrations of cylindrical piezoelectric panel with clamped edges is obtained. The numerical results point to essential influence of mechanical boundary conditions on the size and position of RDI.


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