Nonaxisymmetric Electroelastic Vibrations of a Hollow Cylinder with Radial Axis of Physicomechanical Symmetry

Shulga, V. M.

doi:10.1007/s10778-005-0143-z

Cited by 4 publications

(3 citation statements)

References 4 publications

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“…Copyright (c) 2016 Безверхий О. І., Григор'єва Л. О. В роботі [10] просторову систему рівнянь електропружності для радіально поляризованого циліндра шляхом розкладу розв'язку в ряди по поздовжній та окружній координаті зведено до набору систем рівнянь типу Гамільтона. В статті [11] використовуються рівняння гамільтонового типу по товщинній координаті для аналізу одномірних гармонічних коливань кулі, циліндру і плоского шару.…”

Section: акустичні прилади та системиunclassified

The approach to the calculation of harmonic oscillations of electroelastic cylinders

Bezverkhyi¹,

Hryhorieva²

2018

Mìkrosist. elektron. akust.

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Section: акустичні прилади та системиunclassified

The approach to the calculation of harmonic oscillations of electroelastic cylinders

Bezverkhyi¹,

Hryhorieva²

2018

Mìkrosist. elektron. akust.

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“…Later, Zharii (1990) formulated the general expansion of the Eigen-function in non-stationary dynamic problems based on nonlinear and linear electro-elasticity theories. The extensive use of piezo-electric converters requires the behavior of piezo-ceramic structural members to be studied , Dieulesiant , Royer (1981) and Shul'ga (2005). In this regard, comprehensive studies were carried out on harmonic electro-elastic vibrations of piezo-ceramic (solids Dieulesiant , Royer (1981) and Shul'ga (2005)).…”

Section: Introductionmentioning

confidence: 99%

“…The extensive use of piezo-electric converters requires the behavior of piezo-ceramic structural members to be studied , Dieulesiant , Royer (1981) and Shul'ga (2005). In this regard, comprehensive studies were carried out on harmonic electro-elastic vibrations of piezo-ceramic (solids Dieulesiant , Royer (1981) and Shul'ga (2005)). Eva (2006) tested different methods for establishing numerical algorithms for electro-elasticity, eventually solving the stationary vibration problem for a radially-polarized hollow piezo-electric cylinder under different electrical boundary conditions and mechanical pressure.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the bending of a neo-Hookean electro-elastic shell of arbitrary thickness under an externally-applied hydrostatic pressure

Teymoori

Hatami

2022

Lat. Am. j. solids struct.

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The present study analyzes the bending of a simple electro-elastic cylindrical shell by the compound matrix method. The cross-section of the circular cylindrical shell is a non-circular curved shape, with 𝜇𝜇 1 a function of 𝐴𝐴 𝐵𝐵 � and the mode number, where 𝐴𝐴 and 𝐵𝐵 are the pre-deformation inner and outer radii of the cylindrical shell, and 𝜇𝜇 1 is the ratio of the deformed inner radius to 𝐴𝐴 . In the first step, a numerical model of the problem is developed to obtain specific differential equations. The modeling yields a system of two Ordinary Differential Equations with three boundary conditions of the same type. Next, it is shown that the dependence of 𝜇𝜇 1 to 𝐴𝐴 𝐵𝐵 � has a boundary layer structure. Simple numerical observations were made for bifurcation conditions. The analysis is, in fact, based on the variations of the inner and outer radii 𝐴𝐴 and 𝐵𝐵 , assuming 𝑎𝑎 = 𝜇𝜇 1 𝐴𝐴 and 𝑏𝑏 = 𝜇𝜇 2 𝐵𝐵, and based on the bifurcation of 𝜇𝜇 1 and 𝜇𝜇 2 ratios with respect to radius. For this purpose, the compound matrix method is used to show the validity of the arguments.

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Numerical solution to the initial-boundary-value problem of electroelasticity for a radially polarized hollow piezoceramic cylinder

Grigor’eva

2006

Int Appl Mech

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The paper proposes and analyzes different approaches to constructing numerical schemes to solve the nonstationary vibration problem for a radially polarized piezoelectric hollow cylinder with different electric boundary conditions under mechanical loading. It is established that when the cylinder is subjected to internal pressure, the radial displacements are similar and the longitudinal displacements substantially different in cylinders with electroded and nonelectroded surfaces Keywords: piezoelectric hollow cylinder, nonstationary vibrations, numerical schemes, internal pressure Introduction. The widespread use of miscellaneous piezoelectric transducers [3, 10, etc.] necessitates studying the dynamic behavior of structural members made of piezoceramic materials. The harmonic electroelastic vibrations of piezoceramic bodies were studied in [3, 7, 11, 17, etc.]. The vibrations of piezoceramic rods under shock loading were addressed in [4,5]. Two-dimensional nonstationary problems of electroelasticity were solved in [6,9]. The nonstationary electroelastic acoustic vibrations of piezoceramic shells and cylinders in hydraulic systems were studied in [1, 2, 13].We will use direct integration to solve the initial-boundary-value vibration problem for a radially polarized hollow piezoceramic cylinder under mechanical loading. Different electric boundary conditions will be examined. Integration over time will be carried out using explicit and implicit schemes and the Runge-Kutta method, and the corresponding results will be compared.1. Problem Formulation. Consider a radially polarized hollow piezoceramic cylinder with mid-surface radius R, thickness 2h, and length l described in a cylindrical coordinate frame r z , , q . The end z = 0 of the cylinder is rigidly fixed. The

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Nonaxisymmetric Electroelastic Vibrations of a Hollow Cylinder with Radial Axis of Physicomechanical Symmetry

Cited by 4 publications

References 4 publications

The approach to the calculation of harmonic oscillations of electroelastic cylinders

The approach to the calculation of harmonic oscillations of electroelastic cylinders

Analysis of the bending of a neo-Hookean electro-elastic shell of arbitrary thickness under an externally-applied hydrostatic pressure

Numerical solution to the initial-boundary-value problem of electroelasticity for a radially polarized hollow piezoceramic cylinder

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