Flexural vibration in a finite piezoelectric circular cylinder of crystal class 6 mm
TL;DR: In this paper, a finite piezoelectric circular solid cylinder of crystal class 6mm is studied for traction-free and electric potential-free boundaries, and the solution is obtained in the form of a series, in which the boundary conditions for the shear stresses on curved and plane end surfaces and the electric potential on the plane ends are satisfied term-byterm.
About: This article is published in International Journal of Engineering Science.The article was published on 1994-08-01. It has received 11 citations till now. The article focuses on the topics: Boundary value problem & Piezoelectricity.
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TL;DR: In this article, the free vibration equation of piezoelectric cylindrical shells satisfying SS3 edge conditions was solved by utilizing Bessel functions with complex arguments, and the effects of compressible fluid on shells are considered and some new phenomena which are exclusive for pieziolectric cylinders are reported.
79 citations
TL;DR: In this article, the authors presented an exact three-dimensional free vibration analysis of a transversely isotropic piezoelectric circular cylindrical panel and compared the results with available data in literature.
27 citations
TL;DR: In this article, a functionally graded piezoelectric cylindrical actuator placed in a harmonic electric field based on elastic membrane theory and shell theory was investigated, and non-dimensional expressions were introduced, and analytical solutions for this class of actuator were obtained.
Abstract: This paper focuses on the response of a functionally graded piezoelectric cylindrical actuator placed in a harmonic electric field based on elastic membrane theory and shell theory. The actuator is polarized in the radial direction with its piezoelectric coefficient d31 varying linearly along the axial direction. In the present investigation, non-dimensional expressions are introduced, and analytical solutions for this class of actuator are obtained. The results provided in the present study are compared with other investigations, with good agreement being found. The major differences between a functionally graded actuator and an actuator with homogeneous material properties are identified, and the advantages of the former are demonstrated. In the last section of this paper, limitations of membrane theory and shell theory models are discussed.
23 citations
TL;DR: In this paper, the uniqueness theorem and the reciprocity in the linearized porous piezoelectricity are established under the assumption of positive definiteness of elastic and electric fields.
Abstract: The uniqueness theorem and the theorem of reciprocity in the linearized porous piezoelectricity are established under the assumption of positive definiteness of elastic and electric fields. General theorems in the linear theory of porous piezoelectric materials are proved for the quasi-static electric field approximation. The uniqueness theorem is also proved without using the positive definiteness of the elastic field. An eigenvalue problem associated with free vibrations of a porous piezoelectric body is studied using the abstract formulation. Some properties of operators are also proved. The problem of frequency shift due to small disturbances, based on an abstract formulation, is studied using a variational and operator approach. A perturbation analysis of a special case is also given.
10 citations
Cites background from "Flexural vibration in a finite piez..."
...Paul and Natarajan [ 5 ] studied the flexural vibrations for the traction free and electric potential free...
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TL;DR: In this paper, the authors proposed an approach to study the dynamic characteristics of double layered cylindrical rods based on the three-dimensional theory of elasticity and the mathematical analysis on the representation of the displacement fields in terms of the constructed Navier eigenvectors in cylinrical coordinates.
9 citations
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Book•
01 Jan 1944
TL;DR: The tabulation of Bessel functions can be found in this paper, where the authors present a comprehensive survey of the Bessel coefficients before and after 1826, as well as their extensions.
Abstract: 1. Bessel functions before 1826 2. The Bessel coefficients 3. Bessel functions 4. Differential equations 5. Miscellaneous properties of Bessel functions 6. Integral representations of Bessel functions 7. Asymptotic expansions of Bessel functions 8. Bessel functions of large order 9. Polynomials associated with Bessel functions 10. Functions associated with Bessel functions 11. Addition theorems 12. Definite integrals 13. Infinitive integrals 14. Multiple integrals 15. The zeros of Bessel functions 16. Neumann series and Lommel's functions of two variables 17. Kapteyn series 18. Series of Fourier-Bessel and Dini 19. Schlomlich series 20. The tabulation of Bessel functions Tables of Bessel functions Bibliography Indices.
9,584 citations
97 citations
TL;DR: In this article, the fundamental differential equations of the linear theory of apolar and nonrelativistic, thermopiezoelectricity and also its variational description are presented.
71 citations
TL;DR: In this paper, the flexural and axisymmetric vibrations of piezoelectric cylindrical shells of the crystal class 6mm were investigated and the frequency equations were obtained.
Abstract: Solutions for the flexural and axisymmetric vibrations of piezoelectric cylindrical shells of the crystal class 6mm are investigated. Applying suitable mechanical and electrical boundary conditions, the frequency equations have been obtained.
69 citations
TL;DR: In this article, the axisymmetric vibrational characteristics of an elastic circular rod of finite length with stress-free boundaries are analytically determined, and compared to approximate solutions, with truncation to a 20×20 eigenvalue matrix.
Abstract: The axisymmetric vibrational characteristics of an elastic circular rod of finite length with stress‐free boundaries are analytically determined, and compared to approximate solutions. The solution approach consists of choosing a series of functions which term by term satisfy the governing equations and the boundary conditions on the shear stress. The boundary conditions on the axial and radial stress are satisfied by an orthogonalization procedure. This method yields an infinite eigenvalue matrix, the coefficients of which are transcendental functions of the frequency. It is found that the procedure converges and that sufficient accuracy is achieved, with truncation to a 20×20 eigenvalue matrix. Comparison is made of these results with the Pochhammer‐Chree solutions which do not permit satisfaction of the boundary conditions on the ends of the rod. This comparison shows many similarities, but also some dissimilarities. Comparisons are also made with the lowest mode of the free‐plate solution and the plane stress solution for very short rods, and with the one‐dimensional rod solution for long rods.
68 citations