Three-dimensional vibration analysis of a transversely isotropic piezoelectric cylindrical panel

Sharma, J. N.; Pathania, Vijayata

doi:10.1007/s00707-002-0047-0

Cited by 9 publications

(6 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is noticed that Eq. (18) is similar to the particular case obtained and discussed by Sharma [10] in case of thermo elasticity.…”

Section: Solution To the Problemsupporting

confidence: 71%

“…(14). The material properties of a Zinc is taken from [10] for isotropic material 3 3 7.14 10 kgm The roots of the algebraic Eq. (12) were calculated using a combination of Birge-Vita method and Newton-Raphson method.…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…To uncouple Eqs. (7), we can write three displacement functions which satisfies the simply supported boundary conditions followed by Sharma [10] ( , , , )…”

Section: Solution To the Problemmentioning

confidence: 99%

“…Chadwick [9] studied the propagation of plane harmonic waves in homogenous anisotropic heat conducting solids. Sharma [10] investigated the three dimensional vibration analysis of a transversely isotropic thermo elastic cylindrical panel. The application of powerful numerical tools like finite element or boundary element methods to these problems is also becoming important.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Dispersion of thermo elastic waves in a homogeneous isotropic rotating cylindrical panel

Selvamani

Ponnusamy²

2013

International Journal of Advances in Applied Sciences

View full text Add to dashboard Cite

The three dimensional dispersion of thermo elastic waves in a homogeneous isotropic rotating cylindrical panel is investigated in the context of the linear theory of thermo elasticity. Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equations are obtained for traction free boundary conditions using Bessel function solutions.In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc material. In this study we found that the wave characteristics are more stable and realistic in the presence of thermal and the rotation parameters. Keyword:Bessel Corresponding Author:R .Selvamani, Departement of Mathematics, Karunya University, Coimbatore, Tamil Nadu, India, 64114. Email: selvam1729@gmail.com INTRODUCTIONThe dispersion of displacement, temperature change in a rotating cylindrical panel is plays a vital role in smart material applications and rotating gyroscope. This type of model analysis is very important in bio sensing applications in nuclear magnetic resonance (NMR), magnetic resonance imaging (MRI) and echo planar imaging (EPI). The analysis of thermally induced vibration of rotating cylindrical panel is common place in the design of structures, atomic reactors, steam turbines, supersonic aircraft, and other devices operating at elevated temperature. At the present time applied mathematicians are exhibiting considerable interest in dynamical methods of elasticity, since the usual quasi static approach ignores certain very important features of the problems under consideration. That approach is based on the assumption that the inertia terms may be omitted from the equations of motion. This assumption holds good only when the variations in stresses and displacements, but there arise number of problems in engineering and technology, when this assumption may not hold good and the inertia terms in the equations of motion may have lead to cases of considerable mathematical complications. In the field of nondestructive evaluation, laser-generated waves have attracted great attention owing to their potential application to noncontact and nondestructive evaluation of sheet materials. The high velocities of modern aircraft give rise to aerodynamic heating, which produces intense thermal stresses, reducing the strength of the aircraft structure. In the nuclear field, the extremely high temperatures and temperature gradients originating inside nuclear reactors influence their design and operations. Moreover, it is well recognized that the investigation of the thermal effects on rototing elastic wave propagation has bearing on many structural applications.The static analysis cannot predict the behavior of the material due to the thermal stresses changes very rapidly. Therefore in case of suddenly applied load, thermal deformation and the role of inertia are getting more important. This thermo elastic stress response being significant leads to the propagation of

show abstract

“…It is noticed that Eq. (18) is similar to the particular case obtained and discussed by Sharma [10] in case of thermo elasticity.…”

Section: Solution To the Problemsupporting

confidence: 71%

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…To uncouple Eqs. (7), we can write three displacement functions which satisfies the simply supported boundary conditions followed by Sharma [10] ( , , , )…”

Section: Solution To the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Dispersion of thermo elastic waves in a homogeneous isotropic rotating cylindrical panel

Selvamani

Ponnusamy²

2013

International Journal of Advances in Applied Sciences

View full text Add to dashboard Cite

show abstract

“…Banerjee and Pao [8] investigated the propagation of plane harmonic waves in infinitely extended anisotropic solids by taking into account the thermal relaxation time. Sharma [9] investigated the three dimensional vibration analysis of a transversely isotropic thermo elastic cylindrical panel. Free vibrations of thin cylindrical shells having finite lengths with freely supported and clamped edges was discussed by Yu et.al [10].…”

Section: Introductionmentioning

confidence: 99%

Generalized Thermo Elastic Waves in a Cylindrical Panel Embedded on Elastic Medium

Ponnusamy¹,

Selvamani²

2013

Journal of the Korea Society for Industrial and Applied Mathema

View full text Add to dashboard Cite

In this paper the three dimensional wave propagation in a homogeneous isotropic thermo elastic cylindrical panel embedded in an elastic medium (Winkler model) is investigated in the context of the L-S (Lord-Shulman) theory of generalized thermo elasticity. The analysis is carried out by introducing three displacement functions so that the equations of motion are uncoupled and simplified. A Bessel function solution with complex arguments is then directly used for the case of complex Eigen values .This type of study is important for design of structures in atomic reactors, steam turbines, wave loading on submarine, the impact loading due to superfast train and jets and other devices operating at elevated temperature. In order to illustrate theoretical development, numerical solutions are obtained and presented graphically for a zinc material with the support of MATLAB.

show abstract

An asymptotic theory for dynamic response of laminated piezoelectric shells

2006

Acta Mechanica

View full text Add to dashboard Cite

Three-dimensional vibration analysis of a transversely isotropic piezoelectric cylindrical panel

Cited by 9 publications

References 19 publications

Dispersion of thermo elastic waves in a homogeneous isotropic rotating cylindrical panel

Dispersion of thermo elastic waves in a homogeneous isotropic rotating cylindrical panel

Generalized Thermo Elastic Waves in a Cylindrical Panel Embedded on Elastic Medium

An asymptotic theory for dynamic response of laminated piezoelectric shells

Contact Info

Product

Resources

About