Search results

1 – 5 of 5
Article
Publication date: 4 November 2014

Palaniyandi Ponnusamy

The purpose of this paper is to study the problem of wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal (triangle…

Abstract

Purpose

The purpose of this paper is to study the problem of wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal (triangle, square, pentagon and hexagon) cross-section immersed in fluid is using Fourier expansion collocation method, with in the frame work of linearized, three-dimensional theory of thermo-piezoelectricity.

Design/methodology/approach

A mathematical model is developed to study the wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sections immersed in fluid is studied using the three-dimensional theory of elasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat and electric conductions. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for triangular, square, pentagonal and hexagonal cross-sectional bar immersed in fluid. Since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the curved surface of the polygonal bar directly. Hence, the Fourier expansion collocation method is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.

Findings

From the literature survey, it is clear that the free vibration of an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sectional bar immersed in fluid have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of transversely isotropic thermo-piezoelectric solid bar of circular cross-sections only. So, in this paper, the wave propagation in thermo-piezoelectric cylindrical bar of polygonal cross-sections immersed in fluid are studied using the Fourier expansion collocation method. The computed non-dimensional frequencies are plotted in the form of dispersion curves and its characteristics are discussed, also a comparison is made between non-dimensional wave numbers for longitudinal and flexural modes piezoelectric, thermo-piezoelectric and thermo-piezoelectric polygonal cross-sectional bars immersed in fluid.

Research limitations/implications

Wave propagation in an infinite, homogeneous, transversely isotropic thermo-piezoelectric solid bar of polygonal cross-sectional bar immersed in fluid have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of transversely isotropic thermo-piezoelectric solid bar of circular cross-sections only. So, in this paper, the wave propagation in thermo-piezoelectric cylindrical bar of polygonal cross-sections immersed in fluid are studied using the Fourier expansion collocation method. The computed non-dimensional frequencies are plotted in the form of dispersion curves and its characteristics are discussed, also a comparison is made between non-dimensional wave numbers for longitudinal and flexural modes of piezoelectric, thermo-piezoelectric and thermo-piezoelectric polygonal cross-sectional bars immersed in fluid.

Originality/value

The researchers have discussed the wave propagation in thermo-piezoelectric circular cylinders using three-dimensional theory of thermo-piezoelectricity, but, the researchers did not analyzed the wave propagation in an arbitrary/polygonal cross-sectional bar immersed in fluid. So, the author has studied the free vibration analysis of thermo-piezoelectric polygonal (triangle, square, pentagon and hexagon) cross-sectional bar immersed in fluid using three-dimensional theory elasticity. The problem may be extended to any kinds of cross-sections by using the proper geometrical relations.

Details

Multidiscipline Modeling in Materials and Structures, vol. 10 no. 4
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 10 August 2015

Rajendran Selvamani and Palaniyandi Ponnusamy

The purpose of this paper is to study the wave propagation in a generalized piezothermoelastic rotating bar of circular cross-section using three-dimensional linear theory of…

Abstract

Purpose

The purpose of this paper is to study the wave propagation in a generalized piezothermoelastic rotating bar of circular cross-section using three-dimensional linear theory of elasticity.

Design/methodology/approach

A mathematical model is developed to study the wave propagation in a generalized piezothermelastic rotating bar of circular cross-section by using Lord-Shulman (LS) and Green-Lindsay (GL) theory of thermoelasticity. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been derived by using the thermally insulated/isothermal and electrically shorted/charge free boundary conditions prevailing at the surface of the circular cross-sectional bar. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots.

Findings

In order to include the time requirement for the acceleration of the heat flow and the coupling between the temperature and strain fields, the analytical terms have been derived for the non-classical thermo-elastic theories, LS and GL theory. The computed physical quantities such as thermo-mechanical coupling, electro-mechanical coupling, frequency shift, specific loss and frequency have been presented in the form of dispersion curves. From the graphical patterns of the structure, the effect of thermal relaxation times and the rotational speed as well as the anisotropy of the of the material on the various considered wave characteristics is more significant and dominant in the flexural modes of vibration. The effect of such physical quantities provides the foundation for the construction of temperature sensors, acoustic sensor and rotating gyroscope.

Originality/value

In this paper, the influence of thermal relaxation times and rotational speed on the wave number with thermo-mechanical coupling, electro-mechanical coupling, frequency shift, specific loss and frequency has been observed and are presented as dispersion curves. The effect of thermal relaxation time and rotational speed on wave number for the case of generalized piezothermoelastic material of circular cross-section was never reported in the literature. These results are new and original.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 2
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 27 September 2011

P. Ponnusamy

The purpose of this paper is to study the wave propagation in a homogeneous isotropic, thermo‐elastic plate of arbitrary cross‐sections using the two‐dimensional theory of…

Abstract

Purpose

The purpose of this paper is to study the wave propagation in a homogeneous isotropic, thermo‐elastic plate of arbitrary cross‐sections using the two‐dimensional theory of thermo‐elasticity.

Design/methodology/approach

A mathematical model is developed to study the wave propagation in an arbitrary cross‐sectional thermo‐elastic plate by using two‐dimensional theory of thermo‐elasticity. After developing the formal solution of the mathematical model consisting of partial differential equations, the frequency equations have been derived by using the boundary conditions prevailing at the arbitrary cross‐sectional surface of the plate for symmetric and antisymmetrical modes in completely separate forms using Fourier expansion collocation method. The roots of the frequency equation are obtained by using the secant method, applicable for complex roots.

Findings

The computed non‐dimensional frequencies are compared with those results available in the literature in the case of elliptic cross‐sectional solid plate with clamped edges without thermal field and this result is coincide with the results of Nagaya. The computed non‐dimensional frequencies are plotted in the form of dispersion curves for longitudinal and flexural (symmetric and antisymmetric) modes of vibrations for the material copper.

Originality/value

The wave propagation in a plate of arbitrary cross‐sections with the stress free (unclamped) and rigidly fixed (clamped) edges are analyzed with and without thermal field.

Details

Multidiscipline Modeling in Materials and Structures, vol. 7 no. 3
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 21 June 2013

P. Ponnusamy

This paper aims to describe the method for solving vibration problem of electro‐magneto‐elastic plate of polygonal (triangle, square, pentagon and hexagon) cross‐sections using…

Abstract

Purpose

This paper aims to describe the method for solving vibration problem of electro‐magneto‐elastic plate of polygonal (triangle, square, pentagon and hexagon) cross‐sections using Fourier expansion collocation method (FECM).

Design/methodology/approach

A mathematical model is developed to study the wave propagation in an electro‐magneto‐elastic plate of polygonal cross‐sections using the theory of elasticity. The frequency equations are obtained from the arbitrary cross‐sectional boundary conditions, since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the surface of the plate directly. Hence, the FECM is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.

Findings

From the literature survey, it is clear that the free vibration of electro‐magneto‐elastic plate of polygonal cross‐sections have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of electro‐magneto‐elastic plates are based on the traditional circular cross‐sections only. So, in this paper, the wave propagation in electro‐magneto‐elastic plate of polygonal cross‐sections is studied using the FECM. The computed non‐dimensional frequencies are plotted in the form of dispersion curves and their characteristics are discussed.

Originality/value

The researchers have discussed the circular, rectangular, triangular and square cross‐sectional plates by the boundary conditions. In this problem, the author studied the vibrations of polygonal (triangle, square, pentagon and hexagon) cross‐sectional plates using the geometrical relation which is applicable to all the cross‐sections. The problem may be extended to any kinds of cross‐sections by using the proper geometrical relations.

Article
Publication date: 12 February 2018

Rajendran Selvamani

This study aims to construct a mathematical model to study the dispersion analysis of magneto-electro elastic plate of arbitrary cross sections immersed in fluid by using the…

Abstract

Purpose

This study aims to construct a mathematical model to study the dispersion analysis of magneto-electro elastic plate of arbitrary cross sections immersed in fluid by using the Fourier expansion collocation method (FECM).

Design/methodology/approach

The analytical formulation of the problem is designed and developed using three-dimensional linear elasticity theories. As the inner and outer boundaries of the arbitrary cross-sectional plate are irregular, the frequency equations are obtained from the arbitrary cross-sectional boundary conditions by using FECM. The roots of the frequency equation are obtained using the secant method, which is applicable for complex solutions.

Findings

The computed physical quantities such as radial stress, hoop strain, non-dimensional frequency, magnetic potential and electric potential are plotted in the form of dispersion curves, and their characteristics are discussed. To study the convergence, the non-dimensional wave numbers of longitudinal modes of arbitrary (elliptic and cardioid) cross-sectional plates are obtained using FECM and finite element method and are presented in a tabular form. This result can be applied for optimum design of composite plates with arbitrary cross sections.

Originality/value

This paper contributes the analytical model for the role of arbitrary cross-sectional boundary conditions and impact of fluid loading on the dispersion analysis of magneto-electro elastic plate. From the graphical patterns of the structure, the effects of stress, strain, magnetic, electric potential and the surrounding fluid on the various considered wave characteristics are more significant and dominant in the cardioid cross sections. Also, the aspect ratio (a/b) and the geometry parameters of elliptic and cardioids cross sections are significant to the industry or other fields that require more flexibility in design of materials with arbitrary cross sections.

1 – 5 of 5