Conference Proceeding

Mathematics in Space and Applied Sciences (ICMSAS-2023)
ICMSAS-2023

Subject Area: Mathematics
Pages: 331
Published On: 03-Mar-2023
Online Since: 04-Mar-2023

 Read More >>

Author(s): Anita Devi Thakur

Email(s): anitanithamirpur@yahoo.com

Address: Anita Devi Thakur
Vallabh Govt. College Mandi, Himachal Pradesh, India
*Corresponding Author

Published In:   Conference Proceeding, Mathematics in Space and Applied Sciences (ICMSAS-2023)

Year of Publication:  March, 2023

Online since:  March 04, 2023

DOI:




Transient Response of Rigidly Fixed Piezothermoelastic Half-Space to a Thermal Source

 

Anita Devi Thakur

Vallabh Govt. College Mandi, Himachal Pradesh, India

*Corresponding Author E-mail: anitanithamirpur@yahoo.com

 

ABSTRACT:

Analysis of piezothermoelastic materials under different types of loading can provide important information for the designing of piezothermoelectric devices. Due to various applications, an attempt has been made to explore the effects of temperature gradient on the homogeneous, transversely isotropic, linear generalized piezothermoelastic rectangular half-space. The surface of the half-space is considered to be rigidly fixed, charge free and subjected to impact/continuous temperature gradient. The Laplace and Fourier transforms technique have been employed to solve the system of partial differential equations and boundary conditions in the transformed domain. In order to obtain the results in the physical domain, the quadratic complex polynomial characteristic equation has been solved by using DesCartes’ algorithm. The inverse transform integrals are evaluated by using numerical technique consisting of Fourier series approximation and Romberg integration. Numerical results applicable to a cadmium selenide (CdSe) material are presented graphically. A comprehensive analysis and comparison of the results in the context of different models of thermoelasticity has been presented.

 

KEYWORDS: Piezothermoelastic; Integral transforms; Lord-Shulman theory; Romberg Integration; DesCartes’ Algorithm.

 

1.       INTRODUCTION:

 Lord Kelvin (1853) has provided the first theoretical explanation for thermoelastic phenomenon which is concerned with the coupling between mechanical deformation and change in thermal energy of an elastic material. Whereas piezoelectric materials has been used as sensors, actuators and in structural health monitoring. Residual stress measurement by means of the thermoelastic effect has been given by Wong et al. (1988). Three-dimensional fundamental solution for a generalized thermoelastic infinite medium subjected to a continuous heat source has been given by Aouadi (2006). The general solutions of transversely isotropic piezothermoelastic materials have been used by Hou et al. (2008) to construct the three-dimensional solutions of a steady point heat source on the apex of a transversely isotropic piezothermoelastic cone. The transient, coupled piezothermoelectric response of a functionally graded, radially polarized hollow cylinder under dynamic axisymmetric loadings has been studied by Babaei and Chen (2010a). The piezothermoelectric problem of one-dimensional functionally graded medium excited by a moving heat source has been investigated by Babaei and Chen (2010b).

 

Ailawalia and Khurana (2010) studied the deformation of transversely isotropic piezoelectric medium with an overlying infinite viscous fluid due to steady state response of moving load acting at the interface of both media by applying the Fourier transforms. Akbarzadeh et al. (2011) investigated the dynamic response of a functionally graded piezoelectric medium (FGPM) subjected to a moving heat source. Three-dimensional piezothermoelastic solutions for a finite functionally graded cylindrical shell with piezoelectric layer subjected to axisymmetric thermomechanical loads has been studied by Yong et al. (2013).   The response of continuous mechanical and thermal point loads acting on the surface of a homogeneous piezothermoelastic half-space has been studied by Thakur et al. (2013). Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory has been studied by Mohamed et al. (2017).

 

2.       Formulation of the problem:

A homogeneous, transversely isotropic, thermally conducting generalized piezothermoelastic half-space which is initially at temperature has been considered. We take origin of the co-ordinate system  at any point on the plane surface and axis pointing vertically downward into the half-space, which is thus represented by. It is assumed that a continuous strip thermal source is acting at the surface of the medium. From the symmetry consideration all the field quantities are independent of coordinate. We further assume that the field quantities



1.       REFERENCE:

1.         Ailawalia P.  and  Khurana G. (2010):  Effects of moving load velocity and viscosity in a transversely isotropic piezoelectric medium, Int. J. Appl. Math. Mech., vol.  6, pp. 19-33, 2010.

2.         Akbarzadeh A. H., Babaei M. H. and Chen Z. T.( 2011): Thermopiezoelectric analysis of a functionally graded piezoelectric medium, Int. J. Appl. Mech., vol. 3, pp. 47-68.  

3.         Aouadi M. ( 2006): Generalized three-dimensional heat source problem for small time, Int. J. Comput. Meth. Eng. Sci. Mech., vol. 7, pp. 59-67.

4.         Babaei M. H. and Chen Z. T. (2010a): The transient coupled thermo-piezoelectric response of a functionally graded piezoelectric hollow cylinder to dynamic loadings, Proc. R. Soc. A, vol. 466, pp. 1077-1091.

5.         Babaei M. H. and Chen Z. T. (2010b): Transient thermopiezoelectric response of a one-dimensional functionally graded piezoelectric medium to a moving heat source, Arch. Appl. Mech., vol. 80, pp. 803-81.

6.         Churchill R. V. (1972): Operational mathematics, third edition-McGraw-Hill Kogakusha Ltd.

7.         Hou P. F., Andrew Y. T. and Chen C. P. (2008): Fundamental solution for  transversely isotropic thermoelastic materials, Int. J. Solids Struct., vol. 45, pp. 392-408, 2008.

8.         Kang Y., Wang Z. and Xie G. (2013), Three-Dimensional piezothermoelastic stress of a finite functionally graded cylindrical shell with piezoelectric layer, Mathematical Problems in Engineering, Hindawi Pub. Co., vol. 2013, Article ID 947693, 13 pages.

9.         Mohamed I.A. , Othman and Marin M.(2017): Effect of thermal loading due to laser pulse on thermoelastic porous medium under G-N theory, Results in Physics, vol 7, pp. 3863-3872.

10.      Sharma J. N., Thakur Anita D. and Sharma Y. D.  (2009): Disturbance due to periodic thermal load in a piezothermoelastic half-space. Int. J.  Appl. Mech., vol.1, pp. 607-629.

11.      Thakur Anita D., J. N. Sharma and Y. D. Sharma, Disturbance due to point loads in a piezothermoelastic continuum, J. Thermal Stresses, vol. 36, pp. 259-283, 2013.

12.      Thompson W. (Lord Kelvin) (1853): Trans. R. Soc. Edinb. vol. 20, pp. 261–288.

13.      Wong A.K., Dunn S.A. and Sprraw J.G. (1988): Residual stress measurement by means of the thermoelastic effect, Nature, vol. 332, pp. 613-615.



Related Images:



Author/Editor Information

Dr. Sanjay Kango

Department of Mathematics, Neta Ji Subhash Chander Bose Memorial, Government Post Graduate College, Hamirpur Himachal Pradesh-177 005, INDIA