Integral transform approach for solving dynamic thermal vibrations in the elliptical disk

ABSTRACT

The present article is concerned with the determination of thermally induced transverse vibration of a uniform thin elliptical disk with elastic supports at both radial boundaries. The temperature field on the disk is considered to be a ramp-type prescribed on the top face while the bottom face is kept at zero temperature. In this study, integral transform technique is used to investigate the conductivity equation in an exact manner by the use of Mathieu functions and modified Mathieu functions. The thermal moment is derived on the basis of temperature distribution, and its stresses are derived based on the resultant bending moments per unit width. The numerical calculations of the distributions of the transient temperature and its associated thermoelastic results are performed, and the numerical results are shown in the figures.

KEYWORDS:

• Deflection
• elliptical disk
• heat conduction
• integral transform
• thermal stresses

Acknowledgment

The authors are grateful to the reviewer for his valuable suggestions and constructive comments which resulted in revising the article to its present form.