Generalized coupled thermoelasticity in an orthotropic rotating disk subjected to thermal shock

The problem of thermal shock in an orthotropic rotating disk is solved analytically using the Lord-Shulman coupled theory of thermoelasticity. Finite Hankel transform (Fourier-Bessel expansion) is used to present closed-form relations for the temperature and displacement fields. To simplify the problem, coupled equations of thermoelasticity are transferred into nondimensional form and the effects of the relaxation time on the history and the distribution of the temperature, displacement and stress components are investigated. Differences between boundary conditions in propagation and reflection of the elastic wave from boundaries are observed on figures. To show the effects of considering different mechanical properties in each principal direction, an orthotropicity factor is introduced and the stress components for different values of this factor are plotted. In order to validate the present work, the orthotropic disk is reduced to the isotropic one by considering the same material properties in different directions and the results are compared with a numerical study and an analytical solution, which show good agreement.

Automated summary

This study analytically solves thermal shock in an orthotropic rotating disk using the Lord-Shulman coupled theory of thermoelasticity. Closed-form relations for temperature and displacement fields are obtained using the finite Hankel transform. The effects of relaxation time on temperature, displacement, and stress distribution are investigated, and differences in boundary conditions for elastic wave propagation and reflection are observed. An orthotropicity factor is introduced to examine the impact of different mechanical properties in each principal direction, and the findings are validated through comparison with numerical and analytical solutions.