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Abstract

This paper is concerned with the study of thermoelastic beam in modified couple stress theory. The governing equations of motion for modified couple stress theory and heat conduction equation for non-Fourier (non-classical process) are investigated to model the vibrations in a homogeneous isotropic thin beam in a closed form by employing the Euler Bernoulli beam theory. The generalized theories of thermoelasticity with one and two relaxation times are used to model the problem. Both ends of the beam are simply supported. The Laplace transform technique applied to solve the system of equations which are written in dimensionless form. A general algorithm of the inverse Laplace transform is developed. The thermal moment is approximated as the difference between the upper and the lower surfaces of the beam. The analytical results have been analyzed numerically with the help of MATLAB software. The lateral deflection, thermal moment, axial stress average due to normal heat flux in the beam are derived and computed numerically. Numerical inversion technique has been applied to recover the results in a physical domain. The effect of couple stress on the resulting quantities are depicted graphically for a specific model. Comparisons are made with the results of different theories in the absence and presence of couple stress parameter. Particular cases of interest are also derived. The present study may find applications in medical science, engineering, accelerometers, sensors, resonators etc. The study of lateral deflection, thermal moment and axial stress average is a significant problem of continuum mechanics.

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