Memory and dynamic response of a thermoelastic functionally graded nanobeams due to a periodic heat flux

This study highlights the introduction of a new mathematical model for functionally graded thermoelastic nanobeams (FGNB) which contains a free choice of the kernel function and time delay. The basic equations that govern the proposed model have been constructed on the basis of Hamilton's principle, Euler-Bernoulli's assumptions, Eringen's theory and three-phase-lag memory dependent heat conduction. The FGNB is due to a heat flux depending on time. The nanoscale beams can be regarded as non-homogeneous composite structures and typically vary from the ceramic at the bottom of the beam to the metal on the top with a continuous structural transmission along with the thickness of the beam. Utilizing the Laplace integral transform, the problem is solved analytically. The variations in moment distribution, temperature, displacement and deflection are illustrated graphically for the various kernel functions, time delays, the influence of the nonlocal parameter, and periodic pulse. Compared with the current thermoelastic models, the implications of the present model are discussed.