Coupled thermoelastic nonlocal forced vibration of an axially moving micro/nano-beam

Abstract

Since axially moving material systems were introduced in the 1960s, many different axially moving material systems, such as axially moving strings, beams, and plates have been studied for many decades. In recent years, axially moving micro/nano-beams in micro/nano-electro-mechanical systems become popular. Since thermal effects of micro/nano-beams cannot be ignored, coupled thermoelastic vibrations of axially moving micro/nano-beams are important scientific problems. This work analytically investigates coupled thermoelastic forced vibration and the heat transfer process of an axially moving micro/nano-beam. The small-scale effect is considered not only in the vibration equation but also in the heat transfer equation of the micro/nano-beam. Eringen nonlocal elasticity theory and the classical Euler-Bernoulli beam model are used to model the vibration equation of the axially moving micro/nano-beam. The Type III Green-Naghdi heat transfer model is used to establish the heat transfer equation of the micro/nano-beam. The vibration and heat transfer equations are coupled to each other. Green functions, Laplace transform, and eigenfunction expansion are key mathematical tools used to solve the coupled equations. In the numerical example, by comparing the present solutions with results of some published articles, the correctness of the present solutions is verified. It is found through numerical analyses that the fundamental natural frequency of an axially moving micro/nano-beam decreases with its axial velocity, small-scale parameter, and height-to-length ratio. Heat rotation phenomena are first found in this study. The heat rotation phenomena discovered show synchronization between the displacement and temperature. The rotation direction of the temperature can be controlled by changing the axial velocity, height-to-length ratio, and heating position.