Coupled thermoelastic vibrations of a simply supported beam

The dynamic behavior of a simply supported beam to whose surface (z = +h/2) a step heat flux of intensity q is applied at time t = 0 is investigated. The temperature is assumed to vary linearly in the z direction. This assumption, which is more valid for thinner beams, produces two coupled partial differential equations with x and t as independent variables after integration over the thickness of the beam. The mathematical analysis is based on integral transforms, and an analytical expression is obtained for the displacement w. The results show that, when the coupling between the strain and temperature fields is taken into account, the vibrations of the beam decay with increasing time. When the coupling is ignored, a steady-state mode of vibration is established.