Effect of ramp-type heating on the vibration of functionally graded microbeams without energy dissipation

In the present work, a generalized solution for the vibration of functionally graded microbeam is studied. A vibrational response is presented for a microbeam subjected to a ramp-type heating and which has functionally varying material properties through its thickness. The governing equations of the generalized thermoelasticity without energy dissipation proposed by Green and Naghdi are presented. An analytical technique based on Laplace transform is used to calculate the vibration of deflection and the temperature. The inverses of Laplace transforms are computed numerically using Fourier expansion techniques. The effect of the ramping time parameter is studied on the lateral vibration, the temperature, the displacement, the stress, the bending thermal moment, and the strain energy of the functionally graded microbeam. The influence of the thickness of the beam is also analyzed.