Time-varying frequency characteristics of accelerated rotating functionally graded material beams under thermal shock

In this paper, the time-varying frequency behavior of accelerated rotating functionally graded material (FGM) beams under thermal shock is investigated. The temperature and material properties are assumed to vary along the beam thickness direction. The transient temperature field of the rotating FGM beams under the convective heat transfer boundary condition is obtained through the one-dimensional transient heat conduction equation with temperature-dependent material properties. Based on the Timoshenko beam theory, the governing equation of the beams is obtained via Hamilton's principle. The assumed mode method is used to calculate the time-varying natural frequency of the beams with variable speed and temperature. The present results are verified by comparison with finite element results obtained by ANSYS. Results show that considering the temperature dependence of the elastic modulus is important in analyzing time-varying natural frequencies of accelerated rotating FGM beams under thermal shock. However, the temperature dependence of Poisson's ratio, thermal conductivity and specific heat capacity can be disregarded. Under thermal shock, temperature plays a dominant role in the natural frequencies of accelerated rotating FGM beams in the initial acceleration process, while rotational speed dominates the later acceleration process.