Thermal vibration of FGM beams with general boundary conditions using a higher-order shear deformation theory

Thermo-elastic vibration of FGM beams with general boundary conditions is studied using a higher-order shear deformation beam theory (HSDBT). The HSDBT is proposed by introducing a new transverse shear stress function through the beam thickness. The material properties of the FGM beam are assumed to be temperature-dependent, and change gradually in the thickness direction. Three cases of temperature distribution in the form of uniformity, linearity, and nonlinearity, are considered through the beam thickness. The energy stored in the boundary restraints is transformed into a quantifiable form by introducing a set of artificial springs at each boundary. Rayleigh-Ritz method combined with improved Fourier series is utilized to obtain the vibration characteristics of the heated FGM beam. The convergence and accuracy of the present method are discussed by comparing with the reference data. The effects of the temperature changes, material parameters, and boundary conditions on the thermo-elastic vibration characteristics of the FGM beam are studied. Furthermore, the natural frequency results of the FGM beam subjected to linear and nonlinear temperature distributions are compared.