Free and forced vibration analysis of axially functionally graded Timoshenko beams on two-parameter viscoelastic foundation

The current study aims to analyze free and forced vibrations of axially functionally graded (AFG) Timoshenko beams on two-parameter viscoelastic foundation. In these kinds of beams, material properties alter through the axis. In the dynamic analysis, as research parameters, material inhomogeneity and foundation constants are considered. By using complementary functions method (CFM), in Laplace domain, differential equations are calculated. The calculations are performed in the Laplace domain. Calculations were transformed from Laplace domain to the time domain by applying Durbin's procedure. The free and forced vibrations of AFG Timoshenko beams on elastic/viscoelastic foundation are examined by solving different kinds of problems. The results obtained in this research showed that there is a relation and consistency with findings of the literature.