Transient analysis of axially functionally graded Timoshenko beams with variable cross-section

The present study goals to analyze transient analysis of axially functionally graded (AFG) Timoshenko beams with variable cross-section. Both the materials and geometrical properties of the AFG tapered beam varying along the longitudinal direction. In the analysis, the influences of rotary inertia and shear deformation are taken into account. Complementary functions method (CFM) is applied to solve the differential equations in Laplace domain. By using the modified Durbin's algorithm, the results are transformed to the time domain. For the verification of the recommended method, numerous problems which were solved in the literature are handled with the developed method and benchmarked with the findings in the literature.