Longitudinal vibration analysis of viscoelastic axially functionally graded bars using a hybrid finite element formulation

The integration of viscoelastic functionally graded materials into structural design provides an effective way to reduce vibrations. This study introduces a new hybrid finite element method for analyzing harmonic vibrations in viscoelastic axially functionally graded (AFG) bars. The approach is based on the Hellinger-Reissner principle, where axial force and displacement are treated as separate fields. Material properties such as Young’s modulus, density, and damping vary along the bar according to a power-law function. Numerical examples are given to show how angular frequencies and force transmissibility are influenced by different material gradations.