The effect of attached lumped mass position on the frequency reduction of the radially graded tube

For vibration reduction performance, mass damping system is used as dynamic vibration absorber. The effect of attached lumped mass position on the fundamental frequency reduction of the annular functionally graded beam is studied. For the volume fraction distribution of the functionally graded material tube, the power law is used to model radial gradation. The various classical boundary conditions including simply supported beam, clamped beam, pinned-clamped beam and cantilever beam as well as shear hinge end condition are considered. It is assumed that the lumped mass is connected to the tube at an arbitrary position without sliding. The total potential energy is minimized by employing spectral Ritz method to calculate fundamental frequency and corresponding mode shape. The reduction of the frequencies in the presence of the attached lumped mass is observed. The dimensionless frequency reduction is affected by lumped mass amount and position. The lumped mass position plays an important role for vibration control of the functionally graded tube.

Keywords:

Vibration analysis , Radial gradation , Lumped mass damper , Spectral Ritz method