In this study, the governing equations of a rotating cantilever pipe conveying fluid are derived and the longitudinal and lateral induced vibrations are controlled. The pipe considered as an Euler Bernoulli beam with tip mass which piezoelectric layers attached both side of it as sensors and actuators. The follower force due to the fluid discharge causes both conservative and non-conservative work. For mathematical modeling, the Lagrange-Rayleigh-Ritz technique is utilized. An adaptive-robust control scheme is applied to suppress the vibration of the pipe. The adaptive-robust control method is robust against parameter uncertainties and disturbances. Finally, the system is simulated and the effects of varying parameters are studied. The simulation results show the excellent performance of the controller.

In this paper, an active controller is used to suppress the flutter vibration of a beam. The beam is made of Functionally Graded Material (FGM) and subjected to a follower force and arbitrary lumped mass. The properties of the FGM layer are functionally graded in the thickness direction according to the volume fraction power law distribution. The piezoelectric layers, which are attached to both sides of the beam, are used as sensors and actuators. The beam is fixed from one end and elastically restrained by a spring at the other end. To investigate the effect of the controller on the vibration response of the beam, parameters such as the follower force, spring stiffness, mass ratio and attachment location are included in the analysis based on the generalized function theory and Lagrange–Rayleigh–Ritz technique. The vibration responses of the system are presented in the simulation results, where excellent agreement of the controller scheme is observed.