Nonlinear Stability of Fluid-Conveying Rotating Cylinders in Hydraulic Arms: Application in Robot Automation Technology

In this paper, we provide a global analysis of the nonlinear dynamic stability of rotating composite cylinders conveying fluid enclosed within hydraulic arms, which is a practical problem for automation technology in robotic systems. The structure is treated as a thin-walled ‘Rayleigh-type’ beam resting on an elastic foundation, which is capable of axial, bending, and torsional deformations. Geometric nonlinearities are captured using von Kármán strain-displacement relations to correspond to moderate-to-large amplitude responses. Distributed piezoelectric actuators and sensors are ‘embedded’ within the structure in order to perform active control of vibration, using a negative displacement feedback control law to actively suppress instabilities due to flow dynamic response. The dynamic model takes into account the effects of internal fluid motion, rotational inertia, Coriolis and centrifugal forces, and the elastic foundation’s effect, resulting in a set of coupled nonlinear partial differential equations constructed via Hamilton’s principle. The equations are discretized using the Galerkin method for stability analysis. The parametric studies examine the effects of fluid velocity, rotational speed, piezoelectric layer configuration, feedback gain, and elastic foundation spring constant on the stability limits of the coupled system. The results indicate that, with respect to fluid stability, the active control technique increases the critical flow velocity and increases the overall dynamic stability. This provides valuable insight into the design of the structure in the context of smart fluid-conveying robotic arms and smart automation. The implications of this work are wide-reaching for aerospace, robotics, and automated structural systems.