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An innovative nonlinear optimal control scheme based on θ-D approximation for structural vibration control with R-AMD (active mass damper with rotating actuator) is developed in this paper. In the R-AMD which was proposed in our previous work, rotating actuator rather than linear actuator is used to accelerate and decelerate the inertial mass, thus avoiding stroke-related problems. The rotational motion of the inertial mass makes R-AMD a special nonlinear AMD, which raises the level of difficulty in controller designing. Taking the control-structure interaction (CSI) effect into consideration, the modeling of target structure/R-AMD coupled system is fulfilled using the Lagrange equations. Regarding the nonlinearity in the R-AMD system, a nonlinear optimal control scheme is designed based on θ-D approximation, during which the important role of diffeomorphism transformation of coordinates is presented. Experiments are conducted to validate the effectiveness of the proposed control algorithm and the R-AMD device.

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Pressure-equalizing film is a slice of air layer attached to vehicle exterior with nearly uniform inside pressure, similar to ventilated cavity in composition; it is generated through exhaust process of the inside air chamber as vehicle emerges from deep water, and can reduce the lateral force and pitching moment that vertical launched underwater vehicle suffered. In this work, the emerging process of vehicle from water with pressure-equalizing exhaust was numerically calculated to investigate the evolution and flow characteristics of the generated pressure-equalizing film along its surface. Results indicated that during the whole exhaust process, the film can be obviously classified into different sections according to the distribution of phase volume fraction or pressure. The exhaust velocity ratio and flow rate from vehicle interior chamber were also found to increase as vehicle moves. In the analysis of flow structures, vortex structures such as the horseshoe vortex, “detour-separation” vortex, and counter-rotating vortex pair (CVP) can be figured out in the region of the exhaust hole. Under the effect of re-entrant jet, water around the film tail would be entrained upstream then enter the surface film to mix with the pressure-equalizing air. It leads to the happening of the three-dimensional (3D) wall vortex in the flow field.

The vertically launched underwater vehicle always suffers various hydrodynamic disturbances in its water-emerging process due to the uncertainty of the launch platform motion. Based on the nested sparse grid based stochastic collocation method (NSSCM) and nonintrusive polynomial chaos method, the effect of uncertainty of platform velocity and yaw angle on robustness of vehicle's trajectory and attitude is numerically studied. Results indicate that the uncertainty stemming from platform motion propagates along vehicle's water-emerging process. As the negative horizontal velocity of vehicle gradually changes to positive direction, the uncertainty bar of horizontal velocity presents contracting-expanding mode with an “hourglass” shape while the uncertainty bar of horizontal displacement experiences a “spindle-shaped” one (expanding-contracting-expanding), which is a half cycle later compared with the velocity. The uncertain motion of platform enlarges the uncertainty bar of bottom force via its impact on the gas-leakage process of trail bubble, resulting in the increasing of uncertainty of vertical velocity. Pitching angle (attitude of vehicle) and pitching angular velocity of vehicle persist getting worse driven by the pressure difference between vehicle's front and back sides especially on head part. And their continuous increasing uncertainty bars are formed mainly due to the condition that pressure uncertainty of front side is larger than that on back side, which also leads to the increasing of uncertainty of horizontal force.