Journal of Vibration and Control

Continuous element methods have frequently been used in the modal analysis of structures modeled as flexible beams, extensible strings and rods, but only rarely for purposes of control. In this paper, we define a strategy of active control using the exact transfer matrix of a two-cell planar truss. The closed-loop performance predictions of both collocated and non-collocated controllers are compared as a function of feedback controller parameters.

In this paper, we study bifurcations in systems with impact and friction, modeled with a rigid multibody approach. Knowledge from the field of nonlinear dynamics is therefore combined with theory from the field of non-smooth mechanics. We study the nonlinear dynamics of three commercial wooden toys. The toys show complex dynamical behavior but can be studied with one-dimensional maps, which allows for a thorough analysis of the bifurcations.

We consider shock isolation designs based on the use of nonlinear energy sinks (NESs). These are a priori determined points of a system where unwanted disturbances are transmitted (“pumped”) and then eliminated by passive or active means. The underlying dynamic phenomenon that causes nonlinear energy to pump into a sink is resonance capture on a 1:1 resonance manifold of the dynamics. In this work, essentially nonlinear stiffness elements are used to couple the NES with the primary system in order to achieve robust energy pumping, in a sufficiently fast timescale. “Fast” energy pumping at the early stage of the motion is important in order to achieve the shock isolation objectives. The proposed shock isolation design is practical and realizable. Its modular form enables the alteration of the global dynamics of a system by attaching a number of local NESs. The proposed design has the additional interesting feature of dual mode shock isolation, e.g., the capacity to significantly reduce the level of unwanted disturbances initiated at different points of the system.

In this paper, we present a numerical study of flutter instability of a flexible disk rotating near a rigid wall. The disk is modeled using linear plate theory, and the air flow between the disk and the rigid plate is modeled using the Reynolds equation of lubrication for thin-film flows. The coupled disk-fluid equations are solved numerically. The spatial derivatives are approximated using finite-difference schemes and the time integration is performed using the Runge-Kutta numerical scheme. The transient numerical simulation is used to determine approximations to the exact stability boundaries for stable operation of the disk. The stability boundaries for the disk-fluid system are captured for a wide range of circumferential mode numbers (16-30) and disk rotational speeds, and these predictions are compared to the predictions of an approximate single-mode analysis.

In this paper, we focus on the analysis and control of a simple rigid-body mechanical system with clearance. Contrary to most of the existing works in the literature concerning control, we explicitly treat all the nonlinear non-smooth characteristics of this system considered as a rigid-body mechanical system with unilateral constraints and impacts (dynamic backlash). The model is therefore a hybrid dynamical system, mixing discrete events as well as continuous states. The regulation and tracking capabilities of the proportional—derivative (PD) scheme are investigated. In particular, a complete proof of the existence of a limit cycle for non-collocated PD control is provided, including viability constraints. It is concluded that tracking requires the development of specific control schemes. Consequently, we propose a hybrid control that may be used to track some desired trajectories in conjunction with a PD input. Throughout the paper, the particular features of unilaterally constrained mechanical systems are taken into account, such as the fundamental viability property of closed-loop solutions and controls. This work is a new approach to be considered for application in several areas including the control of kinematic chains with joint clearance and vibro-impact systems, as well as liquid slosh control. Numerical results are presented to illustrate the possible performance of the proposed control scheme and its robustness properties.

In this paper, the dynamic problem of a rigid body colliding with an elastic rod is studied in some detail. Different contact theories for modeling impact responses are compared with experimental measurements. Based on an idea originally presented by Sears for collisions of two rods with rounded ends, a boundary approach combining Hertzian contact law and St. Venant's elastodynamics is developed to describe longitudinal waves in rods. It is shown that this boundary approach agrees very well with experimental results. For the simulation of long-term dynamic behavior after impact, a traditional rigid-body approach is advantageous because the elastic vibration of the rod will decay fast due to the structural damping and the elastic rod then moves like a rigid body. Hence, for modeling longitudinal impacts, it is suggested that both elastodynamics and rigid-body dynamics are combined into a two-timescale model. The short time behavior of wave propagation due to impacts is modeled using elastodynamics, and the state of the rigid-body mode is transferred to the rigid-body approach as the initial condition for the motion. The long-term behavior after impact is then computed using the rigid-body approach.

We show how an energy analysis can be used to derive the equilibrium equations and boundary conditions for an end-loaded variable ply much more efficiently than in previous works. Numerical results are then presented for a clamped balanced ply approaching lock-up. We also use the energy method to derive the equations for a more general ply made of imperfect anisotropic rods and we briefly consider their helical solutions.

The deployment of a subsatellite from a mother spaceship moving on a circular orbit is a delicate operation for a tethered satellite system because this process leads to an unstable motion with respect to the stable radial relative equilibrium of such a system if the tether length is kept constant. Therefore, simulation tools for the implementation of stabilizing control are needed. Usually linear control, for example Kissel's law, is implemented. In this paper, we introduce an optimal control strategy to simulate the force controlled deployment of a tethered satellite from a spaceship. We compare this strategy with free deployment, deployment controlled by Kissel's law and an approach making use of the concept of “targeting” used in the controlling chaos approach.

We investigate a nonlinear active vibration absorber to control the vibrations of plates. The absorber is based on the saturation phenomenon associated with dynamical systems with quadratic nonlinearities and a two-to-one internal resonance. The technique is implemented by coupling a second-order controller with the plate's response through a sensor and an actuator. Energy is exchanged between the primary structure and the controller and, near resonance, the plate's response saturates to a small value. Numerical as well as experimental results are presented for a cantilever rectangular plate. For the numerical studies, finite-element methods as well as modal analysis are implemented. The commercially available software ABAQUS is used in the finite-element analysis together with a user-provided subroutine to model the controller. For the experimental studies, the plate is excited using a dynamic shaker. Strain gages are used as sensors, while piezoelectric ceramic patches are used as actuators. The control technique is implemented using a digital signal processing board and a modeling software. Both numerical and experimental results show that the control strategy is very effective.

Snake-like locomotions of a three-member linkage equipped with actuators are modeled and investigated. Longitudinal, lateral, and rotational motions of the mechanism along a horizontal plane in the presence of the dry friction are analyzed. The desired motions are presented as a combination of more simple elementary motions. Sufficient conditions are deduced under which these motions are possible. The dependence of the average speed of motions on various geometrical and mechanical parameters is investigated. The optimal values of the parameters which maximize the speed are obtained. The numerical results are presented and discussed.

In this paper, we show that, in rotary cranes, it is possible to reduce payload pendulations significantly by controlling the crane's translational and rotational degrees of freedom. Such a control can be achieved with the heavy equipment that is already part of the crane, so that retrofitting existing cranes with such a controller would require little effort. Moreover, the control is superimposed transparently on the commands of the operator. The successful control strategy is based on delayed position feedback of the payload's in-plane and out-of-plane motions. Its effectiveness is demonstrated with a fully nonlinear three-dimensional computer simulation and with an experiment on a scaled model of a rotary crane. The results demonstrate that the pendulations can be significantly reduced, and therefore the rate of operation can be greatly increased. The effectiveness of the controller is demonstrated for both rotary and gantry modes of operation.