Vibration Of Flexible Structures Research Articles

Velocity feedback control with a flywheel proof mass actuator

This paper presents four new proof mass actuators to be used in velocity feedback control systems for the control of vibrations of machines and flexible structures. A classical proof mass actuator is formed by a coil–magnet linear motor, with either the magnet or the armature-coil proof mass suspended on soft springs. This arrangement produces a net force effect at frequencies above the fundamental resonance frequency of the springs–proof mass system. Thus, it can be used to implement point velocity feedback loops, although the dynamic response and static deflection of the springs–proof mass system poses some stability and control performance limitations. The four proof mass actuators presented in this study include a flywheel element, which is used to augment the inertia effect of the suspended proof mass. The paper shows that the flywheel element modifies both the dynamic response and static deflection of the springs–proof mass system in such a way as the stability and control performance of velocity feedback loops using these actuators are significantly improved.

Slew maneuver control of flexible spacecraft for vibration suppression

This paper presents the input shaping technique for reducing the vibrations of flexible structures under attitude control inputs applied to the flexible spacecraft. The input shaping profile is investigated for the effective suppression of transient vibrations of modal responses. It is applied to the input commands to minimize the residual vibrations and suppress the overshoot of the modal responses. The results of numerical simulations, using a simple dynamic model of a flexible spacecraft, show that the input shaping technique is useful for suppressing the residual vibrations caused by attitude maneuvers.

Space robots with flexible appendages: Dynamic modeling, coupling measurement, and vibration suppression

For a space robot with flexible appendages, vibrations of flexible structure can be easily excited during both orbit and/or attitude maneuvers of the base and the operation of the manipulators. Hence, the pose (position and attitude) of the manipulator's end-effector will greatly deviate from the desired values, and furthermore, the motion of the manipulator will trigger and exacerbate vibrations of flexible appendages. Given lack of the atmospheric damping in orbit, the vibrations will last for quite a while and cause the on-orbital tasks to fail. We derived the rigid-flexible coupling dynamics of a space robot system with flexible appendages and established a coupling model between the flexible base and the space manipulator. A specific index was defined to measure the coupling degree between the flexible motion of the appendages and the rigid motion of the end-effector. Then, we analyzed the dynamic coupling for different conditions, such as modal displacements, joint angles (manipulator configuration), and mass properties. Moreover, the coupling map was adopted and drawn to represent the coupling motion. Based on this map, a trajectory planning method was addressed to suppress structure vibration. Finally, simulation studies of typical cases were performed, which verified the proposed models and method. This work provides a theoretic basis for the system design, performance evaluation, trajectory planning, and control of such space robots.

Selective modal control for vibration reduction in flexible structures

The design of a controller for selective reduction of vibrations in flexible low-damped structures is presented. The objective of the active feedback control law is to increase damping of selected modes only, in frequency regions where a disturbance is likely to produce largest effect. Moreover, the stabilizing controller is required to be band-pass, in order to filter out high-frequency sensor noise and low-frequency accelerometer drift, and stable to increase robustness to uncertain parameters. The control design is based on the Inverse Optimal Design approach, through the solution of a matrix Stein equation, resulting in the solution of an optimal H∞ control problem. A grey-box identification approach of the authors is employed for obtaining the model from experimental data or from detailed Finite Element Model (FEM) simulators. The problem of optimal actuator/sensor location is also addressed. Detailed simulation results are provided to show the effectiveness of the strategy.

Complete passive vibration suppression using multi-layered piezoelectric element, inductor, and resistor

This paper describes passive technique for suppressing vibration in flexible structures using a multi-layered piezoelectric element, an inductor, and a resistor. The objective of using a multi-layered piezoelectric element is to increase its capacitance. A piezoelectric element with a large capacitance value does not require an active electrical circuit to simulate an inductor with a large inductance value. The effect of multi-layering of piezoelectric elements was theoretically analyzed through an equivalent transformation of a multi-layered piezoelectric element into a single-layered piezoelectric element. The governing equations were derived using this equivalent transformation. The effect of the resistances of the inductor and piezoelectric elements were considered because the sum of these resistances may exceed the optimum resistance. The performance of the passive vibration suppression using an LR circuit was compared to that of the method where a resistive circuit is used assuming that the sum of the resistances of the inductor and piezoelectric elements exceeds the optimum resistance. The effectiveness of the proposed method and theoretical analysis was verified through simulations and experiments.

An effective trajectory planning method for simultaneously suppressing residual vibration and energy consumption of flexible structures

This paper presents a proposal for a minimum energy feedforward control technique for flexible structures to suppress residual vibrations in point-to-point (PTP) motion. In the proposed method, the trajectory profile of the PTP motion is generated through a cycloidal function whose input is the output of a polynomial function. The obtained trajectory is dependent upon the coefficients of the polynomial function. To achieve the suppression of the residual vibration as well as the operating energy of this PTP motion, the coefficients are tuned by metaheuristic algorithms. In the numerical simulations, we investigated the PTP motions of a single-link flexible manipulator and a robotic arm attached to a flexible link. The simulation results were compared with those of previous studies, revealing the effectiveness of the proposed method.

Boundary control of harmonic disturbances on flexible cantilever beams using piezoelectric patch actuators

This work addresses the control of vibrations in flexible structures caused by external harmonic disturbances using a boundary control method. The research is motivated by practical systems where beam-like structures require vibration suppression to prevent fatigue and system damage, or to increase efficiency. Importantly, this paper addresses a practical constraint of the actuation points being at the boundaries only. The method presented here is an open-loop control scheme which requires knowledge of the harmonic disturbance and a model of the flexible system. The controller uses the model, developed using the Rayleigh–Ritz method, to predict the reaction of the beam to the known input disturbance and compute an optimized control input which reduces the steady state vibration in the system. By properly choosing the cost function, the controller can be used to reduce the total vibration or to reduce the vibration in certain spatial locations. The method's vibration reduction capabilities are studied over a range of frequencies; data collected from experiments on a physical beam model is used to validate the predicted behavior of the system.

Asymptotic behavior of a flexible structure with Cattaneo type of thermal effect

We consider vibrations of a non uniform flexible structure modeled by a 1D viscoelastic equation with Kelvin–Voigt, coupled with an expected dissipative effect : heat conduction governed by Cattaneo’s law (second sound). We establish the well-posedness of the system and we prove the stabilization to be exponential for one set of boundary conditions, and at least polynomial for another set of boundary conditions. Two different methods are used: the energy method and another more original, using the semigroup approach and studying the Resolvent of the system.

Experimental investigation of jet pulse control on flexible vibrating structures

The feasibility of applying on-line fluid jet pulses to actively control the vibrations of flexible structures subjected to harmonic and earthquake-like base excitations provided by a shake table is explored. The operating principles and capabilities of the control system applied have been investigated in a simplified small-scale laboratory model that is a mass attached at the top free end of a vertical flexible slender beam with rectangular cross-section, the other end of which is mounted on an electrodynamic shaker. A pair of opposite jets placed on the mass at the top of the cantilever beam applied the appropriate forces by ejecting pressurized air pulses controlled by on/off solenoid electro-valves via in house developed control software, in order to control the vibration caused by harmonic, periodic and random excitations at pre-selected frequency content provided by the shaker. The dynamics of the structure was monitored by accelerometers and the jet impulses by pressure sensors. The experimental results have demonstrated the effectiveness and reliability of Jet Pulse Control Systems (JPCS). It was verified that the measured root mean square (RMS) vibration levels of the controlled structure from harmonic and earthquake base excitations, could be reduced by approximately 50% and 33% respectively.

Dimensionless Analysis of Segmented Constrained Layer Damping Treatments with Modal Strain Energy Method

Constrained layer damping treatments promise to be an effective method to control vibration in flexible structures. Cutting both the constraining layer and the viscoelastic layer, which leads to segmentation, increases the damping efficiency. However, this approach is not always effective. A parametric study was carried out using modal strain energy method to explore interaction between segmentation and design parameters, including geometry parameters and material properties. A finite element model capable of handling treatments with extremely thin viscoelastic layer was developed based on interlaminar continuous shear stress theories. Using the developed method, influence of placing cuts and change in design parameters on the shear strain field inside the viscoelastic layer was analyzed, since most design parameters act on the damping efficiency through their influence on the shear strain field. Furthermore, optimal cut arrangements were obtained by adopting a genetic algorithm. Subject to a weight limitation, symmetric and asymmetric configurations were compared. It was shown that symmetric configurations always presented higher damping. Segmentation was found to be suitable for treatments with relatively thin viscoelastic layer. Provided that optimal viscoelastic layer thickness was selected, placing cuts would only be applicable to treatments with low shear strain level inside the viscoelastic layer.

Load reduction of a monopile wind turbine tower using optimal tuned mass dampers

ABSTRACTWe investigate to apply tuned mass dampers (TMDs) (one in the fore–aft direction, one in the side–side direction) to suppress the vibration of a monopile wind turbine tower. Using the spectral element method, we derive a finite-dimensional state-space model Σd from an infinite-dimensional model Σ of a monopile wind turbine tower stabilised by a TMD located in the nacelle. Σ and Σd can be used to represent the dynamics of the tower and TMD in either the fore–aft direction or the side–side direction. The wind turbine tower subsystem of Σ is modelled as a non-uniform SCOLE (NASA Spacecraft Control Laboratory Experiment) system consisting of an Euler–Bernoulli beam equation describing the dynamics of the flexible tower and the Newton–Euler rigid body equations describing the dynamics of the heavy rotor-nacelle assembly (RNA) by neglecting any coupling with blade motions. Σd can be used for fast and accurate simulation for the dynamics of the wind turbine tower as well as for optimal TMD designs. We show that Σd agrees very well with the FAST (fatigue, aerodynamics, structures and turbulence) simulation of the NREL 5-MW wind turbine model. We optimise the parameters of the TMD by minimising the frequency-limited -norm of the transfer function matrix of Σd which has input of force and torque acting on the RNA, and output of tower-top displacement. The performances of the optimal TMDs in the fore–aft and side–side directions are tested through FAST simulations, which achieve substantial fatigue load reductions. This research also demonstrates how to optimally tune TMDs to reduce vibrations of flexible structures described by partial differential equations.

Asymptotic Periodicity for Flexible Structural Systems and Applications

We study the existence of pseudo S$S$-asymptotically ?$\omega$-periodic mild solutions for an abstract version of the damped wave equation u?+?u?=βΔu+?Δu?+f$u''+\alpha u'''=\beta\Delta u +\gamma\Delta u'+f$ which model the vibrations of flexible structures possessing internal material damping and external force f$f$. We show concrete applications of our methods to flexible structures, heat conduction, fractional equations and viscoelasticity.

Dependent modal space control: Experimental test rig

This article presents the experimental validation of a new control technique for reducing vibration in flexible structures: Dependent modal space control. While the classic independent modal space control allows only the frequency and the damping of the controlled modes to be changed, dependent modal space control can also impose the controlled mode shapes. Depending on the kind and number of sensors and actuators available for control, the mode shape can be imposed in both a direct and an indirect way. Owing to the need for modal sensors and actuators for direct mode shape imposition, the second methodology is often preferred in many engineering applications. In the indirect method, the optimal closed loop mode shapes set is computed with an optimization algorithm in order to minimize an Input-Output Performance Index. The worsening spillover effects due to errors in the estimates of the system state variables are considered when computing the gain matrix and play an important role in the entire control logic. Experimental validation on a cantilevered beam shows the effectiveness of the dependent modal space control and a good match between the numerical and the experimental results.

Reduction of spillover effects on independent modal space control through optimal placement of sensors and actuators

The independent modal space control (IMSC) technique can be profitably used to suppress vibration in flexible structures by increasing the damping of the modes involved, without changing the corresponding natural frequencies and modal shapes. Reducing vibration means reducing the associated noise and enhancing the performance of the system and its fatigue durability. The main limitations of this approach are related to spillover effects due to the dynamics of unmodeled modes. This work investigates analytically how spillover effects in IMSC are closely related to the number and the position of thesensors and actuators involved, in addition to the reduced model adopted to synthesize the control itself. The performance of the IMSC technique is optimized by means of genetic algorithms to reduce spillover effects, finding the best placements for sensors and actuators. Theoretical aspects are supported by numerical simulations.

Lp‐boundedness and topological structure of solutions for flexible structural systems

This work deals with Lp‐boundedness of mild solutions for an abstract version of the damped wave equation u′′+αu′′′=βΔu + γΔu′+f that models the vibrations of flexible structures possessing internal material damping and external force f. We prove that the set consisting of mild solutions for this problem is compact and connected in the space of continuous functions. This property is known in the literature as the Kneser's property. Copyright © 2015 John Wiley & Sons, Ltd.

G1000203 動的量子化器による柔軟構造物用回転型アクティブ除振装置AWDの低コスト高性能化

This study develops a rotary active vibration control device (AWD) using a flywheel to control vibrations in flexible structures. The AWD achieves lightweight and higher inertia by the flywheel and can be mounted on the flexible structure easily. In addition, the AWD can construct sky-hook control easily because it can measure the absolute angular velocity of the flexible structure by the gyro sensor. Therefore, The AWD use Sky-hook With Adaptive Disturbance Cancellation (SWADC) control which is combined control system of sky-hook control and adaptive disturbance cancellation control. This paper investigates a method for cost-performance improvement of the AWD by using the dynamic quantizer for practical use. In general, performance deteriorates according to using low cost instruments. So this study uses the dynamic quantizer to prevent performance deteriorates of the AWD. In addition, the parameters of the dynamic quantizer is optimized by Genetic Algorithm (GA). Cost-performance improvement of the AWD is shown by simulation.

Wake oscillator model for assessment of vortex-induced vibration of flexible structures under wind action

The wake oscillator model is considered to be the most proper semi-empirical model for qualitatively or even quantitively assessing the vortex-induced vibration of a structure in the design stage. However, the complexities in parameter determination limit its usage in real engineering fields. Moreover, this kind of model is traditionally used to describe the experimental phenomena of two-dimensional cross-section models, the gaps between the results of two-dimensional cross-section model tests and the prototype responses of the three-dimensional real structures should be filled up. In this paper, a detailed study of the wake oscillator model is firstly presented, which demonstrates the influences of model parameters on the VIV features described by the wake oscillator model. Then, a new method for conveniently identifying the model parameters in the wake oscillator model is proposed. Besides, a new procedure, based on the wake oscillator model, for interpreting the wind tunnel test results into real structures is also proposed. The results are validated by wind tunnel tests and compared with field measurements.

Discrete-time dynamic output feedback input shaping control of vibration in uncertain time-delay flexible structures

This paper proposes an observer-based discrete-time neuro-sliding mode control (NSMC) scheme combined with input shaping control for uncertain time-delay flexible structures. Only partial information of system states is known. It is shown that the proposed scheme not only guarantees closed-loop system stability, but also it effectively suppresses residual vibration and yields good robustness in the presence of state delays, input delays, parameter uncertainties, external disturbances and inaccurate impulse application instants simultaneously. The knowledge of upper bound of uncertainties is not required. Furthermore, it is shown that increasing the robustness to parameter uncertainties does not lengthen the duration of the impulse sequence. Simulation results demonstrate the efficacy of the proposed control scheme.

Linear time‐varying control of the vibrations of flexible structures

Recent results on pole placement for linear time-varying (LTV) systems are exploited here for the control of flexible structures. The infinite-dimensional system is approached as usual by a restricted number of modes of interest, according to the frequency range in which the system is exploited. The difference with the previous approaches (e.g. gain scheduling) is that only one finite dimension linear model is used and its parameters (frequency and damping of the modes) are varying according to the operating conditions. The control model is thus LTV and a regulator is analytically synthesised to ensure closed-loop stability and performances. This regulator is also LTV and thus automatically (without any special switching action) tracks the operating conditions of the system. The case of a flexible beam is studied in simulation as well as in the laboratory experimentation. Hence, a suitable application of the proposed LTV synthesis is done to find a compromise between the complexity of interpolation and its efficiency. Furthermore, the bad dissipation factor of flexible systems leads them to be good candidates to proof the efficiency of the proposed gain scheduling strategy. This work validates on a real system the LTV pole placement approach and opens the way to a new gain scheduling strategy for the control of LTV, non-linear or infinite-dimensional systems.

Control of the Thermally Induced Vibration of Space Structures by Using Heaters

Thermally induced vibration of large and flexible space structures is possible. To suppress this kind of adverse response, this paper proposes an active vibration control method by using heaters bonded on the structural surface. In this way, the control forces are generated within the structure by the temperature gradients caused by controlling the heat fluxes of these heaters. To obtain the magnitude of the control heat flux of each heater, the state–space form of the thermal–dynamic formulation is derived, and the linear quadratic regulator optimal control method is adopted. In addition, the Fourier finite element is used to facilitate the thermal–dynamic calculation of space structures subject to thermal radiation. And the placement of these heaters is optimized by an efficient heuristic method with local search operations to minimize the control energy. Numerical examples are presented to demonstrate the capability and efficiency of the proposed method to suppress the vibration induced by solar heating.