Vibration Control Of Flexible Structures Research Articles

A Ball-Track-NES for the vibration control of flexible structures under seismic excitation

Track Nonlinear Energy Sinks (T-NESs) are gravity-based dynamic absorbers oscillating over properly designed curved tracks. Due to the resulting nonlinear restoring forces, they exhibit effective control performance even when the natural frequencies of the host structure shift due to damage. Among the available configurations for gravity-based devices, ball absorbers present a cost-effective option characterized by space efficiency and minimal maintenance requirements. Nevertheless, a comprehensive literature survey reveals that, due to the greater mathematical modeling complexity, fewer works on ball absorbers are available than their translational counterparts. Moreover, all existing papers addressing ball absorbers focus on circular tracks; to the best of the author’s knowledge, not a single paper on Ball Track Nonlinear Energy Sinks (BT-NES) can be found. Hence, this work introduces an original approach dealing with the optimum track shape of BT-NESs installed in flexible structures under seismic excitations. A nonlinear 2D model is developed to capture the motion of a heavy ball on an arbitrarily shaped track installed on the top floor of generic multi-degree of freedom (MDOF) structures modeled through the Finite Element (FE) method. Instead of imposing a fixed shape curvature, a generic rational function obtained from the Padé expansion of the circle equation is integrated into the optimization. The scheme allows for exploring a diverse set of arbitrary curvatures to describe the BT-NES track shape. The application case featured a typical soft-story building subjected to earthquake loadings. The BT-NES exhibited effective control performance, reducing the building’s ISDR by almost 30%.

Vibration control of membrane structures by piezoelectric actuators considering piezoelectric nonlinearity under strong electric fields

Membrane structures, which are widely used in aerospace and civil engineering, are susceptible to large amplitude vibrations due to their low structural damping and high flexibility, leading to the degradation of their working performance. Strong electric fields are commonly needed for piezoelectric actuators to control larger amplitude vibration of membrane structures. However, the effect of piezoelectric nonlinearity due to strong electric fields on the control performance of membrane structures is still underexplored. Given the importance of piezoelectric nonlinearity due to strong electric fields, the present study aims to investigate the vibration control performance of piezoelectric actuators for membrane structures. First, based on the piezoelectric nonlinear constitutive equation, the actuation equation of the piezoelectric actuator is generated. Then, following D′Alembert's principle, a nonlinear dynamic control model of membrane structure containing actuation force is derived. Finally, active vibration control based on velocity feedback algorithms is realized. The results show that the predicted strain without considering the piezoelectric nonlinearity is 80 % smaller than the finite element structure at 500 V. Meanwhile, the errors of Root Mean Squared (RMS) control displacement without considering the piezoelectric nonlinearity are more than 24 % when vibration amplitudes achieve 10 % of the membrane thickness. The developed model provides theoretical implications for active vibration control of flexible structures with piezoelectric actuators in strong electric field environments.

Vibration control of thin shallow paraboloidal shells with light-activated shape memory polymers

With the applications of thin-walled paraboloidal shell structure in aviation, aerospace and communication systems, smart-structure based active vibration control becomes essential to improve the performance of thin-walled parabolic structures. Light-activated shape memory polymer (LaSMP) is a novel actuator material that exhibits dynamic Young's modulus and strain properties under ultraviolet (UV) light exposures, which can be used for non-contact vibration control. This study focuses on investigating the vibration control performance of a shallow parabolic thin shell, with simply supported boundary conditions, with laminated LaSMP patches. Based on the LaSMP strain model, the vibration control effect of LaSMP patch on the thin shell is discussed. A finite element model of the simply supported parabolic thin shell is developed to obtain the natural frequencies. The modal expansion method is employed to investigate the vibration control of the shallow parabolic thin shell laminated with LaSMPs, and independent modal responses are calculated. According to the different control mode, the effects of LaSMP actuators on vibration control of shallow paraboloid shell are studied in three cases with varying actuation position and coverage area of LaSMP actuators. The results indicate that LaSMP can control the vibration of the thin shell by reducing the vibration amplitude and the final vibration control effect is determined by the mode shape, the initial LaSMP strain, and the location and area covered by LaSMP actuators. By establishing the model between the LaSMP actuator force and the attenuations in modal amplitude, this study provides an analytical tool for the application of LaSMPs in vibration control of flexible structures.

Active Vibration Control of Flexible Structures with Super-Coiled Actuators

Flexible structures show low natural frequencies and light damping and often suffer from various dynamic loads, leading to low-frequency vibrations. Active vibration control is necessary for precision operation and long-term service of such structures, and a flexible actuator with a large actuation force and stroke is a key limitation. In this paper, super-coiled (SC) actuators, fabricated from fibers by twisting and inserting, were introduced to actively suppress the low-frequency vibration of flexible structures. Two SC actuators were symmetrically mounted on both surfaces of a cantilever beam to generate actuation forces. The force model of thermally driven SC actuators was developed, and a dynamic model of a cantilever beam with SC actuators was then proposed and validated via experimental actuation. Three types of control strategies, open loop, velocity negative feedback, and linear quadratic regulator (LQR), were adopted for vibration suppression. The results show that the proposed model fits quite well with the experimental data, and the maximum error between the experiment and the prediction is 3.90% among various driven currents. In velocity negative feedback control and LQR control, a 91.83% reduction of dynamic response is achieved, which validates the feasibility of using the actuator for low-frequency vibration control.

Closed-form solutions for the optimal design of lever-arm tuned mass damper inerter (LTMDI)

Tuned mass damper inerter (TMDI) has become a popular choice for vibration control in flexible structures, including long-span bridges, due to its superior performance compared to traditional tuned mass dampers (TMDs), such as improved control effect and smaller static displacement. However, the control effect of TMDI is heavily reliant on the spanning distance of inerter, which typically generates a significant internal additional moment due to the force imbalance, limiting the practical application of TMDI on flexible structures. For this reason, a novel lever-arm TMDI (LTMDI) is proposed in this study, to suppress the vibrations of long-span bridges. The non-dimensional governing equations of the bridge-LTMDI system are established in modal coordinates, and the closed-form solutions of the optimum frequency and damping ratios of LTMDI are derived based on the classical fixed-point theory. Parametric studies are conducted to investigate the influences of the fulcrum position, modal shape ratio, mass ratio, inertance ratio and asymmetric mode on the control effectiveness. Moreover, for comparison, the control effectiveness of LTMDI is further compared to those of the TMD and TMDI. Finally, a long-span bridge is selected as an example to demonstrate the effectiveness of LTMDI in reducing vortex-induced vibration (VIV). The results show that the LTMDI has superior control effect and space feasibility as compared to the TMD and TMDI in both frequency and time domains. The derived analytical formulas can accurately determine the optimal parameters, providing a simple yet efficient guideline for the application of LTMDI in flexible structures.

Traveling wave modes of flexible structures with distributed gyros

With the development of space structures, flexible structures are widely studied. To achieve attitude and vibration control of flexible structures, flywheels or control moment gyros can be introduced. However, the critical challenge in studying gyro flexible structures is establishing a systematic framework to manage its physical properties and calculate the control moment precisely. This study aims to construct a theoretical framework for a two-dimensional flexible structure with distributed gyros using classical methods and explore the contribution of the gyro moment on the dynamic mode shapes. Both eigenvalue and traveling wave mode shape analysis are applied to investigate the dynamical behaviors of the system. It is found that dynamic modes with nodal lines showing whirling phenomena have arisen instead of the traditional modes featured with static nodal lines triggered by the gyro moment, and the dynamic mode shapes can be displayed by the direction and frequency of the mode nodal lines motion. The discovery and research of gyro flexible structure traveling wave modes can provide a solid base for the design of large space structures, improve their stability, and avoid harmful vibrations.

A Double-Tuned Pendulum Mass Damper Employing a Pounding Damping Mechanism for Vibration Control of High-Rise Structures

Recently, enhancing conventional tuned mass dampers (TMDs) with a pounding damping mechanism is demonstrated to be an efficient way for vibration control of flexible structures. In this paper, a double-tuned pendulum mass damper employing a pounding damping mechanism (DTPMD-PD) is proposed. DTPMD-PD dissipates energy through the collision between distributed balls with a smaller mass and viscoelastic (VE) boundary, which can effectively reduce noise during operation compared to conventional impact dampers. Moreover, DTPMD-PD utilizes a double-tuning mechanism, and its control performance is significantly enhanced. The motion equations of a multiple degree of freedom (MDOF) structure equipped with DTPMD-PD are formulated. Based on the H∞ optimization criterion, a numerical optimization is performed to obtain the optimal design parameters of DTPMD-PD. Additionally, the pounding dissipation capacity and the parametric identification of the impact force model are investigated through free pounding experiments, and the control performance and robustness of DTPMD-PD are experimentally studied in the laboratory. The results show that the proposed numerical modeling method has considerable accuracy through experimental verifications. The restitution coefficient of the pounding layer has a significant influence on the performance of proposed DTPMD-PD. Optimized DTPMD-PD has better effectiveness than conventional TMDs under harmonic and seismic loads.

Non-fragile negative imaginary output feedback control for attitude stabilization of flexible spacecraft

The robust non-fragile attitude stabilization controller for flexible spacecraft with model parameters uncertainty is difficult to be synthesized with negative imaginary system which is widely applicable for the vibration control of flexible structures. To address this issue, this paper proposes a negative imaginary output feedback H∞ synthesis strategy, in which the model parameters uncertainty, controller gain perturbations, unknown inertia and actuator faults are considered simultaneously. This strategy can guarantee that the closed-loop attitude control system has asymptotical stability with H∞ performance and approximates to negative imaginary. The iterative algorithm under linear matrix inequality constraints gives the conditions for the existence of such controller. In addition, external disturbance and input saturation are also taken into account. Compared with the general non-fragile H∞ controller, the numerical simulations demonstrate the superiority of the proposed controller in attitude stabilization and vibration suppression of flexible spacecraft.

Application of Shape Memory Alloy Actuators to Vibration and Motion Control of Structural Systems: A Review

This paper comprehensively reviews effective control applications using shape memory alloy (SMA) actuators. Among many applications, this paper focuses on the vibration and stiffness control of flexible structures and shape control in the aerospace engineering field. In the vibration control of flexible structures, three different methods are introduced and discussed, including their merits and demerits. In addition, several control strategies, such as neuro-fuzzy controller, are investigated in terms of the implementation associated with the microchip. In the control process, the inherent hysteretic behavior of SMA is also reviewed as a feedforward loop or actuating force compensator. At the second part, applications on the morphing wing in the field of aerospace engineering are reviewed, and salient characteristics are discussed. In this review, the morphing wing, which is closely related to aircraft stability, is mainly investigated considering control logics and geometrical parameters. For easily understanding morphing control using SMA, a table which summarizes the main contribution of each research is presented. It is expected, since this review article provides numerous approaches for vibration and morphing control conducted over the last decade, it will be very helpful to the same research community to create novel ideas to achieve more advanced and effective results in vibration and morphing control using SMA actuators.

MR Tuned Liquid Colum Damper (MR-TLCD) for Seismic Vibration Control

Seismic vibration control of flexible structure is an important aspect which mostly involves reduction of structure displacement via application of passive damper or mass dampers. Present study focuses on the seismic vibration control of flexible structure against random earthquake, through modified (using MR fluid) tuned liquid column damper (TLCD), known as the MR-TLCD. To this end, stochastic structural response analysis has been performed and results (structure displacement ratio and liquid displacement) are compared with conventional the TLCD. To establish the superior control efficiency of MR-TLCD over conventional TLCD, parametric study has been performed considering wide range of damper, structure, and earthquake loading parameters. Study results shows the existence of optimal value of tuning ratio, head loss coefficient, and yield shear strength of MR fluid of MR-TLCD which minimizes the structure displacement ratio, i.e. maximizes the control efficiency. Another important observation is that, for similar level of control efficiency MR-TLCD requires much less value of mass ratio than that of TLCD, and also at same time it keeps the liquid displacement much less compared to the TLCD, for same value of mass ratio. This aspect increases the applicability of MR-TLCD over TLCD for vibration control of the flexible structure. In comparison to the TLCD, MR-TLCD provides 17 % to 43 % higher structural displacement control efficiency and reduces liquid displacement by 14 % to 45 %.

Wave vibration control of jacket platform by tuned liquid dampers

The studies on the applications of tuned mass and liquid column dampers for wave vibration control of offshore structures are notable. Though, the same is not the case for tuned liquid dampers (TLD). However, TLDs are a natural candidate for vibration control of flexible structure by utilizing the sloshing motion of fluid. The present study explores the effectiveness of TLD to mitigate the wave induced vibration effect of offshore jacket platform. In doing so, the jacket platform is modelled considering soil pile interaction effect and the TLD is represented by a spring mass system with due consideration to sloshing energy of water. The performance of TLD to control the wave induced vibration is studied for regular wave load, obtained by Stokes' fifth order theory and also for random wave load, generated by using the Pierson–Moskowitz wave spectrum. The dynamic response analyses are carried out without and with TLD for varying mass ratio, depth ratio and position of placement to study the effect of different parameters on the performance of TLD system. The results of numerical study in general show that TLD is potential for wave vibration mitigation of offshore jacket platform.

A study on integral resonant control focusing on the angular difference of a torsional vibration system with a rigid body mode

Integral resonant control (IRC) is a vibration control method that has attracted much attention recently. In IRC, the measured displacement is integrated and positively feedback to the input force. It has been shown that IRC is highly effective in vibration control of flexible structures, e.g., nano-positioners, despite its simple first-order controller. IRC cannot apply to the system including poles at the origin (i.e., including rigid body modes). This paper shows that IRC is applicable for a two DoF rotating system including a rigid body mode if we appropriately select the angular difference as the output variable of the system.

Optimization of Piezoelectric Sensor-Actuator for Plate Vibration Control Using Evolutionary Computation: Modeling, Simulation and Experimentation

The development of lightweight, stronger, and more flexible structures has received the utmost interest from many researchers. For this reason, piezoelectric materials, with their inherent electromechanical coupling, have been widely incorporated in the development of such structures to attenuate their vibrations. However, one of the main challenges is to find the optimal control and sensor-actuator placement. This paper presents an active vibration control for flexible structures, whereby a simply supported plate is taken as the benchmark model. A feedback controller with a collocated sensor-actuator configuration is used. Both disturbance and control signal acting on the plate is created by using piezoelectric (PZT) patches. The analytical model is derived based on the Euler-Bernoulli model. The Optimal location of the collocated sensor-actuator, as well as PID controller gains, are determined using Ant Colony Optimization (ACO) technique, then compared with the Genetic Algorithm (GA) and enumerative method (EM). Optimization in this paper is based on minimizing frequency average energy. The optimal performance value of piezoelectric patch sensor-actuator position and PID controller gains are verified experimentally. It was found that PID controller gains and collocated sensor-actuator location optimizations using ACO, GA and enumerative methods give similar results, which implies the effectiveness of ACO as an optimization technique. More than 20 % of attenuation achieved using the available hardware setup.

Tunable vibration control in a microelectromechanical resonator array by means of parametric coupling between mechanical and electrical modes

Vibration control in flexible structures at both the micro and macro scale has been a subject of considerable research interest over the last few decades. Various active, semi-active and passive vibration control schemes have been proposed for applications ranging from attenuating unwanted vibrations in structural components to controlling the ring down time in high-Q mechanical oscillators. Here, we present a simple, yet highly effective method to passively attenuate large amplitude resonant vibrations in an array of membrane-based microelectromechanical (MEM) resonators. By capacitively coupling the MEM array to a resonant electrical circuit tuned to half the mechanical resonance frequency, the vibrational energy in the array can be converted to electrical energy via parametric mode coupling between the mechanical and electrical resonator. Simulation and experimental studies indicate that both the rate of vibration attenuation and the degree of suppression can be effectively controlled by tuning electrical parameters such as the resistance and the initial voltage in the circuit. The extension of the control scheme to multi-mode vibrations by making use of multiple shunted electrical resonators will also be briefly discussed.

Perfect collocation using self-sensing electromagnetic actuator: Application to vibration control of flexible structures

Collocated control has the advantages of robustness and guaranteed stability. In collocated control, the sensor and actuator are placed close to each other. True collocation can be achieved using self-sensing in which the actuator can also be used as a sensor. In this article, we present a self-sensing electromagnetic actuator for vibration control of flexible structures. The back electromotive force (emf) generated in the coil is measured to evaluate the velocity of the structure (and hence, the displacement). The position measurements obtained from self-sensing are found to have good correlation with those obtained using an eddy current sensor. The efficacy of the proposed technique has been verified for the vibration control of a flexible cantilever beam. Self-sensing offers economical, simple and robust control architecture. It can be effectively used for applications where sensors and actuators cannot be collocated due to space and size limitations.

Inverse Shaper Based Active Vibration Control of Flexible Structures with a Collocated Sensor-Actuator Pair

We propose a new control design for active vibration suppression of flexible structures with a collocated sensor-actuator pair. The proposed controller is based on the inverse form of a well-known input zero vibration (ZV) shaper. The inverse ZV shaper is utilized with a serially interconnected all-pass filter. This way, the appropriate controller frequency response properties for vibration suppression of collocated flexible systems is achieved, when the controller is applied in the positive feedback path. We propose two different cost functions to optimize the parameters of the proposed controller for efficient vibration suppression. The performance of the controller is investigated in both frequency and time domains through the vibration control of a cantilever beam model with a collocated piezoelectric sensor-actuator pair. Furthermore, its performance is compared with a recently improved version of the positive position feedback controller, which is a state-of-the-art work. It is shown via the simulations that the proposed controller suppresses vibrations more efficiently.

Vibration Controllability of Sandwich Structures with Smart Materials of Electrorheological Fluids and Magnetorheological Materials: A Review

Vibration control is very significant issue in various engineering fields such as flexible structures, rotor systems, cable and bridge, and vehicle suspension. So far, three different recipes to suppress or control unwanted vibrations are used: passive, semi-active and active. As well known, the passive method has several limitations, such as the lack of real-time avoidance of the time-varying resonances. On the one hand, active vibration control method is very effective, but it is not attractive in terms of cost due to the use of several actuators and sensors. Therefore, recently semi-active vibration control method is popularly used in many practical environments. This article reviews vibration control of flexible structures using the semi-active method associated with smart materials of electrorheological fluids, magnetorheological fluids and magnetorheological elastomers. Modal characteristics of beam, shell and plate incorporating the core (or layer) of smart materials are deeply investigated and discussed in terms of field-dependent controllability. The field-dependent natural frequency and damping property of the sandwich beam type, plate type and shell type are experimentally identified. Subsequently, an appropriate control scheme based on the field-dependent modal properties is formulated to avoid the resonance behavior. In addition, several sandwich beams which are partially filled and fully filled with the magnetorheological fluid are investigated to understand the effectiveness of the modal property change. It has shown that both damping and stiffness properties of the sandwich structures can be effectively controlled by several ways: the change of the field intensity, the location of cores zones, the partial and full treatment and boundary conditions of the structures. In addition, it has identified that mode shapes of the sandwich plates featuring electrorheological core can be partially and fully controlled by applying the input field to an appropriate zone. Smart flexible structures associated with the field-responsive materials can be effectively used for vibration control due to its controllability of the stiffness and damping as well. However, to successfully implement in real environment, a more sophisticated analytical model considering the microscopic aspects of the particle motions needs to developed. Moreover, the field-dependent bucking problem and acoustic characteristics of smart structures subjected to external disturbances need to be explored.

Active rejection control for unknown harmonic disturbances of the transverse deflection of steel strips with control input, system output, sensor output, and disturbance input at different positions

In hot-dip galvanizing lines for steel strips, it is important to ensure a homogeneous zinc layer thickness. For this, vibrations of the strip at the gas wiping dies, where excess liquid zinc is blown off, must be suppressed. These vibrations typically exhibit a dominant sinusoidal shape and the excitation process, the frequency, the amplitude, and the phase are generally unknown.In modern plants, electromagnetic actuators are employed to enable a contactless vibration and shape control of the steel strip. Vibration control of flexible structures is well established in literature. However, in the considered application the disturbance (source of periodic excitation), the control input (force of electromagnetic actuators), the sensor output (strip displacement) and the desired system output (strip displacement at the gas wiping dies) are all located at different positions along the strip, which makes the overall control task quite challenging. In this paper, a control concept consisting of a linear quadratic regulator combined with a disturbance feedforward concept based on the theory of invariant manifolds and an Extended Kalman Filter is developed. The proposed control strategy is successfully tested on an experimental test rig for different scenarios.

Adaptive backstepping fuzzy sliding mode vibration control of flexible structure

An adaptive backstepping fuzzy sliding mode control is proposed to approximate the unknown system dynamics for a cantilever beam in this paper. The adaptive backstepping fuzzy sliding mode control is developed by combining the backstepping method with adaptive fuzzy strategy, where backstepping design approach is used to drive the trajectory tracking errors to converge to zero rapidly with global asymptotic stability and fuzzy logic system is designed to approximate the unknown nonlinear function in the adaptive backstepping fuzzy sliding mode control. The proposed backstepping controllers can ensure proper tracking of the reference trajectory, and impose a desired dynamic behavior, giving robustness and insensitivity to parameter variations. Numerical simulation for cantilever beam is investigated to verify the effectiveness of the proposed adaptive backstepping fuzzy sliding mode control scheme and demonstrate the satisfactory vibration suppression performance.

Experimental study of active vibration control for suppressing impact or moving disturbance-induced vibrations with polyvinylidene fluoride and fiber Bragg grating sensors

In this work, we experimentally study active vibration control of a smart cantilever beam and focus on influences of disturbances to the vibrations and corresponding control performances. The smart cantilever beam is subjected to impacts or moving mass loadings and robust positive position feedback (PPF) control is implemented to suppress the disturbance-induced vibrations. Specifically, we employ high sensitive polyvinylidene fluoride (PVDF) and fiber Bragg grating (FBG) sensors to capture dynamic characteristics of the disturbances. To allow repeatable and controllable experimental conditions for the prescribed disturbances, steel balls or a steel rod are used as the sources of the disturbances applied on the cantilever beam, on which a rail is cut out to guide the motions of the steel ball. Before designing PPF, finite element simulations are carried out to numerically compare sensing performances of the PVDF and FBG sensors. Resonant frequencies of the cantilever beam, including bending, torsional, and lateral modes, are also obtained beforehand numerically and experimentally for understanding behaviors of the disturbance-induced vibrations. By performing fast Fourier transform (FFT) and short-time Fourier transform (STFT) on the detected transient responses, characteristics of the disturbances and their suppressions with the PPF controllers are demonstrated and discussed. The proposed smart cantilever beam with the prescribed repeatable and controllable disturbances serves as a very suitable model in laboratory confirmations for active controller designs. In addition, our experimental work provides suggestions for sensor selections in active vibration control of flexible structures, especially in environments involving impact or moving disturbances.