Vibration Control Performance Research Articles

Assessing Vibration Control Performance of Optimized Tuned Mass Damper Inerter (TMDI) Configurations

Assessing Vibration Control Performance of Optimized Tuned Mass Damper Inerter (TMDI) Configurations

Application of Perturbation Method to Analytical H2 Optimization for a Damped Structure with Inerter-Based Control

Inherent damping exists in all real engineering systems and it affects the dynamic behavior of the structures in vibration reduction. However, it is generally neglected in existing analytical H2 optimization for inerter-based vibration control. Hence, an analytical H2 optimization of a tuned inerter damper (TID) based on the perturbation method is presented to control the vibration of a damped structure subjected to stochastic acceleration ground excitations. Since relative displacement and velocity are crucial to structural damage and absolute acceleration is related to vibration comfort, three sets of closed-form solutions for the optimal stiffness ratio and damping ratio are derived to suppress the corresponding responses. The expressions of these optimal parameters are functions of the inherent damping and inerter-mass ratio. The accuracy of these analytical solutions is demonstrated by comparison with the results provided by the numerical optimization procedure. The relevant parameters affecting the vibration control performance and the robustness of the TID in a damped structure are analyzed in frequency domain. Finally, time–history response and energy dissipation of TID are also explored by numerical examples under real and artificial seismic waves. The results highlight that more than 10% reduction ratio of the mean square value can be further achieved for a structure with a low inherent damping ratio ([Formula: see text]) if the present multi-order perturbation solutions are used for optimization, instead of the existing method which neglects the inherent damping. This superiority of the present perturbation method will become more prominent with the increase of the inherent damping ratio. Therefore, the present perturbation method has a great significance for designing a TID to achieve the best control performance.

Wind and Wave-Induced Vibration Reduction Control for Floating Offshore Wind Turbine Using Delayed Signals

Active vibration control is a critical issue of the wind turbine in the field of marine energy. First, based on a three-degree-of-freedom wind turbine, a state space model subject to wind and wave loads is obtained. Then, a delayed state feedback control scheme is illustrated to reduce the vibration of platform pitch angle and tower top foreaft displacement, where the control channel includes time-delay state signals. The designed controller’s existence conditions are investigated. The simulation results show that the delayed feedback H∞ controller can significantly suppress wind- and wave-induced vibration of the wind turbine. Furthermore, it presents potential advantages over the delay-free feedback H∞ controller and the classic linear quadratic regulator in two aspects: vibration control performance and control cost.

Robustness analysis for the vibration control performance of energy-harvesting tuned mass damper with uncertainties

Energy-harvesting vibration control strategy has been proposed and applied in different applications, including but not limited to automotive, mechanical, and civil engineering. However, when facing uncertainties from both internal and external environments, the robustness of its performance has rarely been evaluated. The energy-harvesting tuned mass damper (EHTMD) is a representative vibration control device integrated with the energy-harvesting function. This study investigates the robustness of an EHTMD installed on a structure with multi-uncertainties. First, the EHTMD modeling, the interval model, and the robustness evaluation framework are introduced. Uncertainties are considered for all parameters of an EHTMD, including the mechanical units, electromagnetic damper, and energy harvesting circuit. Subsequently, a series of dynamic simulations are performed on a damped benchmark single-degree-of-freedom frame with an EHTMD. The lower- and upper-bound structural vibration and generated power are estimated under free-vibration, harmonic-excitation, and random-excitation scenarios. The EHTMD performance robustness is evaluated through the interval response by incorporating the first-passage theory. The key factors in EHTMD that influence its robustness are identified. Results indicate promising robustness when using the energy-harvesting vibration control strategy to replace the conventional dampers, addressing one of the often-questioned issues of the energy-harvesting vibration control strategy.

Comprehensive design strategy of the NSD–TMD controlled system with closed-form frequency-amplitude solutions

A negative stiffness device (NSD) utilizing pre-compressed helical springs has been integrated with diverse vibration control techniques. Recently, the incorporation of NSD has been proposed to enhance the efficacy of a tuned mass damper (TMD) controlled system. This study introduces two design strategies for the NSD–TMD system, which functions either as a TMD with an adjustable operating bandwidth or as a pure non-linear energy sink. First, the non-linear force of NSD was expressed in a Taylor series approximation form incorporating a negative linear stiffness and a positive cubic stiffness term. Second, the equations of motion were formulated, and closed-form solutions were derived using the complexification–averaging method. The accuracy of the Taylor series approximation was substantiated within a specified range through a comparison of force–displacement curves. Third, the accuracy of the dynamic closed-form solutions was affirmed by comparing the amplitude–frequency curves with the numerical simulations. For a case study, an actual timber pedestrian bridge with decaying natural frequency was selected, and the two design strategies were examined individually. The vibration control performance of the TMD and NSD–TMD was also comparatively analyzed. The assessment focused on the peak force transmissibility value and the effective operating frequency bandwidth. Results highlighted a notable enhancement in operational performance, particularly for primary structures exhibiting diminishing modal frequencies. In a TMD-controlled system, the efficacy of vibration control deteriorates and may even amplify the dynamic response when a modal frequency shift occurs in the primary structure. Conversely, both design strategies of NSD–TMD can achieve lower transmissibility and broaden the operating bandwidth.

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.

Investigation on parametric excitation vibration and piezoelectric active control of axially moving viscoelastic beams

The nonlinear dynamics equation governing the behavior of axially moving viscoelastic beams is established in this paper, based on Hamilton’s principles. The Galerkin method is employed to discretize the equation for numerical analysis. Nonlinear parametric vibration control for axially moving viscoelastic beams is explored using piezoelectric laminated actuators based on LQR optimal linear control and SMC sliding mode control strategies. The stability of the moving beam is examined in respect of moving speed and active control. The influence of actuator position and control schemes on vibration control performance for the moving beam is also examined. In respect to linear and nonlinear equations, two control strategies of LQR are given to illustrate the control performances. The sliding mode control (SMC) is also given to reduce the vibration of the moving viscoelastic beam and exhibit the control performance and its robustness.

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.

Analytical optimization of inerter-based dynamic vibration absorbers with negative stiffness (INDVAs) using a reduced 2-degree-of-freedom (2DOF) model

The incorporation of an inerter, with its mass amplification capability, along with a negative stiffness spring characterized by high static-low dynamic stiffness, can significantly enhance the vibration control performance of traditional tuned mass dampers (TMDs). The previous analytical solution for the optimal parameters of inerter-based dynamic vibration absorbers with negative stiffness (INDVAs) is a generalized single-degree-of-freedom (GSDOF) model with INDVAs attached. When utilizing INDVAs for controlling wind-induced responses in high-rise buildings, the accuracy of the GSDOF model is compromised. Therefore, a multi-degree of freedom (MDOF) model is initially reduced to a simplified 2-degree of freedom (2DOF) model using a clustering algorithm in this study. The H-∞ optimization method is then employed to derive simplified analytical solutions for the optimal parameters of the three types of INDVAs. The robustness of the parameters and the control effect of these optimal INDVAs are subsequently compared with those of numerical solutions generated through a multiobjective genetic algorithm and with those of analytical solutions based on the GSDOF model. The results demonstrate that for the same type of INDVA, compared with the multiobjective genetic algorithm, the optimal INDVA calculated by the 2DOF model can achieve the same control effect on the structural wind-induced response, while the time cost is lower. In addition, the optimal INDVA obtained by the 2DOF model has a superior control effect on the wind-induced displacement and acceleration response compared to those of the GSDOF model, especially when the INDVA has a substantial inertance ratio and spans multiple floors.

A3-DOF frog-inspired quasi-zero stiffness isolator and its vibration control performance

To pursue a nonlinear isolator with simpler structure, better load adaptability, and wider quasi-zero stiffness (QZS) region, a 3-DOF bionic vibration isolation device is proposed and analyzed inspired by the superior landing performance of the frog's leg structure. The mechanism's dynamical equation is established using Lagrange's principle. The dynamic model is validated using ADAMS simulation. The effects of spring stiffness and rod length on static mechanical characteristics are analyzed. The vibration attenuation performance of the structure is analyzed under independent three-directional excitation and three-directional coupled excitation. Compared with the typical X-shaped QZS isolator and the traditional QZS isolator, the designed structure's advantages is demonstrated. By tuning the parameters and building a control route based on variable-stiffness dielectric elastomer, optimization of the device's vibration isolation performance under coupled excitation was accomplished.

Seismic and vibration control of segmented isolation layer in underground structure-diaphragm wall system

In this paper, a seismic and vibration reduction measure of subway station is developed by setting a segmented isolation layer between the sidewall of structure and the diaphragm wall. The segmented isolation layer consists of a rigid layer and a flexible layer. The rigid layer is installed at the joint section between the structural sidewall and slab, and the flexible layer is installed at the remaining sections. A diaphragm wall-segmented isolation layer-subway station structure system is constructed. Seismic and vibration control performance of the diaphragm wall-segmented isolation layer-subway station structure system is evaluated by the detailed numerical analysis. Firstly, a three-dimensional nonlinear time-history analysis is carried out to study the seismic response of the station structure by considering the effect of different earthquake motions and stiffness of segmented isolation layer. Subsequently, the vibration response of site under training loading is also studied by considering the influence of different train velocities and stiffness of the segmented isolation layer. Numerical results demonstrate that the diaphragm wall-segmented isolation layer-subway station structure system can not only effectively reduce the lateral deformation of station structure, but also reduce the tensile damage of the roof slab. On the other hand, the developed reduction measure can also significantly reduce the vertical peak displacements of site under training loading.

Parameter optimization of vibration control system for adjacent building structures based on negative stiffness inerter damper

Building structures are subjected to strong earthquakes, which result in lateral collisions between them. Such collisions often cause severe structural damage and exacerbate the seismic hazard risk of building structures during earthquake events. This paper discusses the application of vibration control devices based on negative stiffness inerter damper in single-story adjacent building structures. The dynamic equations of the vibration control system containing different types of negative stiffness inerter damper under seismic excitation are established as a unified model. The H2 norm theory and Monte Carlo pattern search method are used to optimize the design parameters to improve the vibration control performance of the system, and the dynamic characteristics of the system are investigated. The results demonstrate that attaching negative stiffness inerter damper to adjacent building structures can effectively improve the overall seismic capacity reserve of the building and reduce the risk of collision of adjacent building structures; improve the robustness and stability of the system, and better reduce the displacement response of the building structure under seismic excitation. In addition, the potential of NSID-based vibration control devices to convert seismic energy into usable electricity has been investigated.

Shunted piezoelectric patch adaptive vibration absorber set to maximise electric power absorption: A comparison between parallel and series RL-shunts

This paper presents a comparative study on two types of shunted piezoelectric patch adaptive vibration absorbers, which can be bonded in batches on thin-walled structures to control the broad-band resonant response of low order flexural modes. The self-contained control units are formed by a thin piezoelectric patch connected either to a series or to a parallel resistive-inductive (RL) network. The two components of the shunt are adapted online in such a way as to maximise the time-averaged electric power absorbed by the shunt, which corresponds to minimising the time-averaged total flexural response of the hosting structure. The study considers a practical demonstrator formed by a thin rectangular plate with five piezoelectric patches connected to digital RL-shunts, which is excited in bending by a stationary white noise point force. The aim of the paper is to contrast the tuning and vibration control properties of the series and parallel RL shunts. More specifically, the online implementation of a recursive two-paths tuning strategy along R-constant and L-constant paths with an extremum seeking gradient search algorithm is analysed first for the two types of shunts. Then, the vibration control performance produced by the two types of shunts is investigated for the case where they are tuned to control the resonant response of the first flexural mode of the plate.

Sufficient active control of uncertain low-frequency space micro-vibrations near measurement limit of acceleration sensors

High-precision payloads such as ultra-stable optical clocks for next-generation space missions are greatly sensitive to the low-frequency micro-vibrations induced by various flexible appendages equipped on the spacecraft. The frequencies of such micro-vibrations are uncertain and near the measurement limit of acceleration sensors, leading to insufficient vibration control performance of classical feedback control. To solve this problem, a hybrid control algorithm which combines PI controller and the filter-x least-mean-square (FxLMS) algorithm is proposed in the paper. In particular, a frequency estimation algorithm is designed for the active vibration control system to provide the reference signal. In the new system, the rough estimation of disturbance frequency is given by the adaptive notch filter. Then, the frequency is refined by Kalman filter and provided into the autoregressive model, which fine-tunes the estimated frequency and offers the reference signal for the hybrid PI-FxLMS algorithm. Finally, the experimental prototype of active vibration control system is developed and the proposed control algorithm is adopted. The experimental results demonstrate the effectiveness of the frequency estimation algorithm and further validate that the proposed hybrid PI-FxLMS algorithm can effectively suppress the low-frequency micro-vibrations near the measurement limit of acceleration sensors and with uncertain frequency.

Testing, Modelling, and Performance Evaluation of a Rotary Eddy-Current Damper with Inherent Nonlinear Damping Characteristics for Structural Vibration Control

This paper investigates the inherent nonlinear damping characteristics of a rotary eddy-current damper (RECD) and evaluates its vibration control performance on a single-degree-of-freedom (SDOF) system subjected to harmonic and seismic excitations. First, a RECD prototype was manufactured to experimentally identify its intrinsic nonlinear eddy-current damping characteristics. A magic formula model is then proposed to characterize the relationship between the eddy-current damping force and the velocity of the RECD, and its applicability in depicting the nonlinear damping characteristics of the RECD is evaluated by comparing with the electromagnetic finite-element (FE) model and the commonly used Wouterse’s model. Moreover, by comparing the experimental and analytical frequency–domain responses of an SDOF structure equipped with a RECD, the applicability of the magic formula model in evaluating the structural vibration control performance of the RECD is further verified. Finally, the control performance of the RECD for an SDOF structure subjected to earthquake ground motions is numerically evaluated and compared. Results show that the eddy-current damping force of the RECD presents obvious nonlinear characteristics with increasing velocity, and the proposed magic formula model can adequately depict the nonlinear eddy-current damping characteristics of the RECD. Moreover, the RECD exhibits superior structural control performance under harmonic and seismic excitations.

Explicit Formulas for Optimum Parameters of Viscoelastic-type Tuned Mass Dampers

Tuned mass dampers (TMDs) are passive vibration control devices that are attached to a primary system to reduce the dynamic vibrations under exciting motion. The Voigt-type TMD, which is the most widely used one, is known as a standard model of dynamic vibration absorber (DVA). The purpose of this study is to improve the vibration control performance of passive control devices by using viscoelastic-type tuned mass dampers (V-TMDs). The study adopts the Zener model to represent the viscoelastic behavior of V-TMD. In this study, the fixed-point method is used to determine the optimum parameters of a V-TMD. The displacement amplification factor (DAF) of the coupled system is obtained in the frequency domain. The optimal parameters of the V-TMD system attached to an undamped single degree-of-freedom (sdof) main system are obtained by minimizing the DAF (symbolized with 𝛽) under the effect of base excitation. The optimum parameters, such as damping ratio (ξ) and stiffness ratio (𝜅) of the coupled system are derived, and explicit expressions corresponding to the optimum parameters are presented for engineering designs. Moreover, the change in DAF values for different mass ratios (µ) is also discussed. It is proven that V-TMD is very effective in reducing the amplitudes of vibration. The study also provides valuable insights for engineering practitioners who want to design and implement V-TMDs for vibration control applications because accurate expressions, which are simple and easy to use, are derived in order to obtain optimum parameters, and step-by-step procedures are explained.

Experimental study on vibration control performance of TMD-STF damper

A tuned mass damper (TMD) using shear thickening fluid (STF) as an energy dissipation medium is designed and manufactured. In addition, a TMD incorporating silicone oil (TMD-Si49) is fabricated to compare and analyze the vibration control performance of TMD-STF. Free vibration, forced vibration, and random excitation tests are conducted on a single degree of freedom (SDOF) structure model equipped with TMD-STF and TMD-Si49, respectively. The displacement and acceleration response of the SDOF model are recorded to analyze the vibration control performance of TMD-STF and TMD-Si49 under different load conditions. The results of the free vibration test show that TMD-STF affects the coupling damping ratio of the test model, exhibiting time-varying damping characteristics, but does not impact the coupling frequency ratio. In the forced vibration test, TMD-STF effectively expands the effective frequency range of vibration control performance by approximately 17.0% compared to TMD-Si49. The random excitation test demonstrates that TMD-STF exhibits significantly improved control of acceleration response rather than displacement control. The research findings on TMD-STF provide novel insights for vibration control in engineering structures.

Bandgap enhancement of a piezoelectric metamaterial beam shunted with circuits incorporating fractional and cubic nonlinearities

Nonlinear metamaterials have been widely studied for their potential to broaden the bandgap for vibration suppression. However, the bandgap widening effect induced by nonlinearity vanishes when the excitation amplitude is insufficient to trigger the nonlinear behavior. In order to broaden the applicable range of excitation amplitude for nonlinear metamaterials, a novel design of a piezoelectric metamaterial beam shunted with combined nonlinear circuits is presented in this work, which incorporates fractional and cubic nonlinearities in circuits to achieve bandgap enhancement under both low and high excitation amplitudes. Theoretical and numerical models are established for predicting the nonlinear dynamics behaviors of the piezoelectric metamaterial beam, and their computational results are in good agreement. The amplitude-dependent bandgap of the metamaterial beam induced by combined nonlinearity is analyzed through the effective bending stiffness of a unit cell and validated through the frequency response of a piezoelectric metamaterial beam. It is found that based on the complementary nature of fractional and cubic nonlinearities in the amplitude-dependent characteristics, combined nonlinearity of the circuits can effectively improve the bandgap width of the beam under both low and high excitation amplitudes. In addition, the effects of the two nonlinearities on the amplitude-dependent characteristics of the bandgap are studied, and the interplay between the two nonlinearities within the combination is analyzed. The results show that the amplitude-dependent characteristics of the combined nonlinear design can be precisely tuned by adjusting the nonlinear coefficients of the circuits. Overall, a piezoelectric metamaterial beam with both fractional and cubic nonlinearities in circuits possesses superior vibration control performance than those with single nonlinear counterparts in circuits.

A nonlinear analysis of a Duffing oscillator with a nonlinear electromagnetic vibration absorber–inerter for concurrent vibration mitigation and energy harvesting

Several investigators have taken advantage of electromagnetic shunt-tuned mass dampers to achieve concurrent vibration mitigation and energy harvesting. For nonlinear structures such as the Duffing oscillator, it has been shown that the novel nonlinear electromagnetic resonant shunt-tuned mass damper inerter (NERS-TMDI) can mitigate vibration and extract energy for a wider range of frequencies and forcing amplitudes when compared to competing technologies. However, nonlinear systems such as the NERS-TMDI are known to exhibit complex stability behavior, which can strongly influence their performance in simultaneous vibration control and energy harvesting. To address this problem, this paper conducts a global stability analysis of the novel NERS-TMDI using three approaches: the multi-parametric recursive continuationWe emphasize that these assume method, Floquet theory, and Lyapunov exponents. A comprehensive parametric analysis is also performed to evaluate the impact of key design parameters on the global stability of the system. The outcome indicates the existence of complex nonlinear behavior, such as detached resonance curves, and the transition of periodic stable solutions to chaotic solutions. Additionally, a parametric study demonstrates that the nonlinear stiffness has a minimal impact on the linear stability of the system but can significantly impact the nonlinear stability performance, while the transducer coefficient has an impact on the linear and nonlinear stability NERS-TMDI. Finally, the global sensitivity analysis is performed relative to system parameters to quantify the impact of uncertainty in system parameters on the dynamics. Overall, our findings show that simultaneous vibration control and energy harvesting come with a considerable instability trade-off that limits the range of operation of the NERS-TMDI.

Vibration Control of Car Body and Wheel Motions for In-Wheel Motor Vehicles Using Road Type Classification

In-wheel motor vehicles are gaining attention as a new type of electric vehicle due to their efficient power units located inside each wheel hub. However, they are more susceptible to wheel resonance due to the increase in unsprung mass caused by the weight of the motor. This can result in both decreased ride comfort and driving stability. To resolve this issue, in this study, we aim to apply an optimal switching controller with a semi-active actuator—a magnetorheological (MR) damper. For the implementation of the optimal switching controller, road type classification is also carried out. An acceleration sensor is used for the road type classification, and the control logics include a ride comfort controller (the linear quadratic regulator (LQR_Paved Road)) and a wheel motion controller (LQR_Off Road) for improved driving stability. For paved roads, the LQR_Paved Road control input is applied to the MR damper. However, if a road type prone to wheel resonance is detected, the control logic switches to the LQR_Off Road. During the transition, a weighted average of both the LQR_Paved Road and LQR_Off Road control input is applied to the actuator. Computer simulations are performed to evaluate the vibration control performance, including the ride comfort and driving stability on various road profiles.