Multimodal Vibration Suppression Research Articles

A semi-active shunted piezoelectric tuned-mass-damper for multi-modal vibration control of large flexible structures

A semi-active electromechanical Tuned Mass Damper (SATMD), which consists of a combined spring-piezoelectric device connected to an external resistive-inductive electric circuit is presented, aiming to provide robust multi-modal vibration suppression capabilities in large flexible structures. The combined spring-piezoelectric device provides the stiffness for the resonant mass, and also electromechanical energy conversion and coupling. A reduced-ordered mode superposition structural dynamics model coupled with the SATMD device and the RL shunt electric circuit is formulated, to simulate the response of the integrated structural system. The broadband vibration reduction capabilities of the proposed SATMD are numerically and experimentally evaluated and quantified on a down-scaled simplified airframe model. Very good correlation between numerical and measured results is obtained. The results illustrate that a SATMD configuration with an auxiliary mass equal to 1% of the structural mass and combined resistive-inductive impedance, yields substantial simultaneous vibration suppression over the range of 3 low-frequency structural modes, and can be easily retuned to accommodate in-flight changes in structural and loading parameters.

Low-Frequency Multimode Vibration Suppression of an Acoustic Black Hole Beam by Shunt Damping

Abstract The ideal acoustic black hole (ABH) can achieve wave gathering and zero reflection of elastic waves. In practice, ABHs have to be truncated, limiting their application in lower frequency range. Aiming at improving the ABH beam's vibration suppression ability at low frequencies, this study proposes a shunt damping-ABH composite beam by pasting shunt damping instead of ordinary damping on the ABH tip. The energy method is employed to solve the vibration equation of the ABH beam. The admissible function is the Mexican hat wavelet. The proposed method is verified by the finite element method. Compared with the uniform beam, the numerical results show the ABH beam has a noticeable attenuating effect in high-frequency range due to the ABH effect, but almost has no attenuating effect in the low-frequency range. Therefore, we introduce shunt damping to enhance the low-frequency vibration control. The shunt damping is composed of circuits connected to a piezoelectric patch. The effects of different circuits connected to the piezoelectric patch are discussed. The R–L shunt circuit and L–C parallel blocking circuit can simultaneously suppress the multimode vibration peak of the ABH beam at the low frequency successfully. Finally, a vibration experiment of ABH beam combined with shunt damping is implemented to verify the present method's feasibility and the shunt damping effect. The proposed shunt damping-ABH composite beam could improve the suppressing ability in both the low and high-frequency ranges.

Multimodal vibration suppression of nonlinear Euler–Bernoulli beam by multiple time-delayed vibration absorbers

Multimodal vibration suppression of nonlinear Euler–Bernoulli beam by multiple time-delayed vibration absorbers

Establishment of the equal-peak principle for a multiple-DOF nonlinear system with multiple time-delayed vibration absorbers

In this study, a generalized equal-peak principle is established to suppress the multimodal vibration of a multiple-degree-of-freedom (M-DOF) nonlinear system. Based on the proposed generalized principle, the design procedure of the multiple time-delayed vibration absorbers (TDVAs) is carried out. By four conditions in the proposed generalized principle, the objective of suppressing all the resonance peaks around multiple modes to the equal minimum values is realized. For the existence of nonlinearity, the necessary and sufficient conditions in the design procedure can guarantee that the two resonance peaks around each mode are simultaneously equal. Moreover, the two equal resonance peaks are suppressed to minimum values with the minimum peak condition. Two case studies verify the efficiency of the TDVAs designed by the generalized equal-peak principle for multimodal vibration suppression. Due to the multimodal vibration suppression capacity of the proposed TDVAs designed by the generalized equal-peak principle, significant broad frequency band vibration suppression effects are achieved. Thus, TDVAs and the proposed equal-peak principle have potential applications in the fields of high-DOF vibration systems, such as civil engineering, precision machining and aerospace.

Low-frequency multi-mode vibration suppression of a metastructure beam with two-stage high-static-low-dynamic stiffness oscillators

Metastructures with periodic local resonators are effective in attenuating waves in a special frequency range due to their band gap properties. A low-frequency multi-mode resonator based on a two-stage high-static-low-dynamic stiffness oscillator is proposed in this paper to create multiple low-frequency band gaps of flexural waves in a metastructure beam. The theoretical models of infinite and finite metastructure beams are established, respectively. The band structures obtained by the plane wave expansion method are thereafter verified by the mode superstition method. This demonstrates such metastructure features with multiple low-frequency band gaps. Multiple band gaps property is discussed, and a dynamic analysis of a simplified cell shows that locations of band gaps are determined by the natural frequencies of the resonator, which can be adjusted by configuring the physical parameters of the oscillators. The influence of mass ratio and damping on band gaps is numerically analysed, and the results show that mass ratio has an optimal value and damping can suppress the resonance effectively. Finally, a case study is performed, and the results show that the proposed metastructure has good performance in vibration suppression both around concerned multiple low-frequency modes and high-frequency range. The general design procedure of a metastructure beam is also summarized.

Multimodal suppression of vibration in smart flexible beam using piezoelectric electrode-based switching control

This paper describes an active vibration control system combining a piezoelectric electrode configured with a novel switching control system to achieve multimodal vibration suppression in smart flexible structures embedded with only a single piezoelectric actuator. The fact that high-frequency vibrations attenuate more rapidly than do low frequency vibrations motivated the development of a novel scheme in which the resonant excitation of coupled bending and lateral vibrations is applied to a cantilever beam. Switching times are determined using time-frequency analysis of modal responses. A smoothing function was applied to alleviate the effects of high-frequency oscillations during the switching control transition in order to facilitate the suppression of bending mode vibrations. Algorithms for proportional derivative (PD) control and positive position feedback (PPF) control can be tailored specifically for the target vibration modes and implemented in a variety of switching control schemes. The vibration responses induced by various switching control schemes was analyzed in order to derive appropriate control parameters for the development of an efficient switching control system aimed at suppressing multimodal vibrations. Experiment results demonstrate the effectiveness of the proposed piezoelectric electrode configuration in suppressing lateral mode vibrations. The proposed switching control system also proved highly satisfactory in suppressing vibrations in a system subject to simultaneous bending mode excitation.

Vibration Suppression of a Cantilever Plate Using Magnetically Multimode Tuned Mass Dampers

For a few decades, various methods of suppressing structural vibration have been proposed. The present study proposes and exploits an effective method of suppressing the vibration of cantilever plates similar to the solar panels of a satellite. Magnetically tuned mass dampers (mTMDs) are a tuned mass damper (TMD) with eddy current damping (ECD). We introduce the mTMD concept for the multimode vibration suppression of the cantilever plate. The design parameters of the mTMD are determined based on the parametric study of the theoretical four-degree-of-freedom model, which was derived for a cantilever plate with TMDs. Two TMDs are optimized for the first bending mode and first torsion mode of the plate, and they are verified analytically and experimentally. To increase the damping performance of the TMDs, ECD is introduced. Its damping ratios are estimated analytically and verified experimentally.

Active vibration control of a slewing spacecraft’s panel using H∞ control

Application of H∞ control for multimodal vibration suppression of a slewing spacecraft using piezoelectric actuators is presented in this paper. For treating vibration suppression independent of attitude control law while taking into account relative modal responses; a method for modeling effect of attitude maneuver excitations as modal disturbances is proposed. Commercial finite element software ANSYS is used for obtaining system model. Modifications of system model and selection of weights required for control synthesis are explained in detail. The method is applied for suppressing vibration of first two modes of a flexible spacecraft. Results showed effectiveness of the proposed method.

A numerical and experimental implementation and integration of Steiglitz–McBride algorithm with the frequency domain IIR filtering technique for active vibration control

In adaptive control applications for noise and vibration, finite ımpulse response (FIR) or ınfinite ımpulse response (IIR) filter structures are used for online adaptation of the controller parameters. IIR filters offer the advantage of representing dynamics of the controller with smaller number of filter parameters than with FIR filters. However, the possibility of instability and convergence to suboptimal solutions are the main drawbacks of such controllers. An IIR filtering-based Steiglitz–McBride (SM) algorithm offers nearly-optimal solutions. However, real-time implementation of the SM algorithm has never been explored and application of the algorithm is limited to numerical studies for active vibration control. Furthermore, the prefiltering procedure of the SM increases the computational complexity of the algorithm in comparison to other IIR filtering-based algorithms. Based on the lack of studies about the SM in the literature, an SM time-domain algorithm for AVC was implemented both numerically and experimentally in this study. A methodology that integrates frequency domain IIR filtering techniques with the classic SM time-domain algorithm is proposed to decrease the computational complexity. Results of the proposed approach are compared with the classical SM algorithm. Both SM and the proposed approach offer multimodal vibration suppression and it is possible to predict the performance of the controller via simulations. The proposed hybrid approach ensures similar vibration suppression performance compared to the classical SM and offers computational advantage as the number of control filter parameters increases.

Multi-mode vibration suppression of clamped plates based on piezoelectric networks

Multi-mode vibration suppression of clamped plates based on piezoelectric networks

The three-hinged arch as an example of piezomechanic passive controlled structure

Although piezoelectric transducers are employed in a variety of fields, their application for vibration control of civil or industrial structures has not yet been fully developed, at the best of authors’ knowledge. Thanks to a new generation of ever more performing piezoceramic materials and to the recent development of scientific proposals based on a very simple technology, this paper presents a step forward to engineering applications for the control of structural systems. A three-hinged arch controlled by piezoelectric stack actuators and passive RL electrical circuits is chosen as a simple structural model that may represent the starting point for a generalization to the most common typologies of civil and industrial engineering structures. Based on the concept of electromechanical analogy, the evolution equations are obtained through a consistent Lagrangian approach. A multimodal vibration suppression is guaranteed by the spectral analogy between the mechanical and electrical components. Preliminary applications related to free oscillations, with one or more actuators on each member, seem to lead to excellent performance in terms of multimodal damping and dissipated energy.

Semi-active vibration control of an aircraft panel using synchronized switch damping method

Withthe rapid development of the aerospace industry, the control of aircraft structural vibration becomes increasingly important. Semi-active vibration control method based on synchronized switch damping have been attracted more attention due to its robustness compared with passive approaches and simplicity compared with active approaches. In this paper, three SSD semi-active control methods combined with a modal observer were applied to multimodal vibration suppression of an aircraft panel with stiffeners, and their effectiveness was verified by experimental results. A state observer was built based on the experimentally identified state-space model of the panel. Modal displacement of the panel was identified on line using the state observer and used in switch control of different piezoelectric actuators. Since the vibration characteristics of the panel with stiffeners was very complicated and its natural frequencies were distributed densely, use of the identified modal displacement as the reference signal for voltage switching in SSDI, SSDV and SSDNC improved the control effect for some specific modes and simplified the system. Good performances of vibration suppression were achieved in both single-mode control and multimodal control.

Adaptive multimodal vibration suppression using fuzzy-based control with limited structural data

We propose a novel fuzzy-based method of adaptive multimodal vibration suppression with limited structural data. The adaptive control consists of fuzzy inference and a semi-active switching approach. We demonstrate it to be applicable to multimodal vibration suppression for vibrating structures, where a single piezoelectric actuator suppresses two modal vibrations simultaneously. Our fuzzy-based semi-active control requires only the structural information of natural frequencies for real-time adaptive feedback, whereas common adaptive controls require highly precise structural models or complete equations of motion. We conduct experiments in semi-active vibration suppression using the proposed fuzzy-based control, and compare the suppression performance of our fuzzy-based approach with conventional controls. The experiments indicate that the proposed fuzzy-based control demonstrates good adaptability when experiencing sudden changes in disturbance excitation, and also demonstrates high suppression performance. The fuzzy-based control can adapt to a wide range of disturbance conditions, both within and outside the range of vibration excitations assumed when the controller is designed.

Innovative Digital Self-Powered Autonomous System for Multimodal Vibration Suppression

A novel invention, a digital self-powered autonomous system, is proposed to achieve sophisticated vibration suppression dealing with multimodal vibrations. This vibration suppressor can be used ubiquitously at any site because it does not require an external power supply or a central control authority. The digital approach enables the system to be programmed, and thus, it affords some versatility with regard to control schemes. The proposed system is a vast improvement over conventional analog-autonomous systems whose fine-tuning is very difficult. The digital unit can be implemented in multi-input/multi-output systems to suppress complicated structural vibrations, such as multimodal vibrations. This paper provides an analytical discussion on the energy-harvesting effect on suppression performance in terms of the power balance andflow.Experiments demonstrate that the vibrationmagnitude reduces dramatically by as much as 79.7% under force excitation, although the self-powered control unit is used.

Comparison of Analog and Digital Self-Powered Systems in Multimodal Vibration Suppression

This paper compares our analog and digital self-powered systems for vibration suppression, and shows experimental results of multimodal vibration suppression for both self-powered systems. The experimental results are evaluated in light of the damping performance and adaptability under various vibrational conditions. We demonstrate various examples of our innovative vibration suppression method, called “digital self-powered.” Proper status switching of an electric circuit made up of an inductor and a selective switch connected to a piezoelectric transducer attenuates the vibrations. The control logic calculation and the switching events are performed with a digital microprocessor that is driven by the electrical energy converted from the mechanical vibration energy. Therefore, this vibration suppression system runs without any external power supply. The self-powering feature makes this suppression method useful in various applications. To realize an ideal vibration suppression system that is both self-powered and effective in suppressing multimode vibration, sophisticated control logic is implemented in the digital microprocessor. We demonstrate that our digital self-powered system can reduce the vibrational displacements of a randomly excited multimodal structure, by as much as 35.5%.

Active multimodal vibration suppression of a flexible structure with piezoceramic sensor and actuator by using loop shaping

This paper represents active multimodal vibration control of a flexible beam structure with piezoceramic (PZT) actuators and sensors using the loop shaping method. With surface-bonded PZT patch actuators and sensors, the flexible beam has both sensing and actuating capacities. Due to its flat auto spectrum in the specified frequency range, the Schroeder wave is used as an excitation signal for the non-parametric identification of the flexible beam structure. The identified open loop model is then used for the closed loop design by using the loop shaping method based on the extended sensitivity charts. A loop shaping compensator is designed to achieve multimodal vibration suppression. Numerical results showed a reduction of 8 decibels for the first mode and 12–14 decibels for the second and third modes. Experimental results closely match the simulation results. Furthermore, the results of loop shaping method are compared with those of the methods of linear quadratic regulator and pole-placement control, which are designed based on state space models via the parametric identification of the flexible beam. Comparisons show that the loop shaping method is easier to design since a parametric identification is not required and requires less control effort while maintaining the effectiveness in vibration suppression.

128 圧電素子と共振回路を用いたスマート構造の受動/準能動制振

In this study, a semi-active vibration suppression system comprising piezoelectric elements is developed for flexible structures. The vibration suppression system comprises a cantilevered beam with bimorph piezoelectric ceramic tiles shunted by a RL electrical circuit with a switching part. This study shows that the resonant shunt circuit functions as a type of a dynamic damper for mechanical systems and the proposed switching control, inspired by a sliding-mode control law, is more effective than the passive damping system especially for the multi-mode vibration suppression.

Multimodal Vibration Control of a Flexible Structure using Piezoceramic Sensor and Actuator

This study presents results of multimodal vibration suppression of a smart flexible cantilever beam with piezoceramic actuator and sensor by using a pole placement controller. Piezoceramic PZT (lead zirconate titanate) patches are surface-bonded on the beam and function as actuator and sensor. Nonparametric identification for the dynamics of the first three modes is carried out. From the nonparametric model, a parametric model is identified to assist the control system design. The identified model is used for state estimation and development of control algorithm. A linear pole placement controller is designed and simulated using the identified model. Experimental results demonstrate the effectiveness of observer-based multimodal active vibration control of the structure using piezoceramic smart materials.

Multi-mode vibration reduction of a CD-ROM drive base using a piezoelectric shunt circuit

This paper presents a new design methodology for the piezoelectric shunt damping system and applies to the multimode vibration suppression of a CD-ROM drive base. Admittance is introduced to predict the performance of the piezoelectric shunt damping. Numerical admittance obtained by commercial finite element code, ANSYS, is compared with experimentally measured one and the effectiveness of the model is verified. Multimode piezoelectric shunt damping is experimentally realized based on the target mode and frequencies obtained by the admittance analysis. The vibration of the CD-ROM drive base is effectively reduced by activating the piezoelectric shunt circuits. The experimental results presented in this work prove that admittance of the piezoelectric structure is capable of predicting the performance of piezoelectric shunt damping.

Spacecraft Vibration Suppression Using Variable Structure Output Feedback Control and Smart Materials

A hybrid control scheme for vibration reduction of flexible spacecraft during rotational maneuvers is investigated by using variable structure output feedback control (VSOFC) for attitude control and smart materials for active vibration suppression. The proposed control design process is twofold: design of the attitude controller using VSOFC theory acting on the hub and design of an independent flexible vibration controller acting on the flexible part using piezoceramics as sensors and actuators to actively suppress certain flexible modes. The attitude controller, using only the attitude and angular rate measurement, consists of a linear feedback term and a discontinuous feedback term, which are designed so that the sliding surface exists and is globally reachable. With the presence of this attitude controller, an additional independent flexible control system acting on the flexible parts is designed for further vibration suppression. Using the piezoelectric materials as actuator/sensor, both single-mode vibration suppression and multimode vibration suppression are studied and compared for the different active vibration control algorithms, constant-gain negative velocity feedback (CGNVF) control, positive position feedback (PPF) control, and linear-quadratic Gaussian (LQG) control. Numerical simulations demonstrate that the proposed approach can significantly reduce the vibration of the flexible appendages and further greatly improve the precision during and after the maneuver operations.