Vibration Control Applications Research Articles

Metasurface-guided flexural waves and their manipulations

Elastic metasurfaces, being the subject of much attention and discussion, are first designed by phase modulation and now are also considered as a kind of structures with subwavelength size, e.g., layer structures in 3D space or strip structures in 2D space. However, most of elastic metasurfaces, especially those with phase gradient subunits, cannot support elastic wave propagations along them. In this research, we construct non-resonant metasurfaces with an array of slots in plates and explore a unique form of flexural waves propagating along and decaying exponentially with the increasing of the distance from the metasurfaces, which are called metasurface-guided flexural waves. A theoretical framework is established to solve the dispersion relations of these waves by coupling high-order diffraction and waveguide modes. On the basis of this framework, we design three metasurfaces for rainbow reflection, mode conversion and topological interface state, which are realized and verified by finite element simulations and experiments. Our work provides a new idea for the manipulation of flexural waves in plates, which may have wide potential applications in vibration control, structural health monitoring and acoustic device design.

A model for near-perfect transmission through lossy media with acoustic sources

Acoustic metamaterials exhibit effective material properties not found in naturally occurring media, and, as such, have received considerable attention for their potential applications in noise and vibration control, diagnostic imaging, and nonreciprocal transmission. Complementary acoustic metamaterials have been proposed as a means of compensating for the high impedance mismatches of aberrating layers that disrupt the acoustic field and hence distort acoustic images. More recently, a complementary acoustic metamaterial featuring active components was shown in principal to compensate for both the impedance mismatch and energy attenuation of lossy materials, but a physical realization of the concept has not yet been implemented. Here, we present results from a one-dimensional acoustic model showing how a plane wave incident on a lossy material can be augmented by point monopole and dipole sources to allow for near perfect transmission, thus rendering the lossy medium acoustically transparent. We present general expressions for source magnitudes that are dimensionless with respect to frequency, material thickness, and the background medium. We show that these results are consistent with three-dimensional finite element simulations, where the appropriate monopolar and dipolar forces are generated using finite dimensional velocity sources with real loudspeaker characteristics mounted in an acoustic waveguide.

Characterization of elastic topological states using dynamic mode decomposition

Elastic topological states have been receiving increased attention in numerous scientific and engineering fields due to their defect-immune nature, resulting in applications of vibration control and information processing. Here, we present the data-driven discovery of elastic topological states using dynamic mode decomposition (DMD). The DMD spectrum and DMD modes are retrieved from the propagation of the relevant states along the topological boundary, where their nature is learned by DMD. Applications such as classification and synthesis of wave propagation can be achieved by the underlying characteristics from DMD. We demonstrate the classification between topological and traditional metamaterials using DMD modes. Moreover, the model enabled by the DMD modes realizes the synthesis of topological state propagation along the given interface. Our approach to characterizing topological states using DMD can pave the way towards data-driven discovery of topological phenomena in material physics and more broadly lattice systems.

A Hybrid Damper with Tunable Particle Impact Damping and Coulomb Friction

A particle impact damper (PID) dissipates the vibration energy of a structure through impacts within the damper. The PID is not commonly used in practice mainly because of its low damping-to-mass ratio and the difficulty in achieving its optimal design due to its nonlinear characteristics. In contrast, a Coulomb friction damper (FD) can offer a higher damping force-to-mass ratio than other dampers, but it is also difficult to be controlled precisely due to its nonlinear characteristics and excessive frequency sensitivity regarding the resonant frequency. This paper examines a hybrid damper by combining a particle impact damper and a Coulomb friction damper (PID + FD) theoretically and experimentally. A theoretical model of the proposed damper is developed and tested numerically on a single-degree-of-freedom (SDOF) structure. The predicted results are validated by experimental tests on a prototype of the proposed damper. The damping force provided by the FD in the prototype can be varied by adjusting the normal force applied through a compression spring, while the vibration energy dissipation by the PID can be varied by changing the cavity size of the PID. A parametric analysis of the proposed hybrid damper has been performed. The proposed hybrid damper can reduce the maximum vibration amplitude of the SDOF primary structure by 66% and 43% compared with using the FD and PID only. The proposed damper is found to be effective over a wide range of excitation frequencies. Furthermore, the proposed hybrid damper achieves a similar vibration suppression performance to the traditional tuned mass damper (TMD) of a similar mass ratio. The proposed damper does not require an optimally tuned natural frequency and damping, unlike the TMD, and therefore it does not have the detuning problem associated with the TMD. In addition, the performance of the proposed damper is tested and compared with the TMD for random earthquake excitation data. Consequently, the proposed hybrid damper may be a simpler and better alternative to the TMD in passive vibration control applications.

Design and fabrication of 3D-printed composite metastructure with subwavelength and ultrawide bandgaps

Architected composite metastructures can exhibit a subwavelength ultrawide bandgap (BG) with prominent emerging applications in the structural vibration and noise control and, elastic wave manipulation. The present study implemented both forward and inverse design methods based on numerical simulations and machine learning (ML) methods, respectively to design and fabricate an architected composite metastructure exhibiting subwavelength and ultrawide BGs. The multilayer perceptron and radial basis function neural networks are developed for the inverse design of the composite metastructure and their accuracy and computation time are compared. The band structure revealed the presence of subwavelength and ultrawide BGs generated through local resonance and structural modes of the periodic composite lattice. Both in-plane and out-of-plane local resonant modes of the periodic lattice structure were responsible for inducing the BGs. The findings are confirmed by calculating numerical wave transmission curves and experiment tests on the fabricated supercell structures, utilizing 3D-printing technology. Both numerical and experimental results validate the ML prediction and the presence of subwavelength and ultrawide BG was observed. The design approach, research methodology and proposed composite metastructure will have a wide range of application in the structural vibration control and shock absorption.

Vibrational Power Flow Analysis for the Sandwich Cylindrical Shell Structure with a Metal–Rubber Core in the Thermal Environment

This research is designed to investigate the vibrational characteristics of a sandwich cylindrical shell structure with an elastic-porous metal–rubber core in the thermal environment by the power flow method. The finite element models of the homogeneous and sandwich cylindrical shell structures are established for harmonic response analysis completed by the mode superposition method. Further, the structural power flow is calculated and visualized based on the results of the finite element analysis. A comparison is made with the results for a plate available in the literature validating the effectiveness of the power flow visualization method. The effects of some key factors, such as the frequency, the metal–rubber core, the length-to-radius ratio, and the temperature on the power flow of the sandwich cylindrical shell structure, are analyzed using power flow cloud pictures and vector diagrams. The results reveal that the frequency affects the distribution of power flow, and the metal–rubber core can dissipate energy, whereas the length-to-radius ratio and temperature do not have a significant influence on the power flow of the sandwich cylindrical shell structure with a metal–rubber core (SCSMR). This work should be valuable for the noise and vibration control application of the SCS-MR.

Electro-structural modeling of smart laminated composite plate under hygrothermal environment for optimum vibration energy harvesting

Smart laminated composite structures with piezoelectric patches are widely used in vibration control applications in several engineering fields. Precise mathematical models are required for the coupling of base structural and piezoelectric field variables. This paper presents the electro-structural analysis and optimization studies of piezoelectric energy harvester with laminated composite substrate plate subjected to base excitations. The coupled electro-mechanical equations are derived from recently proposed first-order shear deformation theory via the Hamilton’s principle by considering hygrothermal effects. The coupled-field solution is obtained from Ritz-approximation and validated with three-dimensional finite element analysis. Effects of multiple piezoelectric patch topologies over the plate surface on the open-circuit voltage and displacement response are illustrated. Furthermore, the influences of piezoelectric-patch sizes, ply-orientation, size, and location of the tip mass are initially studied on the magnitude of output power and efficiency. An optimization study is conducted to identify the geometric and material variables for improvement of the harvester power output and efficiency.

Tunable reflection and broadband absorption of flexural waves by adaptive elastic metasurface with piezoelectric shunting circuits

Elastic metasurfaces have attracted lots of attention due to their extraordinary ability in manipulating elastic waves. Among various elastic metasurfaces, the adaptive elastic metasurface (AEM) has more flexibility because of the tunability in function and working frequency band without changing the geometrical configuration. In this paper, we propose an AEM composed of sandwiched plates with mass blocks at their free ends to realize tunable reflection and high-efficiency absorption of flexural waves in broadband. The upper and lower parts of the sandwiched plate are piezoelectric patches individually shunted with a hybrid circuit in series of a resistance and negative capacitance. We solve the reflection coefficient/phase shift of the subunit and the full reflected wave field of the AEM by using the transfer matrix method and coupled-mode theory, respectively. The modulation mechanisms of the phase shift and reflection coefficient are revealed. Especially, the influence of negative effective rigidity on the phase shift is investigated. The moment of inertia generated by the mass block plays a key role in reducing the sensitivity of the phase shift to negative capacitance. Based on the theoretical analyses, the AEMs are designed to realize tunable reflection, switchable asymmetric reflection and high-efficiency absorption. The results obtained from analytical solutions and finite element simulations are consistent with each other. The proposed AEM may have potential applications in vibration control and noise reduction.

Tunable elastic metasurface based on adjustable impedances for Gaussian beam manipulation

Different from the common tunable elastic metasurface (TEM), like piezoelectric active metasurface, in this paper, we propose a TEM composed of impedance-adjustable subunits (IASs) to realize tunable manipulations of flexural waves. Based on the impedance theory, the adjustable mechanism of the phase shift of the IAS is clarified according to the derivations for the relationship between the force/moment interface impedances and complex reflection coefficients. The boundary effect is considered, and the difference between the impedances of the flexural and acoustic waves is demonstrated for the subunits with free and clamped boundary conditions. By using the diffraction theory and coupled-mode theory, an analytical model is established for the metasurface subjected to a Gaussian flexural beam incidence, based on which, the total wavefield consisting of all propagating diffraction orders is solved. Its accuracy and the modulation function adjustability of the TEM are demonstrated by the finite element (FE) simulations and experiments. The proposed IAS possesses a flexible and reliable layout for TEM design and has potential engineering applications in vibration control, health monitoring, etc.

Event-Triggered Adaptive Control of Coupled Hyperbolic PDEs With Piecewise-Constant Inputs and Identification

In this article, we present an event-triggered boundary control scheme with a, likewise, event-triggered batch least-squares parameter identification for a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2\times 2$</tex-math></inline-formula> hyperbolic PDE-ODE system, where two coefficients of the in-domain couplings between two transport PDEs, and the system parameter of a scalar ODE, are unknown. The triggering condition is designed based on evaluating both the actuation deviation caused by the difference between the plant states and their sampled values, and the growth of the plant norm. When either condition is met, the piecewise-constant control input and parameter estimates are updated simultaneously. For the closed-loop system, the following results are proved: first, the absence of a Zeno phenomenon; second, finite-time exact identification of the unknown parameters in most situations; third, exponential regulation of the plant states to zero. In the numerical simulation, the design is verified in an application of axial vibration control of a mining cable elevator, where the damping coefficients of the cable and the cage are unknown.

Experimental study on adaptive-passive tuned mass damper with variable stiffness for vertical human-induced vibration control

Serviceability problem and human-induced vibration control of slender footbridges are of increasing interest to structural engineers. Passive tuned mass dampers (TMDs) have a wide range of applications in human-induced vibration control. However, a passive TMD is sensitive to the frequency deviation and, as a result a mistuned TMD will lose its control effect. An adaptive TMD can solve the mistuning problem of a passive TMD. However, there is few adaptive TMDs with variable stiffness in this issue. To fill this gap, an adaptive-passive variable stiffness TMD (APVS-TMD) is proposed in this study. The stiffness and frequency of APVS-TMD can be retuned through changing the length of free end of cantilever beam, while the damping can be retuned by adjusting the air gap between the conductor plate and magnets. As for the target natural frequency to be adjusted, the first two modal frequencies of the TMD-structure coupled system are identified under ambient excitation first, and then, the decoupled structural natural frequency is obtained according to the developed method based on the undamped 2-degree of freedom (DOF) modal analysis. By means of numerical simulation, the identification strategy is verified using a SDOF lumped mass main structure and an ideal simply supported beam model. Then, the identification and stiffness retuning operations of the APVS-TMD are further verified through a footbridge model experiment. Here, control effects of the APVS-TMD to walking- and running-induced vibrations are highlighted and compared with those of a mistuned TMD. Experimental results show that the APVS-TMD can identify the decoupled structural natural frequency from the coupled system accurately, and control human-induced vibrations effectively.

Acoustic Black Holes in a Spinning Beam

Abstract Through creating slow waves in structures, Acoustic Black Hole (ABH) shows promise for potential vibration control applications. However, it remains unclear whether such phenomena can still occur in a structure undergoing high-speed spinning, and if so, what is the interplay among various system parameters and what are the underpinning physical mechanisms. To address this issue, this work establishes a semi-analytical model for a spinning ABH beam based on Euler-Bernoulli beam theory under the energy framework. After its validation, the model is used to reveal a few important vibration features pertinent to the spinning ABH beam through examining its dynamics, modal properties and energy flow. It is shown that the spinning-induced centrifugal effects generate hardening effects inside the structure, thus increasing the overall structural stiffness and stretching the wavelength of the modal deformation of flexural waves as compared with its counterpart at still. Meanwhile, energy flow to the ABH portion of the beam is also adversely affected. As a result, the ABH-induced overall damping enhancement effect of the viscoelastic coating, as observed in conventional ABH beam at still, is impaired. Nevertheless, the study confirms that typical ABH features, in terms of wave compression, energy trapping and dissipation, though affected by the spinning effects, are still persistent in a high-speed spinning structure. This paves the way forward for the embodiment of ABH phenomena in the design of high performance rotating mechanical components such as turbine blades.

Origami-based tunable mechanical memory metamaterial for vibration attenuation

Tunable metamaterials without the necessity to redesign parameters and remanufacture have received increasing interest in recent years due to their rich dynamic characteristics and wide potential applications in vibration and sound control. In this work, we propose and analyze a mechanical memory metamaterial with tunability based on the Kresling origami that can easily be reconfigured for vibration attenuation in a desired frequency range. Unlike previous Kresling origami metamaterials in which rotational motion is transferred along the origami chain, rotations are localized in the proposed tunable metamaterial, which avoids introducing rotations between the ends of the metamaterial. The static and dynamic characteristics of the metamaterial are theoretically analyzed based on the truss model of the origami. By utilizing the bi-stability of the Kresling origami module (KOM) with asymmetric stiffness, the metamaterial can achieve rich dynamic behaviour with various memories. Each memory represents a pattern of periodic repeating cells in the metamaterial by switching the stable states of KOMs. The transmissibility and bandgaps of the metamaterial are determined analytically and verified by numerical simulations. The results demonstrate the tunability of the proposed metamaterial by switching its memories. Besides, the parametric study shows that the bandgap frequency ranges of the metamaterial can be expanded by adjusting the mass moment of inertia of the KOMs’ middle planes, making the antiresonance frequency of the system close to one of its natural frequencies and/or introducing damping. Finally, the proposed Kresling origami metamaterial is implemented and tested, and the tunability of vibration attenuation by memory switching of the proposed origami metamaterial is demonstrated. The proposed origami-based mechanical memory metamaterial will promote the development of dynamics and vibration control technology and advanced mechanical metamaterials.

Performance of wire rope damper in vibration reduction of stay cable

This paper systematically investigates the novel application of wire ropes as a damper rather than as an isolator to reduce the wind-induced high-mode vibration of stay cables. Three-direction cyclic loading tests, including tension–compression direction, shear direction, and roll direction, are conducted to clarify the damping behavior of the proposed wire rope damper. The wire rope damper exhibits asymmetric hysteretic characteristics in the tension–compression direction, while the hysteresis loops in the shear and roll directions are symmetrical. A modified normalized Bouc-Wen model is presented to describe the multi-directional hysteretic characteristics of the wire rope damper. An analysis method considering the nonlinear damping behavior is developed in this study to overcome the limitations of the traditional analysis using an equivalent damping coefficient. The proposed analysis method is validated against the physical experiments. The proposed wire rope damper system was installed on the Su-Tong Yangtze River Bridge to reduce the high-mode vortex-induced vibration of the stay cable. The field monitoring data demonstrate that the proposed wire rope damper can significantly reduce the in-plane and out-of-plane vibrations. The effect of the wire rope damper on the cable vibration control is further examined using the proposed analysis method. The finite element results further demonstrate the effectiveness of the wire rope damper in high-mode vibration reduction of stay cables. The features of the wire rope damper, such as multi-directional damping, broadband applicability, and simple configuration, are beneficial to its application in cable vibration control.

Special Issue on the Application of Active Noise and Vibration Control

Active noise and vibration control aims at attenuating unwanted sound or vibration by automatically generating an anti-sound or vibration [...]

A novel active tendon pendulum tuned mass damper and its application in transient vibration control

Enhancing the performance characteristics of Tuned Mass Dampers (TMDs), in particular extending their narrow frequency band of operation, has been the subject of many researches. In the adaptive type of TMDs, the device's properties can be adjusted gradually in response to a slight alteration in the excitation characteristics and physical properties of the main structure. A novel vibration absorbing system, namely Active Tendon Pendulum TMD (AT-PTMD), is proposed in the present study. The device consists of a simple pendulum whose horizontal movement is restricted by a tendon with an adjustable tensile force which is attached to the pendulum’s rod. The device is designed and formulated, and its efficiency is assessed numerically and experimentally. For this purpose, a 3-degree of freedom structure is considered. Scrutinizing the responses of the uncontrolled, passively controlled and actively controlled structure shows the appropriate performance of the AT-PTMD in comparison with the passive TMD system in transient vibration reduction, particularly in reducing the total vibrational energy of the structure's response. Considering the achieved results, the proposed AT-PTMD system is capable of reducing the maximum displacement and acceleration of the main structure up to 43% and 37%, respectively, which substantiates its excellence over the common passive vibration absorbing devices. The case study also proves that the utilized mechanism for adjusting the equivalent stiffness of AT-PTMD increases its operating frequency range by 105% compared to common TMDs. Unlike active structural control systems, the suggested approach will not induce structural instability in any operating mode.

Investigation on a lightweight type broad band-gap metamaterial beam for low-frequency vibration control

Phononic crystals (PCs) and acoustics/elastic metamaterials (AMs/EMs) have aroused increasing attentions for potential applications in low-frequency vibration control due to their outstanding mechanical and physical performances. So far, most reported metamaterials aim to obtain low-frequency broad band-gaps as required to satisfy the practical application. In this paper, we propose a new lightweight low-frequency broadband metamaterial beam. The low-frequency broadband from 390 to 920 Hz of the proposed metamaterial beam is confirmed through vibration transmittance frequency response functions (FRFs) obtained numerically and experimentally. Finally, the steady-state vibration deformations are acquired to illustrate the attenuating effect of the metamaterial beam band-gaps. The research in this paper offers a novel and advantageous method for designing of structures that both broadband damping and lightweight required, such as space-arm and framework of antenna in the field of aerospace.

Vibration Characteristics of Corn Combine Harvester with the Time-Varying Mass System under Non-Stationary Random Vibration

In field harvesting conditions, the non-stationary random vibration characteristics of the harvester are rarely considered, and the results of vibration frequency calculated by different time–frequency transformation methods are different. In this paper, the harvester’s vibration characteristics under the time-varying mass were studied, and the correlation between vibration frequency and modal frequency was analyzed. Firstly, under the conditions of time-varying mass (field harvesting conditions) and non-time-varying mass (empty running condition), the non-stationarity characteristics of vibration signals at 16 measurement points of a combined corn harvester frame were studied. Then, fast Fourier transform (FFT), short-time Fourier transform (STFT), and continuous wavelet transform (CWT) were used to calculate the vibration frequency distribution characteristics of the corn harvester. Finally, based on the EFDD (enhanced frequency domain decomposition) algorithm, the correlation between the primary vibration frequency and the operating mode frequency is studied. The results show that the mean, variance, and maximum difference of the vibration amplitude under harvesting conditions (mass time-varying system) are 0.10, 26.5, and 1.0, respectively, at different harvesting periods (0~10 s, 10~20 s, 20~30 s). The harvesting conditions’ vibration signals conform to the characteristics of non-stationary randomness. The FFT algorithm is used to obtain more dense vibration frequencies, while the frequencies based on STFT and CWT algorithms are sparse. The correlation between the FFT method and the EFDD algorithm is 0.98, and the correlation between the STFT, CWT, and the EFDD algorithm is 0.99 and 0.98. Therefore, the primary frequency of the STFT methods is closer to the modal frequency. Our research laid the foundation for further study and application of mass time-varying combined harvester system non-stationary random vibration modal frequency identification and vibration control.

Dynamics control for complex mechanical systems with nonlinear actuators using the transfer matrix method for linear multibody systems

Smart actuators, such as magnetorheological dampers, piezoelectric actuators et al., are increasingly being explored for various nano-positioning and vibration control applications. However, those actuators reduce control performance due to the existence of inherent hysteresis nonlinearities between the input and the output. The nonlinearities may cause undesirable inaccuracies, oscillations, poor control performance even leading to instabilities of the closed-loop system. In order to accurately model complex mechanical systems with such nonlinear actuators, a comprehensive mathematical model, which uses the transfer matrix method for linear multibody systems (linear MSTMM) to model the linear dynamics properties and the hysteresis model to describe the hysteresis nonlinearities, is presented. And then a hysteresis observer based on the hysteresis model is established to compensate the hysteresis nonlinearity of actuators. Then, a hybrid controller combining the proposed linearization and PID control for complex mechanical systems based on the comprehensive model is proposed and explored. The experimental results show that the proposed hybrid control method can achieve precise control of the complex mechanical systems with nonlinear actuators.

Study of Distribution of Magnetic Field Strength in Magnetorheological Elastomers using Artificial Neural Network

Magnetorheological elastomers (MRE) find a large number of applications in vibration control. For effective working of MRE, proper design of a magnetic circuit is needed so that it can draw the maximum amount of magnetic field through MRE region and at the same time satisfy all geometric constraints for the related application. With the availability of B-H curve data for MRE, finite element (FE) modelling of the full magnetic circuit is possible. FE modelling presents a good perspective on the distribution of the magnetic field inside the circuit. However, FE results cannot be obtained frequently for different geometries of the circuit. In the present study, the feedforward neural network (FNN) is used to predict the magnetic flux density in the MRE region of magnetic circuit setup. Training data for the FNN is generated from the results of the FE model where a log file has been coded keeping geometric parameters as variables and magnetic flux density as output. The FNN model is trained to have minimum mean square error. The FNN is further used for the optimization of dimensions of the magnetic circuit to have maximum magnetic field in the MRE region for the given geometric constraint.