Magnetorheological Elastomer Layer Research Articles

Vibration analysis of a rotor-bearing system using magneto-rheological elastomers

Magneto rheological materials are considered as a promising adaptive means of vibration control. This paper proposes a new configuration of smart bearings comprising magneto-rheological elastomer (MRE) layer inserted between the bearing pedestal and the foundation. This configuration provides a directional vibration controllability in both horizontal and vertical directions of a rotor-bearing system. The effect of using MRE layer on the vibration response and the resonant speeds of a rotor-bearing system is investigated. The finite element method is used to derive a dynamic model for the rotor-bearing system using shaft elements based on the Rayleigh beam theory and accounting for the gyroscopic effect and internal damping of the shaft. Simulation results reveal that the use of MRE materials in passive mode leads to downshifting of the first two resonant speeds and the attenuation of the steady state vibration response of the rotor bearing system in the horizontal and vertical directions at the resonance frequencies. When the MRE layer is subjected to a magnetic field generated by an electric current produced in the magnetic coil, the horizontal and vertical vibration responses are increased at the resonant speeds but decreased at other rotational speed ranges. Furthermore, the first two resonant speeds in the horizontal and vertical directions decrease further with the increase of the electric current.

An adaptive and space-energy efficiency vibration absorber system using a self-sensing and tunable magnetorheological elastomer

Vibration monitoring and buffering is an important technical task in many industrial fields, such as bridges, machine tools and other specific applications. Recently, a magneto-rheological elastomer (MRE) has been utilized in an intelligent vibration absorber system with tunable stiffness, which can reversibly regulate its resonant frequency in real time to effectively prevent the resonance of the mechanical system. However, this MRE must be integrated with a vibrational sensor and equipped with an external magnetic field (e.g., electromagnetic coils or permanent magnets). Thus, the overall system is usually bulky and energy-intensive, which severely limits its broad application potential. In this work, we present an MRE-based tunable vibration absorber (MRE-TVA) with an elaborate 3-layered architecture integrated with a self-sensing triboelectric nanogenerator (TENG) sensor. The inner two-layer MRE structure exhibits variable stiffness, while the outer layer of the negative Poisson's ratio structure can confine the deformation of the inner MRE layers and form a contact-separation TENG sensor with the MRE, where the sensor can recognize external vibration information in a timely manner. In particular, the TENG sensor enables sensitive identification of the abnormal state of resonant excitation and other mechanical disturbances through dual logic judgment control based on vibration frequency and amplitude. For energy-space efficiency, a bistable permanent magnet controlled by a pulse current is integrated to generate a desirable magnetic field for modulation of the MRE stiffness. Compared with traditional electromagnetic coils, the energy and space utilization rates are increased by 94.25% and 75%, respectively. This combination of self-sensing and vibration damping systems achieves high energy-space efficiency, which will enable the intelligent health monitoring of bridges and other autonomous, smart, and long-term engineering tasks.

Theoretical and experimental investigations on active vibration control of the MRE multifunctional grille composite sandwich plates

This work investigates the active vibration control performance of the magnetorheological elastomer (MRE) multifunctional grille composite sandwich plate (MRE-MGCSP) subjected to a base excitation load, when a multi-regional magnetic field is generated inside the structures due to the magnetorheological effect. Initially, by taking two carbon fiber reinforced polymer (CFRP) skins and an MRE-based grille core as a sandwich example, a theoretical model of the MRE-MGCSPs is proposed, which in fact consists of multiple grille functional units (GFUs) and grid frame beams. Here, each GFU is made up of a rectangular frame and 4-layer functional laminates, including a bottom copper wire layer, an MRE layer, a top copper wire layer and a piezoelectric perception layer. The equations of motion are derived to solve the free and forced vibrations in accordance with the integral first-order shear deformation principle, together with the energy approach, the Biot-Savart law and the improved Rayleigh-Ritz method. The present model is initially validated against the published results in literature. Then, a multi-regional vibration control strategy is proposed to better exert the unique advantages of such the structure with highly integrated vibration control and space-saving functions. Also, the detailed measurements, including pulse excitation, sweeping frequency excitation and resonant excitation tests, are undertaken to comprehensively verify the effectiveness of the proposed model as well as the control strategy. Finally, the influences of critical magnetic control parameters on the anti-vibration performance of the MRE-MGCSPs are discussed to summarize practical conclusions for engineering applications.

Static and dynamic performances of sandwich plates with magnetorheological elastomer core: Theoretical and experimental studies

This paper investigates the static and dynamic performances of sandwich plates with magnetorheological elastomer (MRE) core, in which the MRE core includes two copper wire layers, two inner metal layers, and one MRE layer. First, based on the complex modulus method, the Jolly theory and the pre-defined magnetic coefficients, the dynamic moduli, and loss factors of MRE are assumed as a function of magnetic induction intensity. Furthermore, a theoretical model of the MRE sandwich plates (MRESPs) is proposed, which considers the internal magnetic field excitation and four types of panel materials, namely fiber-reinforced polymer (FRP), fiber-reinforced polymer with carbon nanotubes (CNT-FRP), metal and fiber-metal hybrid (FMH) panels. After the deformation and energy equations are derived to solve the static bearing stiffness, dynamic stiffness, and damping parameters, some literature results are employed to provide the initial validation of the model developed. Subsequently, four MRESP specimens with the FRP, CNT-FRP, metal, and FMH panels are fabricated and measured to further verify the model as well as to evaluate the mechanical performance. The influence of critical geometric and material parameters related to MRE on static and dynamic properties is also discussed to summarize some practical conclusions for engineering applications.

Analysis, optimization and control of an adaptive tuned vibration absorber featuring magnetoactive materials

Excessive vibration may cause premature fatigue failure on structural components if it is not properly controlled. One effective way to attenuate vibration is to attach a tuned vibration absorber to the main structural component. Passive tuned vibration absorbers are mainly effective to attenuate vibration at a specific range of frequencies and thus they become infective under varied environmental conditions which can significantly alter the tuning frequencies. The present study aims at development of a wide-bandwidth and light-weight adaptive tuned vibration absorber (ATVA) featuring a magnetorheological elastomer (MRE) which is tuned to absorb the vibrations of a flexible beam. The accelerance transfer function is derived for both beam with and without ATVA. The effectiveness of the ATVA to control vibration of the flexible beam caused by external excitation under wide range of frequencies is demonstrated. The proposed ATVA consists of C-Shape frame with winding coils, two isometric MRE specimens with 40% volume fraction, and active mass. An empirical model for the MRE has been developed through an experimental identification method in order to predict the MRE's elastic modulus under various levels of excitation frequencies and applied magnetic fields. Using MRE models and magneto-circuit analysis, the frequency bandwidth of the ATVA is analytically obtained. The analytical model is then used to develop a multidisciplinary design optimization formulation to minimize the mass and maximize the frequency bandwidth of an ATVA featuring MRE given several geometrical and physical constraints. Finally, a tuning algorithm has been presented to determine the required applied magnetic flux density to the MRE layers based on the identified phase difference between the absolute acceleration of the host and relative acceleration of the host and ATVA's resonator.

A novel semi-active switching control scheme for magnetorheological elastomer-based vibration isolator under dynamic input saturation

It is still a challenge to guarantee a robust performance of magnetorheological elastomer (MRE)-based isolators under complex and frequency-varying base excitation, due to the highly nonlinear dynamic behavior of the MRE. The dynamic behavior of the MRE-based isolator should be considered properly in the control law to ensure the effectiveness of the MRE-based isolator. In this research study, first a dynamic modeling of an MRE-based isolator is established to formulate the actuation (transmitted) force of the MRE-based isolator. The MRE induced actuation force is limited to a dynamic input saturation and depends on the applied magnetic field density, geometry of the MRE layers, viscoelastic properties of the MREs and system states. Subsequently, a novel semi-active switching control scheme, which adopts the fastest convergence speed of driving the virtual energy toward zero based on Lyapunov theory, is proposed to improve the mitigation performance of the MRE-based isolator. The proposed control law requires less modeling information and does not require a time-consuming adjustment of control parameters, thereby possessing a broad application prospect in MRE-based isolators. Finally, the performance of the MRE-based isolator using the developed control strategy is compared with those based on passive control with different levels of constant magnetic field density, ON–OFF control and PD control under the harmonic, random and bump shock base excitation. The results show a robust and superior performance of the developed vibration control strategy.

Experiments and Numerical Implementation of a Boundary Value Problem Involving a Magnetorheological Elastomer Layer Subjected to a Nonuniform Magnetic Field

Abstract This study investigates experimentally and numerically the response of a magnetorheological elastomer (MRE) layer placed atop an electromagnetic coil. The MRE layer is deflected upon application of a current in the coil, which creates highly nonuniform magnetic fields. Isotropic and transversely isotropic layers (i.e., containing chains of magnetic particles) are tested experimentally, and the isotropic layer exhibits the largest deflection. To enhance the energetic efficiency of the model device, an iron core is introduced inside the electromagnetic coil, thereby leading to an increase in the resulting magnetic field near the center of the MRE layer. In parallel, the boundary value problem —including the MRE layer, the coil, the core (if present) and the surrounding air—is modeled numerically. For this, a magneto-mechanical, vector potential-based variational formulation is implemented in a standard three-dimensional finite element model at finite strains. For the material description, a recently proposed analytical homogenization-guided model is used to analyze the MRE in the “coil-only” configuration. It is then employed to predict the response of the layer in the “coil plus core” configuration, thus circumventing the need for a separate material characterization procedure. The proposed numerical simulation strategy provides a deeper understanding of the underlying complexity of the magnetic fields and of their interaction with the MRE layer. This study also reveals the importance of modeling the entire setup for predicting the response of MRE materials and, as a result, constitutes a step toward designing more efficient MRE-based devices.

A novel magnetorheological elastomer-based adaptive tuned vibration absorber: design, analysis and experimental characterization

The present study aims at the development of a novel semi-active adaptive tuned vibration absorber (SATVA) capable of tuning its natural frequency adaptively in low frequency range. The absorber consists of a multilayer sandwich beam featuring magnetorheological elastomer (MRE) and integrated U-shaped electromagnets which are attached at the top and bottom layers of the sandwich beam. Electromagnets are designed to provide the required magnetic field to alter the stiffness of the MRE layers while also acting as the active mass of the absorber. Based on the characterization of the shear and loss modulus of the fabricated MRE samples, the finite element (FE) model of the proposed SATVA has been developed to analyze the absorber to meet the design requirements and also to evaluate its dynamic performance. The proposed SATVA is then fabricated and experimental set-ups are designed to validate the electromagnet and FE models. The frequency response function of the proposed SATVA is then investigated under different levels of the applied current to the electromagnets. It has been shown that good agreement exists between simulation and FE results. A frequency-shift of approximately 9% was achieved while maintaining a reasonable factor of safety for material constraints. Finally, using the validated FE mode, a parametric study has been conducted to investigate the effect of different design parameters.

A nonlinear analytical model of composite plate structure with an MRE function layer considering internal magnetic and temperature fields

To better exert the vibration suppression effect of magnetorheological elastomer (MRE) embedded into a composite structure with structural and functional integration advantage, this study proposes a nonlinear analytical model of such composite plate with an MRE function (MREF) layer, accounting for internal magnetic and temperature fields for the first time. Initially, a 9-layer fiber metal laminated (FML) plate with the MREF composites, consisting of two layers of metal protective skins, two layers of fiber-reinforced polymer (FRP) and one layer of MREF, is taken as an example to describe such a modelling method. Nonlinear expressions of elastic moduli of MRE and FRP involving thermal and magnetic fitting coefficients are also proposed, followed by derivation of the energy expressions of the constituent layers by the Rayleigh-Ritz method. After the free and forced vibrations are solved, the identification procedure of fitting coefficients is described and some literature results are employed to preliminarily validate this model without consideration of internal magnetic field or temperature field or both. Finally, dynamic experiments under different magnetic and temperature conditions are undertaken. The detailed comparison of the natural frequencies and resonant responses are conducted to provide a solid validation of the model developed. It has been found that enlarging the magnetic and temperature fields both facilitate the improvement of the anti-vibration performance. Also, by further increasing the shear modulus of MRE, the volume fraction of carbonyl iron particles or the thickness ratio of the MRE layer to the overall structure, a better vibration suppression capability can be obtained.

Tunable Young's Moduli of Soft Composites Fabricated from Magnetorheological Materials Containing Microsized Iron Particles.

This study experimentally investigates the field-dependent Young’s moduli of soft composites, which are fabricated from two different magnetic-responsive materials; magnetorheological elastomer (MRE) and magnetorheological fluid (MRF). Four factors are selected as the main factors affecting Young’s modulus of soft composites: the amount of MRF, the channel pattern, shore hardness and carbonyl iron particle (CIP) concentration of the MRE layer. Five specimens are manufactured to meet the investigation of four factors. Prior to testing, the scanning electron microscopy (SEM) image is taken to check the uniform dispersion of the carbonyl iron particle (CIP) concentration of the MRE layer, and a magnetic circuit is constructed to generate the effective magnetic field to the specimen fixed at the universal tensile test machine. The force–displacement curve is directly measured from the machine and converted to the stress–strain relationship. Thereafter, the Young’s modulus is determined from this curve by performing linear regression analysis with respect to the considered factors. The tunability of the Young’s moduli of the specimens is calculated based on the experimental results in terms of two performance indicators: the relative percentage difference of Young’s modulus according to the magnetic field, and the normalized index independent of the zero-field modulus. In the case of the relative percentage difference, the specimens without MRF are the smallest, and the ones with the highest CIP concentration are the largest. As a result of comparing the normalized index of each factor, the change in shore hardness and channel pattern have little effect on the tunability of Young’s moduli, and the amount of MRF injected and CIP concentration of MRE have a large effect. The results of this study are expected to provide basic guidelines for fabricating soft composites whose field-dependent Young’s moduli can be tuned by several factors with different effects.

Two-way controllable magnetorheological elastomer mount for shock and vibration mitigation

Current passive elastomeric mounts are designed to provide mitigation for a given shock and vibration exposure and are not capable of supporting variable payload systems, due to variation in the overall system dynamics. A novel magnetorheological elastomer (MRE) mount that can reduce or increase its stiffness based on payload and shock and vibration input is designed, fabricated, and tested to provide a wide controllable stiffness range for protecting sensitive systems that may require variable weight from external shock and vibration loading. A MRE is a field-controllable material in which the stiffness properties can be altered by changing the applied magnetic field. The two-way controllable MRE mount is designed by using three-dimensional electromagnetic finite element analysis. MRE mounts were developed by using relatively thick MRE layers and built-in electromagnets and permanent magnets. A two-layer MRE mount prototype is characterized by compression and shear tests. Control system hardware and software were developed to detect shock and vibration events, and activate the two-way controllable MRE mount, accordingly. The MRE mount and the control system were tested with variable representative weights. It was demonstrated that the designed control system can detect whether the incoming input is a shock event or a vibration event. The MRE mount demonstrated the ability to soften of stiffen based on the incoming input.

A magnetorheological elastomer rail damper for wideband attenuation of rail noise and vibration

The noise and vibration effects of rails can have a significant impact on the environment surrounding the railways. Rail dampers are elements that are attached to the sides of the rail and can improve the track decay rate of rail and then enhance the rails’ ability to attenuate noises and vibrations. However, in practical applications, the most efficient rail damper design still cannot adjust its own parameters to adapt to different requirements because their stiffness and damping are fixed after designed. In this work, a tunable magnetorheological elastomer rail damper that works on the principle of a dynamic vibration absorber has been designed, analysed, characterised, and experimentally tested for the suppression of railway noise and vibration. The new rail damper incorporates variable stiffness magnetorheological elastomer layers, whose stiffness can be controlled by an externally applied magnetic field, to realise adaptive characteristics. Experimental characterisations of the magnetorheological elastomer rail damper were performed with an electromagnetic shaker. Subsequently, theoretical predictions of the track decay rate of a UIC-60 rail with different rail dampers and without rail damper were conducted; simulation results verified that magnetorheological elastomer rail dampers can improve the track decay rate of rail over a wider frequency range compared to conventional rail dampers and thus the performance of the magnetorheological elastomer rail damper outperforms other conventional rail dampers on rail noise reduction.

Dynamic stability enhancement of laminated composite sandwich plates using smart elastomer layer

The dynamic stability of composite sandwich plates with a smart elastomer layer subjected to an axial periodic load is investigated. A finite element model of the composite sandwich plate with Magnetorheological elastomer (MRE) core is developed. A MRE layer, which its mechanical properties change with the applied magnetic field, is used as a damping layer to improve the stability of the structure. Due to the intrinsic characteristics of the MREs, these materials commonly operate in their pre-yield region. In this region, complex shear modulus is used for these materials. The effect of different parameters such as stacking sequences, boundary conditions, geometry of the sandwich plate, thickness and partial activation of the MRE layer on the damping treatment and stability boundaries is investigated. The presented results show that the application of an MRE layer as a core in the composite sandwich plate changes the stability region of the structure. Therefore, the instability boundaries can be manipulated to achieve the desired dynamic response of the structure.

Edgewise Bending Vibration Analysis of a Rotating Sandwich Beam with Magnetorheological Elastomer Core

The vibration of a rotating sandwich beam with magnetorheological elastomer (MRE) as a core between two elastic layers is theoretically analyzed in this paper. This study is focused on the bending vibration along the edgewise direction of a sandwich beam of rectangular cross-section, which, to the best of our knowledge, has not been addressed yet. The classical Euler–Bernoulli beam theory is used to model the dynamic behavior of the elastic layers. In the modeling, the effect of the MRE layer is considered by incorporating its shear strains and the inertia due to shear deformation and bending motion. The governing equations of motion of the rotating sandwich beam are derived by using the Ritz method and the Lagrange’s equations. The effects of the applied magnetic field, core layer thickness, rotational speed, setting angle and hub radius on the natural frequencies and the corresponding loss factors are investigated parametrically. The results show the significant effect of the magnetic field intensity and the MRE layer thickness on the modal characteristics of the MRE sandwich beam.

Performance of a large-scale magnetorheological elastomer–based vibration isolator for highway bridges

This study presents an experimental investigation on the magnetorheological effect of a new magnetorheological elastomer–based adaptive bridge isolation bearing system. Two identical magnetorheological elastomer–based adaptive bridge bearings (isolators) were designed and fabricated. Electromagnets were incorporated to create a closed-loop magnetic path in the magnetorheological elastomer layers. A double-lap shear and compression test setup was utilized to characterize the mechanical properties of the system subjected to scaled structural cyclic forces and strains. Experimental results demonstrated that the effective stiffness of adaptive bridge bearings increases with increased applied magnetic field and a compressive force resulted in larger apparent shear stiffness. Also, increasing loading frequency resulted in larger apparent shear stiffness and lower magnetorheological effect and similarly, however, a compressive force resulted in smaller magnetorheological effects.

Aeroelastic instability analysis of a turbomachinery cascade with magnetorheological elastomer based adaptive blades

Torsional aeroelastic analysis of a turbomachinery cascade comprised of three-layered sandwich blades embedded with Magnetorheological Elastomer (MRE) core layer is carried out in this paper. The MRE material is used as a constrained damping layer between two elastic skins in order to investigate its effects on the aeroelastic stability of a blade cascade. To formulate the structural dynamic of the blades, torsional theory of rectangular laminated plates is used and the unsteady Whitehead's aerodynamic theory is employed to model the aerodynamic loadings. Assumed modes method and the Lagrange's equations are used to derive the governing equations of motion of the coupled aeroelastic system. Then, the effects of different parameters on flutter stability of the blades cascade are studied in details. It is found that the magnetic field and MRE layer thickness have significant influences on the flutter boundary of the system and the mistuning of the magnetic field intensity has beneficial effect on the flutter stability. Additionally, the results confirm that the concept of sandwich blades provided with MRE core has capability to utilize as a passive treatment in turbomachinery applications for improving the flutter characteristics of the blades.

Torsional vibration analysis of a rotating tapered sandwich beam with magnetorheological elastomer core

In this study, the torsional vibration analysis of a rotating tapered sandwich beam with a magnetorheological elastomer core has been investigated. The magnetorheological elastomer material is used as a constrained damping layer embedded between two elastic constraining skins in order to improve the vibrational behavior of the sandwich beam. The three layers of the sandwich beam have rectangular cross-sections with symmetric arrangement. The problem formulation is set up based on the torsional theory of rectangular laminated plates. The assumed modes method and the Lagrange equations are used to derive the governing equations of motion of the system. The validity of the presented formulation is confirmed through comparison of the obtained results with those available in the literature. A detailed parametric study is carried out to investigate the effects of applied magnetic field, tapering ratios, magnetorheological elastomer layer thickness, rotating speed, hub radius, and setting angle on the free vibration characteristics of the sandwich beam. The results show that magnetic field intensity, magnetorheological elastomer layer thickness, and tapering ratio have significant influences on the torsional vibrating characteristics of the sandwich beam, and the effects of rotating speed and hub radius are considerable. The setting angle has no substantial effect on the torsional vibration characteristics.

Dynamic analysis of tapered laminated composite magnetorheological elastomer (MRE) sandwich plates

In the present study, the dynamic performance of the sandwich plate with magneto rheological elastomer (MRE) as the core layer and tapered laminated composite plates as the face layers is investigated. Various MRE tapered laminated composite sandwich plate models are formulated by dropping-off the plies longitudinally in top and bottom composite layers to yield tapered plates as the face layers and uniform MRE layer as the core layer. The governing equations of motion of tapered composite MRE sandwich plates are derived using classical laminated plate theory and solved numerically. Further, silicon based MRE is being fabricated and tested to obtain the shear and loss moduli using MR rheometer. The efficacy of the finite element formulation is validated by carrying out experiments on the various prototypes of tapered composite silicon based MRE sandwich plates and comparing the results in terms of natural frequencies obtained at various magnetic fields with those obtained numerically and with available literature. Also, the effects of magnetic field, taper angle of the top and bottom layers, aspect ratio, ply orientations and various end conditions on the various dynamic properties of tapered laminated composite MRE sandwich plate are investigated. Further, the transverse vibration responses of three different tapered composite MRE based sandwich plates under harmonic force excitation are analyzed at various magnetic fields.

Experimental nonlinear dynamics of a geometrically imperfect magneto-rheological elastomer sandwich beam

Experimental investigations were carried out on the nonlinear dynamic response of a clamped–clamped geometrically imperfect magneto-rheological elastomer (MRE) sandwich beam with a concentrated mass at the centre when loaded with a point excitation. Experiments have been conducted for: (i) a geometrically imperfect aluminium beam; (ii) a geometrically imperfect MRE sandwich beam in the absence of a magnetic field; (iii) a geometrically imperfect MRE sandwich beam in the presence of a magnetic field; (iv) a MRE sandwich beam with different geometric imperfection amplitudes. An electrodynamic shaker excited each system and the corresponding displacement of the concentrated mass was measured; an array of magnets has been used to investigate the effects of changing magnetic field strength on the nonlinear dynamic response of the geometrically imperfect MRE sandwich beam. It has been shown that the geometrically imperfect aluminium beam displays initial softening behaviour followed by strong hardening-type nonlinearity; with a MRE layer the motion characteristics of the geometrically imperfect sandwich beam no longer exhibits initial softening behaviour however, the MRE layer in the absence and presence of an external magnetic field all exhibit strong hardening-type nonlinearities—a significant qualitative change was observed in the nonlinear dynamical behaviour of the system.

Finite element design and analysis of adaptive base isolator utilizing laminated multiple magnetorheological elastomer layers

Available magnetorheological elastomer devices normally consist one to two layers of small-size magnetorheological elastomer materials. To be used in large-scale structures, magnetorheological elastomer devices with multiple larger magnetorheological elastomer materials are expected. This article addresses the critical issue in designing a large-scale device with multiple layers of low magnetic conductive magnetorheological elastomer materials, that is, magnetic circuit design. The primary target in magnetic circuit design for magnetorheological elastomer devices is to provide sufficient and uniform magnetic field to all magnetorheological elastomer layers in the device. In this article, finite element investigations are conducted. An innovative magnetic circuit design is proposed for magnetorheological elastomer base isolator with multi-layer of magnetorheological elastomer materials. In the design, laminated magnetorheological elastomer and steel structure is adopted as part of the magnetic core together with two steel blocks. Cylindrical steel tube is used as the yoke of the magnetic circuit. Two plates are placed on the top and bottom of the device to form enclosed magnetic path in the device. Finite element results showed that such innovative magnetic design is able to provide sufficient and uniform magnetic field to all magnetorheological elastomer layers, that is, 25 magnetorheological elastomer layers with thickness of 1 mm and diameter of 120 mm in this case. Finally, the influence of lateral deformation of the magnetorheological elastomer base isolator on the magnetic field is investigated. It is found that the magnetic field in magnetorheological elastomer materials deteriorates when the deformation of the device increases.