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The rapid development of the aviation industry has put forward higher and higher requirements for material properties, and the research on smart material structure has also received widespread attention. Smart materials (e.g., piezoelectric materials, shape memory materials, and giant magnetostrictive materials) have unique physical properties and excellent integration properties, and they perform well as sensors or actuators in the aviation industry, providing a solid material foundation for various intelligent applications in the aviation industry. As a popular smart material, piezoelectric materials have a large number of application research in structural health monitoring, energy harvest, vibration and noise control, damage control, and other fields. As a unique material with deformation ability, shape memory materials have their own outstanding performance in the field of shape control, low-shock release, vibration control, and impact absorption. At the same time, as a material to assist other structures, it also has important applications in the fields of sealing connection and structural self-healing. Giant magnetostrictive material is a representative advanced material, which has unique application advantages in guided wave monitoring, vibration control, energy harvest, and other directions. In addition, giant magnetostrictive materials themselves have high-resolution output, and there are many studies in the direction of high-precision actuators. Some smart materials are summarized and discussed in the above application directions, aiming at providing a reference for the initial development of follow-up related research. [ABSTRACT FROM AUTHOR]

The rapid development of the aviation industry has put forward higher and higher requirements for material properties, and the research on smart material structure has also received widespread attention. Smart materials (e.g., piezoelectric materials, shape memory materials, and giant magnetostrictive materials) have unique physical properties and excellent integration properties, and they perform well as sensors or actuators in the aviation industry, providing a solid material foundation for various intelligent applications in the aviation industry. As a popular smart material, piezoelectric materials have a large number of application research in structural health monitoring, energy harvest, vibration and noise control, damage control, and other fields. As a unique material with deformation ability, shape memory materials have their own outstanding performance in the field of shape control, low-shock release, vibration control, and impact absorption. At the same time, as a material to assist other structures, it also has important applications in the fields of sealing connection and structural self-healing. Giant magnetostrictive material is a representative advanced material, which has unique application advantages in guided wave monitoring, vibration control, energy harvest, and other directions. In addition, giant magnetostrictive materials themselves have high-resolution output, and there are many studies in the direction of high-precision actuators. Some smart materials are summarized and discussed in the above application directions, aiming at providing a reference for the initial development of follow-up related research.

• From the perspective of magnetic domain, single crystal, and polycrystalline structures, a multi-scale combined vector constitutive model for giant magnetostrictive materials is established. • The influence of stress demagnetization field on the constitutive model of giant magnetostrictive materials is proposed. • The constitutive model for giant magnetostrictive materials considers the influence of multi-physical field coupling effects such as demagnetization field, temperature, and stress. • The hysteresis effect on the constitutive model of giant magnetostrictive materials is taken into account. The magnetization and magnetostrictive strain of giant magnetostrictive materials exhibit a complex nonlinear trend under the coupling of multiple fields, including magnetic field, temperature field, and prestress field. To enhance prediction accuracy, we propose a three-dimensional magnetic-thermal-force coupled nonlinear multi-scale hysteresis vector model. This model is derived from the principles of thermodynamics and continuum mechanics, taking into account the interactions among magnetic domains, grains, polycrystals, and macroscopic scales. It combines the volume-averaging principle of magnetic domain microscopy with the generalized Jiles-Atherton hysteresis model. The predicted hysteresis magnetization and magnetostrictive strain curves obtained from this model are in good agreement with experimental results. By analyzing the predicted hysteresis magnetization and magnetostrictive strain under different conditions, we demonstrate that our proposed model can comprehensively describe the effects of temperature and prestress on the multi-field coupled hysteresis behaviors of giant magnetostrictive materials. Moreover, it provides theoretical guidance for both macroscopic and microscopic optimization in designing active devices incorporating super magnetostrictive materials. [ABSTRACT FROM AUTHOR]

Accurate calculation of magnetic energy losses for magnetostrictive material is a necessary step in designing high-power magnetostrictive transducer. In this article, based on the losses separation formula and measured data of Terfenol-D, the changing trends of the losses coefficients are investigated. An improved magnetic energy losses calculation method with variable coefficients is established. The measured and calculated values of magnetic energy losses at different frequencies and flux densities of driving magnetic field are compared and analyzed. The results show that the calculation method can accurately calculate the magnetic energy losses at higher frequencies (1–20 kHz). The average error between the calculated and the measured values is 4.32%. This research can provide theoretical and experimental guidance for the higher frequency applications of magnetostrictive materials. [ABSTRACT FROM AUTHOR]

A type of new intelligent micro-deformation material called giant magnetostrictive materials (GMMs) has a wide range of potential applications in the field of micro-vibrations. In this paper, the dynamic response of the output force of GMMs is investigated, and their internal magnetic fields are simulated via the finite element analysis software ANSYS. A test system that primarily includes a force sensor, a GMM, and a DAQ card is constructed to study the dynamic response characteristics of the output force. By changing the applied current in the coils and the pre-tightening force applied on the GMMs, the dynamic response time of the output force is determined. The experimental results show that, when the current in the coils is less than 2.5 A, the response time of the output force decreases with the increase of the outer current. Additionally, the response time of the output force is related to the applied preload, and is the fastest when the preload reaches 300 N. Before the pre-pressure reaches 300 N, the response time of the output force is negatively correlated with the pre-pressure. Finally, when the pre-pressure exceeds 300 N, the response time of the output force becomes greater than before. [ABSTRACT FROM AUTHOR]

Rotary ultrasonic machining (RUM) has been regarded as a promising method for processing difficult-to-cut materials due to improved machining efficiency and surface quality. Due to the machining load-induced resonant frequency shift of the RUM system, frequency tracking is a critical function to ensure the RUM system works at a resonance state to output an efficient tool vibration. However, current frequency tracking methods assume that the system's impedance circle is unchanged under load, which is not unsatisfactory, especially for large loads, resulting in a narrow bandwidth of frequency tracking. This study proposes a high-bandwidth resonant frequency tracking method valuing the dynamic resonance impedance characteristics of the giant magnetostrictive RUM system. The resonant frequency of the system is derived from the electrical feedback based on a RUM system's novel electrical model, which assumes a dynamic resonance impedance circle. Control simulation is conducted on the Modelsim software to verify the feasibility of the proposed frequency tracking method preliminarily. Then, an ultrasonic power supply with a new frequency tracking module is built. Loading experiments and machining tests are conducted to evaluate the load response of the RUM system. The results demonstrate that the frequency tracking bandwidth can be improved from 450 Hz to >750 Hz or 200 Hz to >1000 Hz for two different RUM system configurations, verifying the proposed method's efficacy. [ABSTRACT FROM AUTHOR]

Giant magnetostrictive materials are gaining interest in the field of smart material, especially the commercially known Terfenol-D, that is an alloy made out of iron, terbium and dysprosium (Tb0.3Dy0.7Fe1.9). Since these smart materials are subjected to both mechanical loads and magnetic field during their industrial applications, an extensive characterization on the influence of a magnetic field and of defects on their fracture behavior is needed. Very few works can be found in literature about this topic and, thus, the purpose of this work is to partially fill this lack by means of three-point bending tests on single-edge pre-cracked Terfenol-D specimens. Failure loads have been measured at different loading rates and under magnetic fields of various intensities. Since giant magnetostrictive materials are very brittle, the strain energy density (SED) approach has been exploited by means of couplefield finite element analyses. SED has revealed itself as a robust parameters in the assessment of the magnetic field and loading rate effects on fracture resistance, allowing also to propose a relationship between the radius of the control volume and the loading-rate

A new type of intelligent micro displacement materials, giant magnetostrictive materials (GMM), have a wide range of potential applications in the fields of micro vibrations. In this paper, a novel type of giant magnetostrictive actuator (GMA), mainly made by the giant magnetostrictive materials, is designed, and its inner structure and working principle are also discussed. To investigate the output force of giant magnetostrictive actuator, a test system, including the force sensor, data acquisition card and power supply equipment are established. The experimental results show, when the excited current increased from 0.5 A to 2 A gradually, the output force of the giant magnetostrictive actuator also gradually increased, in the condition of the pre-compress force from 100 N to 400 N, the output force of the giant magnetostrictive actuator will also increase with the increasing of the pre-compress force. [ABSTRACT FROM AUTHOR]

The paper presents the numerical and experimental investigations of the axisymmetric magnetostrictive actuator with a Terfenol-D rod. The applied model consists of equations that describe the magnetic and mechanical displacement fields. The equations of both fields are coupled through a nonlinear magneto-mechanical constitutive law. The model is considered as 2D axisymmetric. The finite element method is used to solve the field equations. Special attention is paid to the proper definition of magneto-mechanical relations. These relations are formed from measurements. A unique test stand is designed for the experimental investigation. The selected results of the simulation are compared with the measurement results. The comparison shows that the applied numerical model is sufficiently accurate.

The aim of this work was to observe the changes in the magnetomechanical properties of composite materials with different Tb0.3Dy0.7Fe1.9 (Terfenol-D) powder particle-size distributions and varying volume fractions in the polyurethane matrix. The results show a direct relationship between the properties and the particle size of the Tb0.3Dy0.7Fe1.9 powder: the increases in the particle-size distribution of the Tb0.3Dy0.7Fe1.9 powder in the matrix amplify the magnetostrictive responses and the compressive modulus values. Moreover, it was found that the key role in efficiency of the transformation of magnetic energy into mechanical plays the initial compressing pre-stress.

Based on the thermodynamic theory, by introducing the Weiss molecular field and considering current eddy loss, a 1D nonlinear elasto-thermo-magnetic multi-field coupling hysteresis constitutive model is proposed for giant magnetostrictive materials. This new model can fully describe the effects of the stress, frequency and ambient temperature not only on the curves of magnetostriction and magnetization under the static frequency, but also on the hysteresis characteristics of magnetostriction and magnetization at the dynamic frequency. This model, which has more concise mathematical form compared with other related models, shows a good agreement with experimental results on the magnetostrictive strain and magnetization hysteresis loops. Furthermore, the predicted results have indicated the necessary of considering the Weiss molecular field. This model is of convenient for both theoretical researches and engineering applications of magnetostrictive materials due to being without piecewise function and implicit functions in magnetostrictive constitutive relations. [ABSTRACT FROM AUTHOR]

Giant magnetostrictive materials are gaining interest in the field of smart material, especially the commercially known Terfenol-D, that is an alloy made out of iron, terbium and dysprosium (Tb0.3Dy0.7Fe1.9). Since these smart materials are subjected to both mechanical loads and magnetic field during their industrial applications, an extensive characterization on the influence of a magnetic field and of defects on their fracture behavior is needed. Very few works can be found in literature about this topic and, thus, the purpose of this work is to partially fill this lack by means of three-point bending tests on single-edge pre-cracked Terfenol-D specimens. Failure loads have been measured at different loading rates and under magnetic fields of various intensities. Since giant magnetostrictive materials are very brittle, the strain energy density (SED) approach has been exploited by means of couplefield finite element analyses. SED has revealed itself as a robust parameters in the assessment of the magnetic field and loading rate effects on fracture resistance, allowing also to propose a relationship between the radius of the control volume and the loading-rate. [ABSTRACT FROM AUTHOR]

• A comprehensive circuit model was proposed to design the magnetostrictive transducers. • The multi-physics coupling effects, inlcuding eddy current effect and the multi-rods structure are considered. • The cut-off frequency of the magnetostrictive is reduced by cutting, thus suppressing the eddy current loss. • An UMLT and the experimental platform were built. Results indicate that the proposed model offers higher accuracy. • The proposed model has a good prediction accuracy of TCR and impedance characteristics of UMLT. Underwater magnetostrictive longitudinal-type transducers (UMLT) are widely used for high-power sonar applications to generate sound waves. When designing an UMLT, to establish an effective model is one of the most necessary but difficult tasks. However, due to the special properties of giant magnetostrictive materials (GMM), the traditional design methods of transducer are completely inapplicable. Therefore, an electro-magneto-mechanical multi-field coupling model is established in this paper, and the eddy current effect, multi-GMM rod structure and other factors are fully considered. Based on the model, the resonant frequency, impedance characteristics and transmitting current response can be calculated to guide the design of UMLT. To verify the feasibility of the proposed model, a measurement experiment platform is constructed. The results validate that the proposed model is effective and more accurate than the conventional model. Thus, it can also be considered as a guideline for the design and analysis of UMLT. [ABSTRACT FROM AUTHOR]

The aim of the present study is to characterize the fracture behavior of the giant magnetostrictive Terfenol-D alloy, both experimentally and numerically. Three-point bending tests have been carried out on single-edge precracked specimens, and fracture loads have been measured at different loading rates, in the presence or absence of a magnetic field. In recent years, it has been shown that the strain energy density (SED), averaged in a finite control volume, can successfully predict brittle failures of cracked, U- and V-notched specimens made of several materials. By performing coupled-field finite element analyses, the effects of the magnetic field and he loading rate on Terfenol-D failures have been analyzed, and the capability of SED criterion to capture these effects has been discussed. A relationship between the SED control volume size and the loading rate has been proposed, and failures have been quite accurately predicted in terms of the averaged SED. [ABSTRACT FROM AUTHOR]

Nonlinear magneto-electric response characteristics of a giant magnetostrictive-piezoelectric composite sensor subjected to harmonic and colored noise magnetic excitation are discussed in this paper. A nonlinear dynamic model for such a sensor has been developed. The expression of the system's dynamic response was obtained, and the bifurcation conditions were determined. Finally, the effects of the system parameters on the dynamic characteristics were analyzed. The results of numerical simulation and experiments show that the stochastic noise intensity has an important influence on the system's dynamic response, and the stochastic resonance phenomenon occurs as the stochastic noise intensity varies. The results of this study are helpful for achieving the optimal design and improvement of giant magnetostrictive-piezoelectric composite sensors. [ABSTRACT FROM AUTHOR]

The effect of temperature on the performance of a giant magnetostrictive ultrasonic transducer (GMUT) was investigated by measuring variations in the resonance frequency and mechanical quality factor of the GMUT at different temperatures. The equivalent circuit model of the GMUT was presented and the total electrical impedance equation was obtained. Curves of the impedance circle were obtained at different temperatures to determine the resonance frequency and mechanical quality factor. To verify the impedance-based results and obtain precise values of the resonance frequency and effective frequency bandwidth, the amplitude-frequency response within the same temperature range was examined experimentally. These results were consistent with those of the impedance analysis, which demonstrates the validity of the equivalent circuit model. Moreover, the resonance frequency and effective bandwidth of the GMUT were found to decrease with increasing temperature, which means that the vibration amplitude is more sensitive to variation in the resonance frequency at high temperature owing, for example, to static or dynamic system loading, changes in the material properties, or drive-signal variability. Accordingly, the temperature in the GMUT should be precisely controlled to improve the stability of vibration. [ABSTRACT FROM AUTHOR]

• The study of temperature characteristics of magnetic and elastic parameters of giant magnetostrictive material. • Comprehensive measurement of magnetization curve, magnetostriction curve and acoustic wave propagation velocity variation with temperature of giant magnetostrictive materials. • The research of giant magnetostrictive transducer to meet the actual needs is not only of great significance for the remote transmission technology of acoustic wave data with drilling, but also can drive the development of oil viscosity reduction and oil recovery rate, etc. The magnetic and elastic parameters of the Terbium Dysprosium Iron (abbreviated as TFD)giant magnetostrictive material are important fundamental parameters for the design of magnetostrictive transducer based on the piezomagnetic analogy method. Therefore, the study of temperature characteristics of magnetic and elastic parameters of giant magnetostrictive material can help to grasp the law of temperature influence on the working performance of the giant magnetostrictive transducer. In this paper, the variation patterns of magnetic and elastic parameters with temperature for a total of three tangential types of giant magnetostrictive material samples, including the sample along the magnetostrictive direction(TFD-1#), the sample perpendicular to the magnetostrictive direction(TFD-3#) and the sample at an angle of 45° to the magnetostrictive direction(TFD-2#), were comprehensively measured under different external magnetic field conditions. The experimental results showed that: The magnetostriction coefficient is linearly related to the external magnetic field in the range of 10 MPa pre-stress and 50∼150 kA/m external magnetic field (the same below), corresponding to the dynamic operating range of the magnetostrictive transducer. In this interval, the magnetostrictive strain constants d 31 and d 33 show a single-peak pattern of increasing and then decreasing with increasing external magnetic field, it changes slowly and modestly with increasingly temperature; The relative permeability of the giant magnetostrictive materials μ r 11 and μ r 33 decreases with increasing external magnetic field and temperature at an external magnetic field below 150 kA/m; The elastic constant increases with increasing external magnetic field and decreases with increasing temperature. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear and coupled constitutive model for giant magnetostrictive materials (GMM) is employed to predict the active vibration suppression process of cantilever laminated composite plate with GMM layers. The nonlinear and coupled constitutive model has great advantages in demonstrating the inherent and complicated nonlinearities of GMM in response to applied magnetic field under variable bias conditions (pre-stress and bias magnetic field). The Hamilton principle is used to derive the nonlinear and coupled governing differential equation for a cantilever laminated composite plate with GMM layers. The derived equation is handled by the finite element method (FEM) in space domain, and solved with Newmark method and an iteration process in time domain. The numerical simulation results indicate that the proposed active control system by embedding GMM layers in cantilever laminated composite plate can efficiently suppress vibrations under variable bias conditions. The effects of embedded placement of GMM layers and control gain on vibration suppression are discussed respectively in detail. [ABSTRACT FROM AUTHOR]

The variations of magnetization and magnetostriction with temperature and stress were investigated through the analysis of the effective field, induced by temperature and stress. A nonlinear magnetostrictive model of giant magnetostrictive materials was proposed. The proposed model can be used to calculate the magnetostrictive characterization of giant magnetostrictive materials in different temperatures and under different stresses. The coupling effects of axial stress, magnetic field, and temperature on the magnetostriction of a Terfenol-D rod were numerically simulated as well as experimentally tested. Comparison between the calculating and experimental results shows that the proposed model can better describe the magneto-thermo-mechanical characteristics of Terfenol-D rod under different temperatures and compressive stress. Therefore, the proposed model possesses an important significance for the design of magnetostrictive devices. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the development of a magneto-elastic coupling dynamic loss hysteresis model for giant magnetostrictive materials (GMMs). Considering the eddy current loss and anomalous loss, a dynamic constitutive model is proposed to predict the dynamic hysteresis behavior of GMMs. The model is validated by comparing the predicted results with experiments. At first, the frequency effect and anisotropy effect on the domain distribution can be obtained. Moreover, the magnetostriction cannot return to the initial value near the coercive field as the magnetization does with the increasing frequency. It can be explained that the domain distribution changes with the increasing energy loss. The model is benefit for the design and control of GMMs actuators. [Copyright &y& Elsevier]

Giant magnetostrictive materials are a kind of functional materials developed since 1970s, known as their large magnetostrain and high energy density. In this paper, an introduction of magnetostriction and the history of magnetostrictive materials are described firstly. Then we review the recent developments of both rare earth and non-rare earth magnetostrictive materials. Finally, the tendency of developing new giant magnetostrictive materials is presented. [ABSTRACT FROM AUTHOR]

Conclusions . A new giant magnetostrictive bone conduction transducer (GMT) measuring 8 mm (length) by 2 mm (diameter) is capable of outputting sounds over a wider range of frequencies than conventional electromagnetic transducers (EMTs). The GMT can vibrate the rat skull about 3–100 times faster than the EMT, especially above 2 kHz. Objectives . Since the GMT can generate high sound quality and output sounds above 10 kHz, we investigated the width of the frequency response of the GMT and evaluated its mechanical performance. Materials and methods . We chose Wistar rats to estimate the GMT performance by measuring the bone-conducted ABR and the skull vibratory velocity because their hearing frequency range extends from 0.15 kHz to 67 kHz. We also measured the bone-conducted auditory brainstem responses (ABRs) and the skull vibratory velocity of rats with the EMT. Skull vibratory velocity was measured with a laser Doppler vibrometer (LDV). Results . The skull vibratory velocity at the ABR threshold obtained with each transducer was within the -35 to -50 dB range (0 dB re 1 mm/s). When 1 Vpp was applied to each transducer, the GMT had a higher velocity at frequencies of 2–30 kHz, and the EMT at frequencies of 0.5–1 kHz. [ABSTRACT FROM AUTHOR]

Abstract: The magnetic properties and the phase structure of Tb1− x Pr x Fe1.96 () were studied. It is found that the saturation magnetization on easy axis is decreased with increasing of Pr content, from 77.24Am2 kg−1 for , reduces to minimum value of 11.84Am2 kg−1 for , and returns to 37.14Am2 kg−1 for . The non-cubic phases appear beyond and the matrix changes from TbFe2 phase for to (Tb, Pr)Fe3 phase for , at last to (Tb, Pr)2Fe17 phase for . The compound structures turn more complex as the Pr content increased. [Copyright &y& Elsevier]

Abstract: The melt-textured technique in a magnetic field for giant magnetostrictive materials TbFe x and Tb0.3Dy0.7Fe x (1.9⩽ x ⩽2) alloy was investigated. The cooling rate, melt temperature, and the chemical composition were found to influence the texture formation along the easy magnetic axis during crystallization in a field. The experiments showed that the 〈111〉 orientation of Tb0.3Dy0.7Fe1.9 and TbFe1.9 alloy was dominant in the samples when those alloys were solidified at a cooling rate of less than 0.8°C/min from a temperature slightly above their melting point, respectively, while in a magnetic field of above 100mT. However, with the Fe concentration increasing from x =1.93, excessive RFe3 phases precipitate in the melt and degrade the orientation degree of the sample during the slow solidification. Therefore the chemical composition of Tb0.3Dy0.7Fe x and TbFe x alloy should be controlled within 1.90⩽ x ⩽1.93 for better orientation and comprehensive performance. [Copyright &y& Elsevier]

Aiming at a reduction in time and high efficiency in computation, a set of simple formulas characterizing a giant magnetostrictive material is proposed. It can represent nonlinearity of the magnetic properties with respect to both the magnetic field intensity and the mechanical stress, using easy-to-handle formulas with some adjustable parameters read from measured data resources. [ABSTRACT FROM AUTHOR]

Local re-orientation of magnetization and stress which occurs during changes of global magnetization in magnetostrictive multilayers is quite complicated. However, if the local magnetic state is known and if the multilayer is deposited on a typical substrate, the local stresses can be calculated. A general method for stress calculations is given and is illustrated for spring-magnet-type multilayers whose layers exhibit no magnetocrystalline anisotropy or are amorphous. When the substrate is isotropic, the stored elastic energy is the same for all magnetic domains. Consideration of other energies such as magnetoelastic, potential magnetic energy, and domain wall energy indicates that the domain structure must depend on entropy. As the applied magnetic field is varied, a variation in the local magnetoelastic anisotropy occurs for each region in the material. [Copyright &y& Elsevier]

There is a strong interaction of stress and magnetization in magnetostrictive materials which can be traced back to the corresponding elastic energy and magnetoelastic energy terms. In particular, an applied stress or magnetic field can be used to provide a bias which can then ensure large magnetostrictive actuation at minimum coercive field. The use of stress is especially interesting in the case of thin films because it can be conveniently introduced by means of the substrate. In this work, the basic formulations for the elastic, magnetoelastic and potential magnetic energies of an isotropic material, and the assumption that the film is in state of plane stress are combined in a consistent model that is used to study the effect of a stress bias which is created by bending a substrate during deposition of a magnetostrictive multilayer. Using this framework, the biaxial stresses induced in the thin film after the substrate is released and the multilayer total energy are calculated. The effect of energy contributions from strains in the thickness direction is shown to be unimportant, since they provide a constant, orientation-independent contribution which does not affect in-plane magnetization switching. The multilayer total energy, which is shown to vary with magnetic domain orientation, is minimized to find the orientation of the easy axis as well as to estimate the magnetization along various hard axis directions when an external field is applied in those directions. The uniaxial anisotropy energy and the anisotropy field are also calculated and the results are in good agreement with reported data. These calculations are seen to offer significant improvement over the ones obtained with previous models that consider films subjected to uniaxial stresses and to be governed only by variations of the magnetoelastic energy. [Copyright &y& Elsevier]

• The first study to establish a mathematical model for optimum compensation of a GMUT. • The first study showing resonance characteristics for frequency tracking of a GMUT. • The optimum compensation capacitance can maximize the use of ultrasonic energy. • The feedback current signal can be used for the frequency tracking method of a GMUT. Giant magnetostrictive materials (GMMs) have been widely used to fabricate transducers with high-energy output because of their excellent properties. However, there are few reports on mathematical models to optimize the impedance compensation and resonance characteristics of giant magnetostrictive transducers. In this study, a giant magnetostrictive ultrasonic transducer (GMUT) suitable for rotary ultrasonic machining systems is proposed. A mathematical model for optimum impedance compensation that considers the loss in energy conversion is established to maximize the use of ultrasonic energy. The frequency characteristics of the electrical feedback signal in the resonance state are investigated, and the resonance zone found is used for frequency tracking. An impedance analyzer is used to determine the parameters of the mathematical model, and the validity of the optimum compensation capacitance is verified by experiments. The frequency characteristics of the minimum current, active power, and amplitude are obtained to obtain the resonance zone in the GMUT with the lowest energy consumption. The results of this study provide a reference for frequency tracking. [ABSTRACT FROM AUTHOR]

The paper presents the numerical and experimental investigations of the axisymmetric magnetostrictive actuator with a Terfenol-D rod. The applied model consists of equations that describe the magnetic and mechanical displacement fields. The equations of both fields are coupled through a nonlinear magneto-mechanical constitutive law. The model is considered as 2D axisymmetric. The finite element method is used to solve the field equations. Special attention is paid to the proper definition of magneto-mechanical relations. These relations are formed from measurements. A unique test stand is designed for the experimental investigation. The selected results of the simulation are compared with the measurement results. The comparison shows that the applied numerical model is sufficiently accurate. [ABSTRACT FROM AUTHOR]