Electromagneto-mechanical fields of giant magnetostrictive/piezoelectric laminates

This paper presents the nonlinear electromagneto-mechanical behavior of magnetostrictive/piezoelectric laminated pieces under magnetic fields both numerically and experimentally. The pieces are fabricated using thin Tb_0.3Dy_0.7Fe₂ (Terfenol-D) and Pb(Zr,Ti)O₃ (PZT) layers, and the magnetostriction of the pieces is measured. A nonlinear finite element analysis is also employed to evaluate the second-order magnetoelastic constants in Terfenol-D layer bonded to the PZT layer, and the nonlinear displacement, internal stresses and induced voltage for the magnetostrictive/piezoelectric laminated pieces under magnetic fields are discussed.     

A theoretical study of nonlinear magnetoelectric effect in magnetostrictive–piezoelectric trilayer

A novel nonlinear theoretical model is established for magnetoelectric (ME) effect in trilayer of magnetostrictive and piezoelectric phases, in which the nonlinear magnetic–mechanical coupling behavior for the magnetostrictive phase is firstly taken into account. In this theoretical model, the interface coupling parameter k is used for characterizing actual bonding conditions at the interface. The coupled magnetic–mechanical–electric effect involving linear and nonlinear coupling interactions in the ME laminated composites is numerically simulated using this nonlinear model. The numerical results predict giant ME effect for Terfenol-D based ME laminated composites. The quantitative dependences of the giant ME effect on the applied magnetic field, the piezoelectric property of piezoelectric phase, the volume fraction of magnetostrictive phase and the interface coupling parameter k are discussed in details. All of these dependences indicate that the nonlinear theoretical model established in this article can accurately capture nonlinear magnetic–mechanical–electric coupling behavior for Terfenol-D based ME laminated composites. The giant ME effect predicted for the Terfenol-D/PMN-PT/Terfenol-D composites is in excellent agreement with recent experimental data available. It confirms the validity and reliability of the obtained nonlinear theoretical model, and demonstrates the significance and necessity of considering the nonlinear magnetic–mechanical coupling behavior of Terfenol-D.     

Effect of Electric Field on the Response of Clamped-FreeMagnetostrictive/Piezoelectric/Magnetostrictive Laminates

This work deals with the response of clamped-free magnetostrictive/piezoelectric/magnetostrictive laminates under electric field both numerically and experimentally. The laminate is fabricated using two magnetostrictive Terfenol-D layers and a soft piezoelectric PZT layer. Easy axis of Terfenol-D layers is length direction, while the polarization of PZT layer is the thickness direction. The magnetostriction of the Terfenol-D layers bonded to the upper and lower surfaces of the PZT layer is first measured. Next, a nonlinear finite element analysis is employed to evaluate the second-order magnetoelastic constants in the Terfenol-D layers bonded to the PZT layer using measured data. The induced magnetic field and internal stresses for the laminates under electric field parallel to the poling are then calculated and discussed in detail. In addition, the induced magnetic field is measured, and test results are presented to validate the predictions.     

层状复合材料磁电效应的数值分析

压电与压磁(或磁致伸缩)层合板具有大的乘积效应磁电效应。本文采用有限元分析方法对压电/压磁层合板的磁电转换进行了计算,结果表明:外磁场方向对磁电转换效应有很大的影响,在层合板上下两面增加约束可以大大提高层合板的磁电转化效应;感生电压值随压磁/压电板厚比的增加而增加,而整个层合板的电场强度值在板厚比为1时达到最大。     

Design of magnetostrictive/piezoelectric laminate composite for coil-less magnetic force control

We propose a magnetic force control device consisting of laminate composites of magnetostrictive material and piezoelectric material. The magnetic force control is based on energy conversion in the composite, such that the variation of magnetization of the magnetostrictive material induced by the piezoelectric material is converted to the variation of magnetic force by magnetic circuits. Because of the capacitive property of the piezoelectric material, the device requires little current in order to maintain control of a constant force. The laminate composite can be fabricated easily and in small sizes. In this paper, we report the magnetic force control properties of a composite of Terfenol-D and piezoelectric material plates (PZTs) and discuss the design of the laminate composite. Our theoretical magnetic force formulation derived by an equivalent magnetic analysis and finite-element analysis of strain distribution in the Terfenol-D, and measurements with various thicknesses of PZT demonstrated that there are appropriate thicknesses to provide large variation of the magnetic force and energy conversion efficiency. Stacking the composites was found effective for increasing the effective area of the Terfenol-D.     

Numerical Simulation of Nonlinear Dynamic Responses of Beams Laminated with Giant Magnetostrictive Actuators

This paper presents some simulation results of nonlinear dynamic responses for a laminated composite beam embedded by actuators of the giant magnetostrictive material (Terfenol-D) subjected to external magnetic fields, where the giant magnetostrictive materials utilizing the realignment of magnetic moments in response to applied magnetic fields generate nonlinear strains and forces significantly larger than those generated by other smart materials. To utilize the full potential application of the materials in the function and safety designs, e.g., active control of vibrations, the analysis of dynamic responses is requested in the designs as accurately as possible on the basis of those inherent nonlineary constitutive relations among stain, force and applied magnetic field existed in the materials. Here, a numerical code for the nonlinear vibration of laminated beams is proposed on the basis of a nonlinearly coupling constitutive model which fully behaves for the characteristics what are measured in experiments. It is found from this code that the natural frequency of the laminated beams changes with both the bias magnetic field and the pre-stresses, and the dynamic responses excited by an alternating magnetic field of simple harmonic form display strong nonlinear characteristics, for example, the frequency multiplication and the ultraharmonic resonance phenomena.     

Longitudinal and transverse magnetoelectric voltage coefficients of magnetostrictive/piezoelectric laminate composite: theory

This paper presents a novel, long-type of magnetostrictive and piezoelectric laminate composite design in which the layers are, respectively, magnetized/poled along their length axes, and a theory for modeling its behavior. Using piezoelectric and magnetostrictive constitutive equations, and an equation of motion, a magneto-elasto-electric bieffect equivalent circuit is developed. The circuit is used to predict the longitudinal and transverse magnetoelectric (ME) voltage coefficients of our Terfenol-D/Pb(Zr/sub 1-x/Ti/sub x/)O/sub 3/ laminate design. It is found that the longitudinal ME voltage coefficient is significantly higher (/spl sim/5x) than the transverse one, and that our new laminate design has significantly higher ME voltage coefficients under small applied direct current (DC) magnetic bias fields than designs reported previously by other groups. Experimental values were found to be coincidental with predicted ones.     

An analytical nonlinear model for laminate multiferroic composites reproducing the DC magnetic bias dependent magnetoelectric properties

In this work, we propose an analytical nonlinear model for laminate multiferroic composites in which the magnetic-field-induced strain in magnetostrictive phase is described by a standard square law taking the stress effect into account, whereas the ferroelectric phase retains a linear piezoelectric response. Furthermore, differing from previous models which assume uniform deformation, we take into account the stress attenuation and adopt non-uniform deformation along the layer thickness in both piezoelectric and magnetostrictive phases. Analysis of this model on L-T and L-L modes of sandwiched Terfenol-D/lead zirconate titanate/Terfenol-D composites can well reproduce the observed dc magnetic field (H(dc)) dependent magnetoelectric coefficients, which reach their maximum with the H(dc) all at about 500 Oe. The model also suggests that stress attenuation along the layer thickness in practical composites should be taken into account. Furthermore, the model also indicates that a high volume fraction of magnetostrictive phase is required to get giant magnetoelectric coupling, coinciding with existing models.     

Field-Circuit Hybrid Method for Magnetic Actuator Using a Laminate Composite

The magnetic actuator using a laminate composite of piezoelectric (PZT) and magnetostrictive materials (MM) achieves active control of magnetic force without Joule heat loss. To study its characteristics, the field-circuit hybrid method is proposed based on the equivalent magnetic circuit and the finite element analysis (FEA) of piezoelectric and magnetic fields. The strain of laminate composite under different voltage is obtained through the piezoelectric FEA. On the basis of magnetostrictive equation, the MM branch in the magnetic circuit of the actuator is transformed equivalently, the work point of the actuator is determined, and the corresponding FEA model of magnetic analysis is then set up. The relationships between magnetic force, gap, and voltage are discussed by the hybrid method, which can be expanded into the design and analysis of the magnetostrictive actuator and sensor to improve simulation efficiency and precision.      

Active control of forced vibrations in adaptive structures using a higher order model

This paper deals with a finite element formulation for active control of forced vibrations, including resonance, of thin plate/shell laminated structures with integrated piezoelectric layers, acting as sensors and actuators, based on third-order shear deformation theory. The finite element model is a single layer triangular nonconforming plate/shell element with 24 degrees of freedom for the generalized displacements, and one electrical potential degree of freedom for each piezoelectric element layer, which are surface bonded or embedded in the laminate.

The Newmark method is considered to calculate the dynamic response of the laminated structures, forced to vibrate in the first natural frequency. To achieve a mechanism of active control of the structure dynamic response, a feedback control algorithm is used, coupling the sensor and active piezoelectric layers. The model is applied in the solution of illustrative cases, and the results are presented and discussed.     

An adhesively laminated plate element for PZT smart plates

An adhesively laminated element taking into consideration peel stress is developed for a piezoelectric smart plate. In this novel finite element analysis formulation, a four node piezoelectric element is firstly derived, and an adhesive element of finite thickness with both shear and peel stiffness is sandwiched between two collocated four node plate elements to form an adhesively laminated element for a piezoelectric smart plate. In this framework of finite element analysis, because the displacement filed in this adhesively laminated element is continuous and a plate element is derived based on the Reissner–Mindlin plate theory, and thus it can be accurately applied to a thin or moderately thick host plate with bonded or debonded piezoelectric actuators and sensors. The formulation is performed for an isotropic host plate and a fiber reinforced laminate plate. Numerical results are presented to compare with those of the exact solutions for smart beams, and validate with the experimental results of the isotropic and composite host plates available in the literature. Using the present finite element analysis formulation, energy transfer stresses in the adhesive and equivalent forces induced in the host plate are investigated. The present formulation is demonstrated to allow debondings of piezoelectric patches and the debonding detection.The authors are grateful to the support of the Australian Research Council via a Discovery Projects grant (grant No: DP0346419).     

Magnetic force control with composite of giant magnetostrictive and piezoelectric materials

We propose a new magnetic force control device, composed of a giant magnetostrictive material (Terfenol-D) and a piezoelectric material (PZT), for coilless magnetic force control. The device uses the inverse magnetostrictive effect, whereby the variation of magnetization of a Terfenol-D rod controlled by PZT is converted to the variation of magnetic force by a magnetic circuit. Because PZT is electrically capacitive, the method has the advantage of low power consumption and low heat generation in static operation. We have fabricated several devices with different geometrical shapes of the rods and magnetic yokes, and we describe their characteristics such as power consumption, heat generation, and response. We discuss a magnetic circuit design strategy that uses the /spl Delta/E effect in magnetostrictive materials to increase the energy conversion efficiency.     

压电/磁致伸缩/环氧树脂层合复合材料的磁电效应及其频响特性

磁电复合材料在磁-电能量转换等领域具有重要的潜在应用价值, 研究磁电复合材料在较高频率下的磁电耦合特性对于实际应用具有重要意义。本文中以0-3型的Terfenol-D(Tb_0.30Dy_0.70Fe₂)/环氧树脂复合材料为磁致伸缩层, 以PZT 压电陶瓷为压电层, 制备了三明治结构的层合磁电复合材料。研究了Terfenol-D/环氧树脂复合材料层的磁致伸缩性质, 并对所制备的层合磁电复合材料磁通密度、 介电常数以及磁电电压系数等随频率和偏磁场的变化规律进行了系统研究。结果表明, 由于Terfenol-D/环氧树脂复合材料的引入, 层合磁电复合材料呈现出良好的频率响应特性, 可靠工作范围大大拓宽。层合磁电复合材料具有优良的动态磁电耦合性能, 在优化偏磁场630 Oe和共振频率69.6kHz下的磁电效应高达21.2 V/cmOe。此外, 层合磁电复合材料的磁电效应随偏磁场的变化发生明显变化, 并存在优化偏磁场。对上述现象和结果进行了详细讨论, 并给出了层合磁电复合材料的磁电耦合机制。      

Modeling of magnetostriction in particulate composite materials

By combining a magnetostrictive material with a polymer or a metal, the magnetostrictive composites can have a reasonably large magnetostriction response for various sensor and actuator applications. In this paper, a relatively simple model for studying the magnetostrictively induced deformation behavior of magnetostrictive composites is presented. For illustrative purposes, we calculate the magnetostriction responses of composites containing Terfenol-D and nickel. Through numerical calculation, we have obtained the macroscopic longitudinal strains parallel to the applied magnetic field for Terfenol-D/glass composite and both longitudinal and transverse strains for the nickel/epoxy composite. Comparison with experimental data for both material systems shows our model is applicable up to very high volume fraction of magnetostrictive inclusions.     

Coupled mechanics and finite element for non‐linear laminated piezoelectric shallow shells undergoing large displacements and rotations

A theoretical framework is presented for analysing the coupled non‐linear response of shallow doubly curved adaptive laminated piezoelectric shells undergoing large displacements and rotations. The formulated mechanics incorporate coupling between in‐plane and flexural stiffness terms due to geometric curvature, coupling between mechanical and electric fields, and encompass geometric non‐linearity effects due to large displacements and rotations. The governing equations are formulated explicitly in orthogonal curvilinear co‐ordinates and are combined with the kinematic assumptions of a mixed‐field shear‐layerwise shell laminate theory. Based on the above formulation, a finite element methodology together with an incremental‐iterative technique, based on Newton–Raphson method is formulated. An eight‐node coupled non‐linear shell element is also developed. Various evaluation cases on laminated curved beams and cylindrical panels illustrate the capability of the shell finite element to predict the complex non‐linear behaviour of active shell structures including buckling, which is not captured by linear shell models. The numerical results also show the inherent capability of piezoelectric shell structures to actively induce large displacements through piezoelectric actuators, by jumping between multiple equilibrium states. Copyright © 2005 John Wiley & Sons, Ltd.     

Non-linear coupled multi-field mechanics and finite element for active multi-stable thermal piezoelectric shells

In this paper, a coupled multi-field mechanics framework is presented for analyzing the non-linear response of shallow doubly curved adaptive laminated piezoelectric shells undergoing large displacements and rotations in thermal environments. The mechanics incorporate coupling between mechanical, electric and thermal fields and encompass geometric non-linearity effects due to large displacements and rotations. The governing equations are formulated explicitly in orthogonal curvilinear coordinates and are combined with the kinematic assumptions of a mixed-field shear-layerwise shell laminate theory. A finite element methodology and an eight-node coupled non-linear shell element are developed. The discrete coupled non-linear equations of motion are linearized and solved, using an extended cylindrical arc-length method together with a Newton–Raphson technique, to enable robust numerical predictions of non-linear active shells transitioning between multiple stable equilibrium paths. Validation and evaluation cases on laminated cylindrical strips and cylindrical panels demonstrate the accuracy of the method and its robust capability to predict non-linear response under thermal and piezoelectric actuator loads. Moreover, the results illustrate the capability of the method to model piezoelectric shells undergoing large shape changes by actively jumping between stable equilibrium states and quantify the strong relationship between shell curvature, applied electric potential, applied temperature differential and induced shape change. Copyright © 2008 John Wiley & Sons, Ltd.     

磁致伸缩层合悬臂梁式作动器的振动分析

为了分析磁致伸缩薄膜型层合悬臂梁式作动器的振动问题,应用磁致伸缩材料的非线性本构关系,由哈密尔顿原理导出了双层悬臂梁的振动微分方程。采用分离变量方法和常微分方程组的解析解法对磁致伸缩薄膜型层合悬臂梁的自由振动和受迫振动进行了理论分析。数值算例表明本文计算结果与有限元结果吻合较好,从而佐证了本文理论模型和求解方法的正确性,并讨论了几何参数、材料参数对层合梁固有频率的影响。还分析了在周期输入磁场激励下悬臂梁的挠度响应,且挠度响应呈现出倍频效应的动态特性。      

压电层合板层间应力新研究

综述了压电层合板数值分析方面的一些进展，在一般层合板理论的基础上提出一个多层压电层合板单元，依据线性压电理论建立压电层合板单元的杂交元模型，利用三维8节点块状单元建立多层压电层合板的有限元列式，解决了压电层合板层间应力的连续性。     

一种基于Layerwise理论的压电复合材料层合圆柱壳机电耦合有限单元

基于Reddy的Layerwise理论,对含压电铺层的复合材料层合壳的静力响应特性进行了理论研究。基于Layerwise理论,推导了含压电层的复合材料层合壳的应变分量与电场强度表达式。利用Hamilton原理和变分法,推导了压电智能层合壳的欧拉-拉格朗日方程,并采用有限元解法,建立了相应的有限元控制方程及其机电耦合刚度矩阵。通过算例结果与文献中的精确解和试验值进行了对比,表明相较于传统的经典层合板壳理论,本文理论方法的有效性和优势性;并分析了径厚比等参量对两端简支压电智能层合壳静力响应值的影响规律。      

Modeling of a rotary motor driven by an anisotropic piezoelectric composite laminate

This paper proposes an analytical model of a rotary motor driven by an anisotropic piezoelectric composite laminate. The driving element of the motor is a three-layer laminated plate. A piezoelectric layer is sandwiched between two anti-symmetric composite laminae. Because of the material anisotropy and the anti-symmetric configuration, torsional vibration can be induced through the inplane strain actuated by the piezoelectric layer. The advantages of the motor are its magnetic field immunity, simple structure, easy maintenance, low cost, and good low-speed performance. In this paper, the motor is considered to be a coupled dynamic system. The analytical model includes the longitudinal and torsional vibrations of the laminate and the rotating motion of the rotor under action of contact forces. The analytical model can predict the overall characteristics of the motor, including the modal frequency and the response of motion of the laminate, the rotating speed of the rotor, the input power, the output power, and the efficiency of the motor. The effects of the initial compressive force, the applied voltage, the moment of rotor inertia, and the frictional coefficient of the contact interface on the characteristics of the motor are simulated and discussed. A selection of the numerical results from the analytical model is confirmed by experimental data.