Piezoelectric Laminates Research Articles

Improved one-dimensional model of piezoelectric laminates for energy harvesters including three dimensional effects

The application of piezoelectric composites in energy harvesters is continuously increasing even at the microscale, with the immediate corollary of a fundamental need for improved computational tools for optimization of performances at the design level. In this paper, a refined, yet simple model is proposed with the aim of providing fast and insightful solutions to the multi-physics problem of energy harvesting via piezoelectric layered structures. The main objective is to retain a simple structural model (Euler–Bernoulli beam), with the inclusion of effects connected to the actual three-dimensional shape of the device. A thorough presentation of the analytical model is presented, along with its validation by comparison with the results of fully 3D computations.

Broadband energy harvesting by exploiting nonlinear oscillations around the second vibration mode of a rectangular piezoelectric bistable laminate

Recently bistable composite laminates have been investigated for broadband energy harvesting, by taking advantage of their nonlinear oscillations around the first vibration mode. However, it has been reported that the excitation acceleration needed for the desired large amplitude limit cycle oscillation is too high, if the first vibration mode is elevated to relative higher frequencies (60 Hz e.g.). This study investigates the feasibility of exploiting the nonlinear oscillations around the second vibration mode of a rectangular piezoelectric bistable laminate (RPBL), for broadband vibration energy harvesting at relative higher frequencies, but with relative low excitation acceleration. The proposed RPBL has three oscillation patterns around the second vibration mode, including single-well oscillation, chaotic intermittency oscillation and limit cycle oscillation. The broadband characteristics and the considerable energy conversion efficiency of the RPBL are demonstrated in experiments. The static nonlinearity and the dynamic responses of the RPBL are investigated by finite element method. Finite element analysis (FEA) reveals that the enhanced dynamic responses of the RPBL are due to its softening bending stiffness and the local snap through phenomenon. The FEA results coincide reasonably well with experimental results.

Finite Element Formulation for Active Composite Laminates

Smart structures are characterized by a synergistic integration of active materials into a passive structure connected by a control system to enable an automatic adaptation to changing environmental conditions. Piezoelectric materials are widely used as distributed sensors and actuators in smart structures, where especially hybrid composites - a combination of fiber-reinforced and piezoelectric laminae - are very powerful smart material systems. First, a brief review of the developed shell type finite element for smart composite structures is presented. It is a degenerated shell element based on the Reissner-Mindlin kinematical assumptions for modeling thin and moderately thick structures made of multilayered material including piezoelectric active layers polarized in the thickness direction. The main focus of the paper is put on the test examples originally proposed by other authors. The finite element results were compared with the reference solutions obtained by Ritz type approximations. The considered test cases investigate the effects of shell shallowness, bending/twisting coupling and the influence of the piezoelectric layer thickness on the deformation of the laminated structure.

Modeling and design of field programmable gate array based real time robust controller for active control of vibrating smart system

The current paper focuses on accurate mathematical modeling of a vibrating piezoelectric laminate cantilever beam theoretically as well as experimentally so as to obtain the best replication of the system dynamics on the software platform for simulation studies. The developed models were tested for accuracy in time as well as frequency domain by employing the sweep sine test. The focus of the study is on the flexural modes of vibrations of the cantilever beam. Here, modeling is focused on the first vibratory mode as it has been observed that the effects of felt vibrations would be maximum in terms of system stability and its operational efficiency when the excitation frequency matches with the first natural frequency of the system (fn1). This was validated by appropriate non-parametric modeling of the smart system by subjecting it to the Impact Hammer test. Development of accurate system models play an important role in designing and testing various control algorithms for reliable active vibration control (AVC). In the final stage, a real time active vibration robust controller was designed using a proportional derivative sliding mode control (PDSMC) technique and deployed on a Field Programmable Gate Array (FPGA) platform. The efficiency of the developed real time controller was proved in time as well as frequency domains by subjecting the closed loop system to harmonic excitations at first natural frequency as well as sweep sine test focussing on the first vibratory mode with the conclusion that the developed controller will function satisfactorily at higher modes of vibrations.

OS0507-129 界面に垂直なき裂を有する傾斜機能圧電積層平板の電気熱弾性応答

OS0507-129 界面に垂直なき裂を有する傾斜機能圧電積層平板の電気熱弾性応答

Higher-order 2-D/3-D layerwise mechanics and finite elements for composite and sandwich composite plates with piezoelectric layers

Coupled higher-order layerwise piezoelectric laminate mechanics are presented, applicable to composite and sandwich composite plates subjected to static mechanical loads and/or electric voltages. In the development of these formulations through-thickness compressibility is either considered (3-D) or neglected (2-D). Their advantage compared to linear layerwise theories lies in the efficient prediction of the local through-thickness response by using a gross through-thickness discretization, while retaining simplicity in through-thickness kinematic assumptions. Moreover, they enable prediction of interlaminar shear and transverse normal stress at the interface between discrete layers, which is crucial information for prediction of delamination initiation. Using the developed mechanics, the effects of transverse compressibility and ply angle on the local through-thickness response of composite and sandwich plates are studied.

2D semi-analytical solutions for single layer piezoelectric laminate subjected to electro-mechanical loading

Analysis of a piezoelectric laminate under plane strain condition of elasticity (cylindrical bending) has been performed with mixed semi-analytical model developed by Kant et al. (2007). The in-plane displacement, transverse displacement, transverse normal and shear stresses, electric potential and transverse electric displacement have been considered as fundamental dependent variables. The mathematical model consists of defining a two-point boundary value problem (BVP) governed by a set of coupled first order ordinary differential equations (ODEs). The accuracy and efficiency of the proposed model are assessed by comparing the numerical results from the present investigation with available elasticity solutions.

Transient waves propagating in a two-layered functionally graded piezoelectric strip

In this study, transient waves propagating in a functionally graded piezoelectric laminate subjected to uniform anti-plane mechanical and in-plane electric displacement impacts were investigated. An integral transform method was applied to obtain solutions of shear stresses and electric displacements in the Laplace transform domain. The Durbin method was then used to implement numerical inversion. The accuracy of the numerical results for the shear stress at the interface was examined, and superior parameters for Durbin inversion were suggested. The results show that the functionally graded parameters of the two-layered functionally graded piezoelectric material can either increase or decrease the values of the transient shear stresses.

Zigzag-shaped piezoelectric based high performance magnetoelectric laminate composite

We demonstrate a 33-mode piezoelectric structure with zigzag shape for high sensitivity magnetoelectric laminates. In contrast to the 33-mode macro fiber composite (MFC), this zigzag shape piezoelectric layer excludes epoxy bonding layer between the electrode and piezoelectric materials, thereby, significantly improving the polarization degree, electromechanical coupling, and the stability of loss characteristics. The polarization degree was monitored from the change in phase angle near resonance, and the loss stability was determined from the changes in dielectric loss and rate of capacitance variation defined by (C − Cf)/Cf, where C is capacitance at a given frequency and Cf is capacitance at 100 Hz. Magnetoelectric composite with zigzag patterned piezoelectric layer was found to exhibit giant magnetoelectric response both in low frequency off-resonance region (6.75 V cm−1 Oe−1 at 1 kHz) and at anti-resonance frequency (357 V cm−1 Oe−1).

Cylindrical bending responses of angle-ply piezoelectric laminates with viscoelastic interfaces

The time-dependent behavior of a simply supported, angle-ply piezoelectric laminate in cylindrical bending with viscoelastic interfaces is investigated. The interfacial bonding in piezoelectric laminates is considered to be dielectrically weakly (or highly) conducting, and mechanically compliant characterized by the Kelvin–Voigt viscoelastic law. The state-space approach, which is directly based on the piezoelectricity equations and very effective in analyzing laminated structures, is employed. For exact analysis, a state equation of the relative sliding displacements with respect to the time variable is further presented. Comparison study shows that the numerical results by the present analysis agree well with those reported before. Numerical results also indicate that the electromechanical response of the piezoelectric laminates with viscoelastic interfaces changes remarkably with time elapsing. Thus, the bonding imperfection should be considered carefully in the practical design of piezoelectric laminates.

Low-energy impact response of composite and sandwich composite plates with piezoelectric sensory layers

An efficient model reduction based methodology is presented for predicting the global (impact force, plate deflection and electric potential) and through-thickness local (interfacial strains and stresses) dynamic response of pristine simply-supported cross-ply composite and sandwich composite plates with piezoelectric sensory layers subjected to low-energy impact. The through-thickness response of the laminate is modelled using coupled higher-order layerwise displacement-based piezoelectric laminate theories. Linearized contact laws are implemented for simulating the impactor–target interaction during impact. The stiffness, mass, piezoelectric and permittivity matrices of the plate are formulated from ply to structural level and reduced by applying a Guyan reduction technique to yield the structural system in state space. This reduction technique enables the formulation of a plate–impactor structural system of minimum size (1 term per vibration mode for composite plates – 2 terms for sandwich plates) and reduces computational cost, thus facilitating applicability for real-time impact and vibration control.

Accurate prediction of free-edge and electromechanical coupling effects in cross-ply piezoelectric laminates

3D hybrid analyses on the interlaminar stresses near the free edges of piezoelectric laminated plates are presented on the basis of three-dimensional piezoelasticity. The state space equations for cross-ply piezoelectric laminates subjected to a uniform axial extension are obtained by considering all the independent elastic and piezoelectric constants. With the application of the transfer matrix and recursive solution approach, the equations satisfy the traction-free and open-circuit boundary conditions at free edges and the continuity conditions across the interfaces between material layers. Three-dimensional exact solution is sought and validated by comparing the present analytical results with those from existing approximate and finite element models. The singularities of interlaminar stresses near free edges are observed and the significant electromechanical influence on the free-edge effect is found.

Parametric modeling and FPGA based real time active vibration control of a piezoelectric laminate cantilever beam at resonance

The operational efficiency and life of mechanical systems/structures depends to a large extent on their vibration control. Continuously occurring vibrations on the systems can cause fatigue and the effects of these vibrations are particularly severe if they occur at a frequency matching with that of the concerned system’s natural frequency – a stage called resonance. This paper focuses on achieving active vibration control of a smart cantilever beam at its first resonant frequency as it is at this stage that maximum damage to the system performance is expected. The smart system is modelled in the parametric domain using finite element modeling techniques and the obtained model is validated through experimental means. The active vibration control is achieved by employing two control algorithms namely – output feedback and error based control through general purpose operating system (LabVIEW on Windows 7) as well as in real time operating system (LabVIEW FPGA coupled with compact reconfigurable input output modules) and the performances are compared thereby justifying the importance of the deterministic and reliable real time control over the usual PC based control in experimental studies.

1114 熱負荷を受ける圧電複合平板大変形のフィードバック制御に関する理論的研究(GS-3 圧電材料)

1114 熱負荷を受ける圧電複合平板大変形のフィードバック制御に関する理論的研究(GS-3 圧電材料)

Analysis of Cantilevered Laminate with Piezoelectric Ceramics PZT5A Based on ANSYS

The finite element model of piezoelectric cantilever laminate is established with ANSYS and the vibration character of the model is carried out. The vibration characters of different size of piezoelectric laminate and different voltage is compared. The maximum displacement demonstrates the trend of decreasing step by step with increasing the thickness of the base steel layer. The displacements of the same base steel layer and piezoelectric layer are increasing with the incremental voltage.

Non-linear buckling for the surface rectangular delamination of laminated piezoelectric shells

An analytical method is presented to study the non-linear buckling characteristic of rectangular local delamination near the surface of fiber-reinforced piezoelectric lamination shells under coupled mechanical and electric loads. The stacking sequence of fiber reinforced lamination shells with piezoelectric layers is considered as symmetry, but the stacking sequence of rectangular local delamination sub-shells is arbitrary. Based on the nonlinear displacement mode of delaminated sub-shells, the effects of electric fields, the geometrical, physical parameters and stacking sequences of piezoelectric laminated shells on the non-linear local buckling for rectangular delamination near the surface of piezoelectric laminated base-shells are solved.

Analytical Solutions of Loaded Multifunctional Multilayered Plates

Analytical solutions are derived for multifunctional N-layered rectangular plates. The multilayered plate may consist of linear elastic or piezoelectric laminates of arbitrary thickness. The related equations and formulae are developed based on the Stroh like formalism. Solutions for multilayered plates are expressed in terms of the propagator matrix and satisfy the continuity conditions of material layers. Various types of electrical and mechanical loading may be considered. Numerical results of stresses, electric potential and displacement for some multifunctional multilayered plates are analyzed

Explicit solution format for complex-valued natural frequency of beam with R-shunted piezoelectric laminate transducer

Analysis and design of resistive shunt circuits for piezoelectric damping of beam structures is often based on a representation in terms of the single target vibration mode of the beam, neglecting spill-over effects from the out-of-bandwidth or residual vibration modes. In this article, a solution format is derived for the complex-valued natural frequency of the beam with a shunted piezoelectric laminate transducer, where the influence from the residual modes is taken into account by a quasi-static representation. This explicit solution format contains system parameters that directly represent the authority of the transducer and the spill-over from residual modes, and it recovers the short- and open-circuit frequencies as limit solutions. Furthermore, the frequency solution format provides the basis for design expressions for the optimal resistance and the corresponding attainable damping of the beam. The accuracy of the explicit frequency solution format is verified by comparison with numerical results. It is found that the complex-valued natural frequency of the first vibration mode of a beam with a piezoelectric laminate transducer shunted to a resistance is estimated with sufficient accuracy for engineering design purposes.

Bio-inspired aquatic robotics by untethered piezohydroelastic actuation

This paper investigates fish-like aquatic robotics using flexible bimorphs made of macro-fiber composite (MFC) piezoelectric laminates for carangiform locomotion. In addition to noiseless and efficient actuation over a range of frequencies, geometric scalability, and simple design, bimorph propulsors made of MFCs offer a balance between the actuation force and velocity response for performance enhancement in bio-inspired swimming. The experimental component of the presented work focuses on the characterization of an elastically constrained MFC bimorph propulsor for thrust generation in quiescent water as well as the development of a robotic fish prototype combining a microcontroller and a printed-circuit-board amplifier to generate high actuation voltage for untethered locomotion. From the theoretical standpoint, a distributed-parameter electroelastic model including the hydrodynamic effects and actuator dynamics is coupled with the elongated-body theory for predicting the mean thrust in quiescent water. In-air and underwater experiments are performed to verify the incorporation of hydrodynamic effects in the linear actuation regime. For electroelastically nonlinear actuation levels, experimentally obtained underwater vibration response is coupled with the elongated-body theory to predict the thrust output. The measured mean thrust levels in quiescent water (on the order of ∼10 mN) compare favorably with thrust levels of biological fish. An untethered robotic fish prototype that employs a single bimorph fin (caudal fin) for straight swimming and turning motions is developed and tested in free locomotion. A swimming speed of 0.3 body-length/second (7.5 cm s−1 swimming speed for 24.3 cm body length) is achieved at 5 Hz for a non-optimized main body-propulsor bimorph combination under a moderate actuation voltage level.

Self-biased Dual-phase Energy Harvesting System

ABSTRACTIn this study, we report the design and fabrication of a dual-phase energy harvester which can synchronously harvest both mechanical and magnetic energy in the absence of DC magnetic field. The harvester consists of a magnetostrictive cantilever beam and a magnetostrictive/ piezoelectric (M/P) self-biased laminate composite structure. This structure allows us to utilize piezoelectric and self-biased magnetoelectric effect simultaneously. By combining these mechanisms together, a sum effect for harvesting both magnetic and vibration energy was realized under DC magnetic field free condition. The bilayer structure provides a simplified geometry that can be easily incorporated into MEMS devices. We demonstrate a hybrid synthesis method for fabrication of complex three-dimensional thin films using a cost-effective and mask-less aerosol jet deposition process. The combination of the hybrid aerosol jet process with dual phase harvester design provides the opportunity to fabricate small scale power sources required for structural health monitoring applications.