Piezoelectric Laminates Research Articles

A general solution for electromechanical analysis of electroelastic composite plates with arbitrary holes

Stroh formalism provides an elegant method of solution for two-dimensional anisotropic elasticity problems through the generalized eigen relation associated with the dual coordinate system that gives the material eigen values and eigen vectors, and also the fundamental elasticity matrix and its associated Barnett-Lothe tensors. The extended Stroh-like formalism of Hwu and Hsieh has expanded the scope of basic Stroh formalism by addressing the electro-mechanical coupling effects in electro elastic plates. This paper presents an inclusive solution that addresses the two-dimensional problems in infinite electro-elastic, anisotropic, and isotropic plates with an arbitrary hole under remote arbitrary coupled electro-mechanical loading. This is achieved by adopting the Stroh formalism and its subsequent versions to consider the anisotropic and electro-elastic plates, and further, by incorporating the arbitrary biaxial loading condition into the boundary conditions, and the generalized mapping function into the basic formulation to accommodate all types of in plane loading and a variety of hole shapes respectively. Various equations of the solution are derived explicitly for easy understanding and computer implementation. The stress function is derived explicitly to satisfy the condition of traction free hole with remote electro-mechanical loading under generalized plane stress-open circuit condition. The stresses and electric displacements around the hole boundary are obtained by taking the derivative of the stress function with respect to unit normal along the hole boundary. The solution presented can be degenerated to the anisotropic or isotropic case by choosing the corresponding material properties, or appropriate values of complex parameters respectively. This general solution has exactly reproduced the results of other solutions in the literature for piezoelectric plates given by different methods. New results of stresses and electric displacements are obtained for various arbitrary holes in [PZT5H/45/-45/PZT5H]s graphite/epoxy plate and PZT 4 plates. Results for holes in piezoelectric laminates and PZT 4 piezo layer are also presented by FEM.

Segmented layered bistable piezoelectric laminates for enhanced energy harvesting from wind‐induced vibration

AbstractIn this study, a segmented layered bistable piezoelectric energy harvester (SBPEH) has been developed and thoroughly investigated for its wind energy harvesting capabilities. The SBPEH's performance was comprehensively evaluated through the creation of a detailed 3D finite element model using Abaqus and XFlow software, and further validated via rigorous wind tunnel experiments. The results of this research demonstrate the SBPEH's remarkable potential for wind energy harvesting. With a wide operational wind speed range, it achieved a maximum measured power output of 5.476 mW, coupled with an outstanding power density of 68.45 mW/cm3, both of which were realized at a wind speed of 13 m/s. It is worth noting that as the wind speed surpasses a specific threshold, the energy harvesting efficiency of the SBPEH experiences a decline, emphasizing the importance of identifying the optimal operational wind speed range for maximizing energy output. These findings offer valuable insights for the enhancement and application of SBPEHs, contributing to the advancement of renewable energy technologies and providing an eco‐friendly solution for power generation.Highlights The study introduces a new segmented layered bistable piezoelectric energy harvester (SBPEH) design for wind energy harvesting, addressing the limitations of traditional harvesters. Performance is evaluated through 3D finite element modeling, ABAQUS, Xflow simulations, and wind tunnel experiments. The SBPEH operates efficiently across a broad wind speed range (6–14 m/s), showcasing optimal output power of 5.476 mW at 13 m/s.

Interface crack analysis of piezoelectric laminates considering initial strain

Interface crack analysis of piezoelectric laminates considering initial strain

Mechanical Analysis of Functionally Graded Multilayered Two-Dimensional Decagonal Piezoelectric Quasicrystal Laminates with Imperfect Interfaces

Quasicrystals have a wide range of applications due to their unique multi-field coupling effects and distinctive physical and mechanical characteristics. In this paper, the static and dynamic problems of imperfectly bonded, multilayered, functionally graded, two-dimensional decagonal piezoelectric quasicrystal laminates under mixed boundary conditions are investigated. The state equations in a concise and compact matrix form can be expressed by using differential quadrature regional discrete point expansions in any layer of the laminate. This allows for the representation of displacement, stress, electric potential, and electric displacement components. Then, different imperfect interface conditions are introduced to characterize specific structural and electric contact properties at the bounding interfaces, which are further converted to the interface propagator matrix. Numerical examples are carried out to investigate the impact of varying interface compliances, load types, and functional gradient factors on the static bending and vibration phenomena of QC laminates. These results can be used as references to validate existing or future numerical work on QC laminates and could further guide the design of related QC laminate structures.

Investigation of guided wave propagation in nanoscale layered periodic piezoelectric plates based on Eringen's nonlocal and strain gradient theory

This paper investigates the dynamic propagation behavior of guided waves in nanoscale media composed of alternating layers of piezoelectric phases. The study employs Eringen's nonlocal and strain gradient theories to derive equations for symmetric wave propagation and the scattering relations of guided waves perpendicular to these structures. Dispersion curves are calculated and plotted to compare these theories, considering the influence of nanoscale size-effect, volume ratio of constituent layers, and material length scale. Using the strain gradient theory, the paper explores the impact of length scale parameters on the propagation behavior of horizontally polarized guided waves in an alternating layer structure of nanoscale piezoelectric material, specifically nanoscale piezoelectric laminates. The analysis involves calculating localization factors and dispersion curves to analyze the effects of size-effect and length scale parameters on wave propagation and band structures. Additionally, the study plots and analyzes changes in mechanical displacement and electrical potential, followed by an investigation and discussion of nanoscale size effects and the effects of the material's length scale parameter on dispersion curves and conversion modes within specific regions. The results highlight that the length scale effect parameter significantly impacts the mode conversion zones and band gap structures, more so than the NLPE continuum theory suggests. As the strain gradient parameter increases, these zones shift towards higher wavenumbers and to the right . Furthermore, introducing the length scale factor results in a substantial decrease in both the formation of conversion zones and the density of dispersion curves.

Analysis and experiments of bi-stable laminate configuration control based on MFC piezoelectric actuation

This paper studies the configuration change control and the snap-through phenomenon of bi-stable laminate with the MFC piezoelectric plate. The kinetic and potential energy expressions of the piezoelectric bi-stable laminate were obtained based on the von-Karman hypothesis. The constitutive equations of the system were given using a six-parameter displacement model, and the potential function of the system was derived using Hamilton’s principle. The configuration changes of the piezoelectric bi-stable laminate under different geometrical conditions were analyzed. The influence of voltage on the bi-stable laminate configuration was studied by applying different driving voltages. The snap-through energy variation of the piezoelectric bi-stable laminate under different geometrical conditions was investigated. In the experimental part, the changes in bi-stable laminate configuration with different geometrical conditions and after attaching the piezoelectric plate were compared. Different driving voltages were applied to measure the difference in piezoelectric bi-stable laminate configuration, and the critical snap-through voltages were recorded. The measured changes in bi-stable laminate configuration and snap-through voltage at different voltages prove the correctness of the theoretical presentation.

Fractional-Order Rate-Dependent Piezoelectric Thermoelasticity Theory Based on New Fractional Derivatives and its Application in Structural Transient Response Analysis of Smart Piezoelectric Composite Laminates

Ultrafast heating technology (e.g., high-energy pulse-burst laser, laser-aided material processing, etc.) has been extensively used in micro-machining and manufacturing of piezoelectric devices (e.g., piezoelectric resonator, piezoelectric generators, etc.), and the related thermo-electromechanical coupling analysis becomes more significantly important. In recent years, although rate-dependent piezoelectric thermoelasticity theories were historically proposed, the memory-dependence feature of strain relaxation and heat conduction has not been considered yet. In this work, the unified forms of fractional order strain and heat conduction are developed by adopting fractional derivatives of the Caputo (C), Caputo–Fabrizio (CF), Atangana–Baleanu (AB), and Tempered–Caputo (TC) types. Following these models, a fractional-order rate-dependent piezoelectric thermoelasticity is established. With the aid of an extended thermodynamics framework, the new constitutive and governing equations are derived. The proposed theory is applied to investigate dynamic thermo-electromechanical responses of smart piezoelectric composite laminates with imperfect interfacial conditions by the Laplace transformation approach. The influences of different fractional derivatives, imperfect interfacial conditions, and materials constants ratios on wave propagations and structural thermo-electromechanical responses are evaluated and discussed in detail.

Screening significant properties of macro-fiber composite laminate substrate anisotropy with viscoelastic and thermal considerations at the quasi-static level

A macro-fiber composite (MFC) is a class of smart material actuator that employs piezoceramic fibers to extend or contract under an applied electric field. When embedded on a thin substrate, actuated MFCs induce surface pressure, resulting in out-of-plane motion. Design characteristics of the substrate, such as anisotropy, give rise to unique bend/twist behavior. Previous studies on MFC applications have focused on optimizing patch location in relation to the local design to achieve optimal bend/twist motion. However, the resolution to these approaches is restricted to the design space of the application, presenting an absence in piezoelectric laminate design intuition. This research aims to streamline the initial optimization process by analyzing the significant material properties associated with substrate design. To accomplish this, a viscoelastic piezoelectric plate theory model is developed to accurately capture the displacement behavior of the MFC laminate for any given substrate design. Experimental data is used to validate and refine the model, ensuring it closely represents real-world physics. A 2k fractional factorial design of experiments approach is used to identify significant substrate properties per MFC laminate configuration, assigning each material property a two-level coding system. Three configurations are observed, with each exhibiting distinct significant properties and effects compared to others. Furthermore, the study explores the impact of thermal factors on substrate behavior for these MFC laminates, highlighting how significant properties can be temperature dependent. The contributions to the kinematic response due to substrate property perturbation varies uniquely per material property and MFC laminate configuration. Statistical evidence supports the notion that the hysteretic behavior of a material is unaffected by thermal influences and is solely determined by the elastic constants of the substrate. The maximum remanent hysteretic response is shown to be proportional to the maximum actuation response at near room temperature.

Thermal treatment improvement and energy harvesting capability promotion of a rotating piezoelectric aggregated CNT-reinforced beam-like structure resorting to an auxetic lamina

Numerous examinations have demonstrated the shortage of CNT-strengthened structures encountering a thermal ambient. In this paper, for the first time a multi-layered nanocomposite structure is suggested for the sake of improving the thermal response as well as energy harvesting capability of a rotating nanocomposite beam. In line with these promotions a honeycomb layer is integrated to a rotating CNT-aggregated beam with two piezoelectric laminae. The linearized equations of motion are projected into the prestressed configuration for the sake of study the linear free vibrations and the static instability of the rotating beam. The results elucidate how effectively the critical temperature results into the buckling of the rotating nanocomposite beam improves. It is confirmed that a simply-supported non-aggregated beam rotating at 1500 rpm with a core layer composed of an 80% auxetic core and 20% nanocomposite in its height with the honeycomb angle −20o has the first natural frequency 2.89 % smaller than the associated beam with a 100% nanocomposite core layer in the room temperature while the former weighs 22.05 % less than the latter. Meanwhile by the elevation of the room temperature by 10 K the first natural frequency of the former is 139.53 % larger than the latter. Moreover, the voltage observed by the sensor layers develops as a result of the enlargement of the absolute value of the honeycomb angle. It is confirmed that for a rotating simply-supported beam making the advantage of an auxetic core with the angle of −65o a higher voltage is detected by the magnification factor of 31.6 % relative to a regular honeycomb with the angle of 65o. On the other hand, the increment of the rotational speed from 1500 rpm to 2500 rpm induces a higher voltage by the magnification factor of 177.8 %. Accordingly, for the purpose of energy harvesting a rotating auxetic PZT-CNT beam with the maximum absolute angle is proposed.

Thermo-electro-mechanical shape morphing of structures using smart piezoelectric laminates

Smart composite laminates (SCLs) consist of active piezoelectric layers bonded to or embedded in a host structure to form self–adaptive systems. The importance of SCLs is evident in their potential use for shape morphing, self–health monitoring, and active vibration control. In this paper, the effect of temperature upon shape morphing of an SCL plate subject to coupled electro-mechanical inputs is investigated. Specifically, fully coupled field equations are developed for an SCL plate in which the mechanical displacement is described in terms of the third order shear deformation hypothesis and the experienced geometric nonlinearity in terms of von Kármán’s strain–displacement relationships. The nonlinear thermo-electro-mechanical governing equations are converted into a tractable finite element form. Additionally, the temperature dependent behavior of the constituents of the SCL plate is also considered in our simulations. The work introduces two control modes to study the influence of temperature upon the morphed geometry subject to varied electro-mechanical loading. The results reveal that the change in temperature affects the stiffness of the plate and induces voltage shift in electrical outputs. SCL with surface bonded piezoelectric laminates is believed to have a better controllability than embedded ones, and SCL performs better in shape morphing at higher temperatures.

Integrated a nonlinear energy sink and a piezoelectric energy harvester using simply-supported bi-stable piezoelectric composite laminate

A nonlinear device is presented for simultaneous vibration absorption and energy harvesting. This device is composed of a nonlinear energy sink and a piezoelectric energy harvester (NES-EH), and its core component is the simply-supported bi-stable piezoelectric composite laminate (BPCL). Its outstanding advantages are light weight, simple and reliable structure. The theoretical model is developed to model a harmonically excited linear oscillator coupled with NES-EH. The Runge–Kutta method and the harmonic balance method (HBM) are used to solve the theoretical model numerically and analytically. The vibration suppression efficiency is utilized to quantify the vibration absorption performance, while the energy harvesting performance is assessed by bandwidth for energy harvesting and maximum voltage within the bandwidth. The effects of the excitation amplitude, the concentrated mass of NES-EH, the length and width of BPCL, and the load resistance are considered on the performances of NES-EH. The vibration absorption and energy harvesting performances of NES-EH can be improved by adjusting these parameters. In addition, the proposed NES-EH can achieve the goal of higher power density and normalized power density under low-amplitude excitation and simultaneously have a good vibration absorption effect. Finally, approximate analytical solutions are obtained by using HBM to exhibit various bifurcations and singularities.

The dynamic regimes and the energy harvesting of the energy harvester based on the bistable piezoelectric composite laminate

The dynamic regimes and the energy harvesting of the bistable energy harvester based on the bistable piezoelectric composite laminate are elaborated here. To identify the all-around dynamic regimes and assess the bistable energy harvesting performance, the forward frequency sweep, the reverse frequency sweep and the resistance sweep are conducted. The peak-to-peak frequency–amplitude response curves on the displacement and the voltage output are graphically presented. The single-well vibration, the limit cycle oscillations, the intermittency between the limit cycle oscillations and the chaotic snapthrough, the intermittency between the multiple periods snapthrough and the chaotic snapthrough, the multiple periods snapthrough and the chaotic snapthrough are elaborated by the Time history diagram, the Phase diagram and the Poincare map. The dynamic regimes are graphically presented delivering the stability zone for the dynamic responses and the optimal region for the energy harvesting. The RMS power output and the Max voltage output are checked to be the value judgements. Due to the softening nonlinear effect and the hysteresis, the conspicuous biases between the forward and reverse frequency sweeps are found to exist illustrating that the limit cycle oscillations expand the bandwidth of the double-well regimes during the reverse frequency sweep. From the perspective of the energy harvesting capacity, the limit cycle oscillations are demonstrated to be optimal, the double-well responses generally outperform the single-well responses concerning the off-resonance and the single-well responses concerning the primary resonance around the reduced modal frequency may outperform the double-well responses except the limit cycle oscillations. The load resistance is crucial to the power generation performance and needs optimizing with the change of the external excitation. The load resistance, the external excitation amplitude and frequency are interrelated and can be optimized simultaneously for the maximum power generation efficiency.

Tunable self-biased magnetoelectric effect in magnetization-graded magnetoelectric composites

Magnetoelectric (ME) composites, which are magnetostrictive-piezoelectric composites, have garnered attention for use in various application fields owing to their large ME coupling compared with single-phase multiferroic materials. The maximum ME coupling is observed when an increased DC magnetic bias field is applied, which results in large devices with degraded sensitivity due to electromagnetic noise. To address this problem, a strong self-biased ME composite that generates the maximum ME response in a zero-bias field was proposed in this study. Highly self-biased ME composites were prepared by combining soft magnetic Ni and highly permeable Metglas magnetostrictive layers with a Pb(Mg1/3Nb2/3)O3–PbZrTiO3 piezoelectric single-crystal laminate structure and inducing a magnetization gradient. The maximum ME voltage value without a DC bias field was evaluated to be 4.2 V/cm∙Oe for an MMNPNMM (M: Metglas foil, N: nickel, P: PMN-PZT) structure, which is 625 % higher than that of conventional ME composites. Therefore, the relatively bulky means of the DC-bias application on ME materials could be eliminated, resulting in a simple ME device with a small volume using the magnetization gradient concept.

Electrospun Polyvinylidene Fluoride Piezoelectric Fiber Glass/Carbon Hybrid Self-Sensing Composites for Structural Health Monitoring.

In this study, a polyvinylidene fluoride (PVDF)/graphene nanoplatelet (GNP) micro-nanocomposite membrane was fabricated through electrospinning technology and was employed in the fabrication of a fiber-reinforced polymer composite laminate. Some glass fibers were replaced with carbon fibers to serve as electrodes in the sensing layer, and the PVDF/GNP micro-nanocomposite membrane was embedded in the laminate to confer multifunctional piezoelectric self-sensing ability. The self-sensing composite laminate has both favorable mechanical properties and sensing ability. The effects of different concentrations of modified multiwalled carbon nanotubes (CNTs) and GNPs on the morphology of PVDF fibers and the β-phase content of the membrane were investigated. PVDF fibers containing 0.05% GNPs were the most stable and had the highest relative β-phase content; these fibers were embedded in glass fiber fabric to prepare the piezoelectric self-sensing composite laminate. To test the laminate's practical application, four-point bending and low-velocity impact tests were performed. The results revealed that when damage occurred during bending, the piezoelectric response changed, confirming that the piezoelectric self-sensing composite laminate has preliminary sensing performance. The low-velocity impact experiment revealed the effect of impact energy on sensing performance.

A bi-stable device for simultaneous vibration absorption and energy harvesting using bi-stable piezoelectric composite laminate

A bi-stable device is presented for simultaneous vibration absorption and energy harvesting by introducing the piezoelectric element into the bi-stable nonlinear energy sink (BNES), which is called the bi-stable piezoelectric absorber (BPZA). BPZA only consists of the cantilever bi-stable piezoelectric composite laminate (BPCL) and tip masses. This BPZA is a lightweight, simple and reliable structure since it does not need any external devices to maintain bistability. A finite element model (FEM) and an equivalent theoretical model are developed to model a harmonically excited linear oscillator coupled with BPZA. The Runge-Kutta method is used to solve the theoretical model numerically. The effects of the excitation amplitude, the tip mass of BPZA and the load resistance are considered on the vibration suppression efficiency and energy harvesting of BPZA. The results show adjusting these parameters can improve the vibration suppression efficiency and energy harvesting of BPZA. In addition, the experimental prototype is prepared and verifies the rightness of the finite element model and theoretical model. The BPZA achieves the goal of higher power density at lower acceleration and simultaneously has a good vibration absorption effect. Maximum power of 15.8mW is generated at an excitation frequency of 22 Hz and acceleration of 0.5 g.

Uncertainty-oriented optimal PID control design framework for piezoelectric structures based on subinterval dimension-wise method (SDWM) and non-probabilistic time-dependent reliability (NTDR) analysis

Piezoelectric system is widely used in vibration control, but due to the influence of uncertainty in the system, the control rate designed for determined system may not meet the design requirements in practical application. In order to solve the uncertainty problems in the system, a set of NTDR reliability optimization framework for piezoelectric active control system is proposed in this paper. Taking the most widely used PID controller as an example, a new controller design method is proposed: the response interval of the closed-loop system is calculated by the novel SDWM. Based on the first crossing theory, a new time-dependent reliability index is defined to calculate the time-dependent reliability of the piezoelectric system. Through an example of piezoelectric laminate, the layout of different piezoelectric materials is compared. Then, taking piezoelectric curved shell as an example, the influence of piezoelectric uncertainty and uncertainty parameter radius on vibration control of piezoelectric system is studied. Finally, the accuracy of the method is verified by Monte Carlo algorithm.

Thermoanalytic characterization of binder burnout and sintering of lead-free piezoelectric KNNLT multilayer laminates with Ni electrodes

For competitive lead-free piezoceramic multilayer actuators (MLA) it is required to include base metal electrodes (BMEs). However, thermal processing of KNN-based multilayers with Ni electrodes necessitates precise control of the oven atmosphere in order to control the phase composition and functional performance of the piezoceramics and electrodes. Sintering of KNN-based MLAs with BMEs is performed at low oxygen partial pressure followed by a reoxidation treatment to reduce the concentration of oxygen vacancies and increase the resistivity of the ferroelectric, and simultaneously, the BME must not be oxidized. Within this complex thermal treatment protocol, the debindering of the multilayer laminates is a very important process step and proper binder removal is critical to avoid formation of defects or flaws and oxidation of electrodes. We have studied the debindering behavior of a KNN-based MLA with Ni electrodes fabricated from a PVB-based slip formulation using thermal analysis and complementary binder burnout experiments under reducing atmospheres. It is shown that binder burnout in reducing atmosphere allows for protection of Ni layers, but incomplete binder decomposition occurs at lower pO2. On the other hand, after debindering at 350 °C in air complete binder removal and little Ni oxidation only was observed, allowing to use these binder burnout conditions to prepare MLAs.

Static solution of two-dimensional decagonal piezoelectric quasicrystal laminates with mixed boundary conditions

Piezoelectric quasicrystals have attracted the tremendous attention of researchers for their unique properties. In this paper, the semi-analysis solutions of the functionally graded multilayered two-dimensional decagonal piezoelectric quasicrystal plates are investigated for mixed boundary-value problems. Based on the quasicrystal linear elastic theory, the state-space method is employed to derive the state equations composed of partial differential along the thickness direction. The differential quadrature method is utilized to discretize state variables to satisfy the mixed boundary conditions in the horizontal plane. Different from the conventional propagator matrix, a new propagator relationship is proposed to study numerical instability caused by extensive discrete points. Comprehensive numerical results are shown for the sandwich quasicrystal plate with four different stacking sequences. The numerical results reveal the effect of the functional gradient index factors, and boundary conditions on the electric potential, electric displacements, stresses, and displacements under the mechanical/electric loadings.

New Optimal Design of Multimode Shunt-Damping Circuits for Enhanced Vibration Control

In this study, a new method for the optimal design of multimode shunt-damping circuits is presented. A modification of the “current-flowing” shunt circuit is employed to control multiple vibration modes of a piezoelectric laminate beam. In addition to the resistor damping components, the method considers the capacitances and the shunting branch inductors as new design variables. The H∞ norm of the damped system is minimized using the particle swarm optimization (PSO) method in the suggested optimization strategy. Two additional numerical models are addressed in order to compare the proposed method with other methods from the literature and to thoroughly examine the effect of the design variables on damping performance. To simulate the dynamic behavior of the piezoelectric composite beam, a finite-element model is created which provides more accurate modeling of thick beam structures. Results show that the suggested method may improve damping efficiency when compared to other models, since it generates a highest peak amplitude reduction of 39.61 dB for the second mode and 55.92 dB for the third mode. Finally, another benefit provided by the suggested optimal design is the reduction of the required shunt inductance values.

Analytical modeling of panel flutter and active control in supersonic variable stiffness composite laminates

This work focuses on panel flutter and active control in supersonic variable stiffness composite laminates, making progress on the analytical modeling and combined exploration of curvilinear fiber composites tailoring and piezoelectric sensors/actuators, as promising structural design technologies, for aeroelastic control. The Classical Laminated Plate Theory and the First-Order Piston Theory are used as structural and aerodynamic models, respectively. Flutter analyses are carried out for simply supported plates, either purely elastic laminates or piezoelectric composite laminates. The tailor-ability of curvilinear fiber composites and the effect of proportional control are discussed. Ultimately, the presented results provide a comprehensive benchmark for future assessments.