Design of laminated piezocomposite shell transducers with arbitrary fiber orientation using topology optimization approach

Sensor and actuator based on laminated piezocomposite shells have shown increasing demand in the field of smart structures. The distribution of piezoelectric material within material layers affects the performance of these structures; therefore, its amount, shape, size, placement, and polarization should be simultaneously considered in an optimization problem. In addition, previous works suggest the concept of laminated piezocomposite structure that includes fiber‐reinforced composite layer can increase the performance of these piezoelectric transducers; however, the design optimization of these devices has not been fully explored yet. Thus, this work aims the development of a methodology using topology optimization techniques for static design of laminated piezocomposite shell structures by considering the optimization of piezoelectric material and polarization distributions together with the optimization of the fiber angle of the composite orthotropic layers, which is free to assume different values along the same composite layer. The finite element model is based on the laminated piezoelectric shell theory, using the degenerate three‐dimensional solid approach and first‐order shell theory kinematics that accounts for the transverse shear deformation and rotary inertia effects. The topology optimization formulation is implemented by combining the piezoelectric material with penalization and polarization model and the discrete material optimization, where the design variables describe the amount of piezoelectric material and polarization sign at each finite element, with the fiber angles, respectively. Three different objective functions are formulated for the design of actuators, sensors, and energy harvesters. Results of laminated piezocomposite shell transducers are presented to illustrate the method. Copyright © 2012 John Wiley & Sons, Ltd.     

Broadband piezoelectric energy harvesting devices using multiple bimorphs with different operating frequencies

This paper presents a novel approach for designing broadband piezoelectric harvesters by integrating multiple piezoelectric bimorphs (PBs) with different aspect ratios into a system. The effect of 2 connecting patterns among PBs, in series and in parallel, on improving energy harvesting performance is discussed. It is found for multifrequency spectra ambient vibrations: 1) the operating frequency band (OFB) of a harvesting structure can be widened by connecting multiple PBs with different aspect ratios in series; 2) the OFB of a harvesting structure can be shifted to the dominant frequency domain of the ambient vibrations by increasing or decreasing the number of PBs in parallel. Numerical results show that the OFB of the piezoelectric energy harvesting devices can be tailored by the connection patterns (i.e., in series and in parallel) among PBs.     

Polymer-based nanopiezoelectric generators for energy harvesting applications

Abstract

Energy harvesting from ambient vibrations originating from sources such as moving parts of machines, fluid flow and even body movement, has enormous potential for small power applications, such as wireless sensors, flexible, portable and wearable electronics, and bio-medical implants, to name a few. Nanoscale piezoelectric energy harvesters, also known as nanogenerators (NGs), can directly convert small scale ambient vibrations into electrical energy. Scavenging power from ubiquitous vibrations in this way offers an attractive route to provide power to small devices, which would otherwise require direct or indirect connection to electrical power infrastructure. Ceramics such as lead zirconium titanate and semiconductors such as zinc oxide are the most widely used piezoelectric energy harvesting materials. This review focuses on a different class of piezoelectric materials, namely, ferroelectric polymers, such as polyvinlyidene fluoride (PVDF) and its copolymers. These are potentially superior energy harvesting materials as they are flexible, robust, lightweight, easy and cheap to fabricate, as well as being lead free and biocompatible. We review some of the theoretical and experimental aspects of piezoelectric energy recovery using Polymer-based NGs with a novel emphasis on coupling to mechanical resonance, which is relevant for efficient energy harvesting from typically low frequency (<1 kHz) ambient vibrations. The realisation of highly efficient and low cost piezoelectric polymer NGs with reliable energy harvesting performance could lead to wide ranging energy solutions for the next generation of autonomous electronic and wireless devices.     

Analysis of active damping in composite laminate cylindrical shells of revolution with skewed PVDF sensors/actuators

Active damping in a FRP composite cylindrical shell with collocated piezoelectric sensors/actuators is studied. The electrode on the sensors/actuators are spatially shaped to reduce spillover between circumferential modes. A three noded, isoparametric, semianalytical finite element is developed and used to model the cylindrical shell. The element is based on a mixed piezoelectric shell theory which makes a single layer assumption for the displacements and a layerwise assumption for the electric potential. The effects of location of patch of collocated piezoelectric sensors/actuators, percentage length of the shell covered with these patches, fiber angle of the laminae in the composite laminate, stacking sequence of laminae in a laminate and skew angle of the sensor/actuator piezoelectric material, on the system damping for various modes is studied.     

Time and frequency domain analysis of piezoelectric energy harvesters by monolithic finite element modeling

The successful design of piezoelectric energy harvesting devices relies upon the identification of optimal geometrical and material configurations to maximize the power output for a specific band of excitation frequencies. Extendable predictive models and associated approximate solution methods are essential for analysis of a wide variety of future advanced energy harvesting devices involving more complex geometries and material distributions. Based on a holistic continuum mechanics modeling approach to the multi‐physics energy harvesting problem, this article proposes a monolithic numerical solution scheme using a mixed‐hybrid 3‐dimensional finite element formulation of the coupled governing equations for analysis in time and frequency domain. The weak form of the electromechanical/circuit system uses velocities and potential rate within the piezoelectric structure, free boundary charge on the electrodes, and potential at the level of the generic electric circuit as global degrees of freedom. The approximation of stress and dielectric displacement follows the work by Pian, Sze, and Pan. Results obtained with the proposed model are compared with analytical results for the reduced‐order model of a cantilevered bimorph harvester with tip mass reported in the literature. The flexibility of the method is demonstrated by studying the influence of partial electrode coverage on the generated power output.     

Dynamic stress intensity factors of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material under a time‐harmonic elastic P‐wave

The dynamic behavior of two 3D rectangular permeable cracks in a transversely isotropic piezoelectric material is investigated under an incident harmonic stress wave by using the generalized Almansi's theorem and the Schmidt method. The problem is formulated through double Fourier transform into three pairs of dual integral equations with the displacement jumps across the crack surfaces as the unknown variables. To solve the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. Finally, the relations among the dynamic stress field and the dynamic electric displacement filed near the crack edges are obtained, and the effects of the shape of the rectangular crack, the characteristics of the harmonic wave, and the distance between two rectangular cracks on the stress and the electric intensity factors in a piezoelectric composite material are analyzed. Copyright © 2015 John Wiley & Sons, Ltd.     

Three-dimensional nonlinear thermo-elastic analysis of functionally graded cylindrical shells with piezoelectric layers by differential quadrature method

Three-dimensional nonlinear thermo-elastic analysis of a functionally graded cylindrical shell with piezoelectric layers under the effect of asymmetric thermo-electro-mechanical loads is carried out. The strain–displacement relations are based on the nonlinear Lagrangian strain–displacement relations; that is, nonlinear terms containing derivatives of the displacement in the radial direction are included. Material properties of the shell are assumed to be graded in the radial direction according to a power law but the Poisson’s ratio is assumed to be constant. Cylindrical shells are assumed to be under the effect of pressure loading in cosine form, ring pressure loads, electric and temperature fields. Numerical results of stress, displacement, electric and thermal fields are obtained by using two versions of the differential quadrature methods, namely polynomial and Fourier quadrature methods. The convergence of the solution is studied, and results of the axisymmetric loadings are verified with reported results for a cylindrical shell with material properties obeying a power law. Effects of the grading index of material properties, the temperature difference, the ratio of the mean radius to the thickness of the shell, boundary conditions, the thickness of piezoelectric layers and electric excitation on stress, displacement, electric and temperature fields are presented.     

A shear lag model of Piezoelectric composite reinforced with carbon nanotubes-coated Piezoelectric fibers

A novel hybrid piezoelectric composite in which the microscopic piezoelectric fiber reinforcements are coated with radially aligned carbon nanotubes (CNTs) is analyzed in this study. A shear-lag model is developed to analyze the load transferred to such coated fibers from the aligned-CNT reinforced matrix in a hybrid composite application in the absence and the presence of the electric field along the length of the fiber. It is found that if the aligned CNTs are radially grown on the surface of the piezoelectric fiber then the axial load transferred to the fiber is reduced in the absence of the electric field while the axial stress in the fiber increases in the presence of the electric filed only. The radial stress in the active piezoelectric fiber significantly increases due to the radial growth of aligned CNTs on the surface of the fibers. This indicates a probable critical window for engineering the surface of the piezoelectric fiber for improving the effective piezoelectric properties. Effects of the variation of the aspect ratio of the piezoelectric fiber and the CNT volume fraction on the load transferred to such CNT-coated piezoelectric fibers are also investigated.     

Transient piezothermoelastic problem for a laminated composite strip composed of angle-ply and piezoelectric laminae

This paper is concerned with the theoretical treatment of transient piezothermoelastic problem which is developed for a laminated composite strip composed of angle-ply laminae and a piezoelectric material of crystal class mm2, subject to nonuniform heat supply in the width direction. We obtain the exact solution for the two-dimensional temperature change in a transient state and the transient piezothermoelastic response of a simple supported composite strip under the state of generalized plane deformation. As an example, numerical calculations are carried out for a angle-ply laminated composite strip made of an alumina fiber reinforced aluminum composite, associated with a piezoelectric layer of a cadmium selenide solid. Some numerical results for temperature change, displacement, stress and electric potential distributions in a transient state are shown in figures. Furthermore, the influence of the thickness of the piezoelectric layer on the thermal stress or electric field is investigated.     

Electrospinning Triboelectric Laminates: A Pathway for Scaling Energy Harvesters

Herein, a new paradigm of triboelectric polymers—the triboelectric laminate—a volumetric material with electromechanical response comparable to the benchmark soft piezoelectric material polyvinylidene difluoride is reported. The electromechanical response in the triboelectric laminate arises from aligned dipoles, generated from the orientation of contact electrification in the laminates bulk volume. The dipoles form between sequential bilayers consisting of two different electrospun polymer fibers of different diameter. The loose interface between the fiber bilayers ensures friction and triboelectric charging between two polymers. The electric output from the electrospun triboelectric laminate increases with increasing density of the bilayers. This system design has clear benefits over other flexible devices for mechanical energy harvesting as it does not require any poling procedures, and the electromechanical response is stable over 24 h of continuous operation. Moreover, the electromechanically responsive electrospun laminate can be made from all types of polymers, thus providing ample room for further improvements or functionalities such as stretchability, biodegradability, or biocompatibility. The concept of a triboelectric laminate can be introduced into existing triboelectric nanogenerator form factors, to dramatically increase charge harvesting of a variety of devices.     

Advanced pyroelectric materials for energy harvesting and sensing applications

Heat energy is among the most wasted energy in the environment which is available in an ample quantity. So, developing new technology for harvesting and detecting wasted thermal energy to produce electrical energy which may be used as reliable energy sources for ultra-low power devices like nanogenerators and self-powered sensor applications. In this approach, pyroelectric energy harvesting technology has gained a huge attraction for application in power generation and sensing systems. Currently, a class of pyroelectric and piezoelectric materials has drawn enormous attraction because of its pyroelectric effect caused by spontaneous polarization and successful thermal energy harvesting for producing electrical energy for application in many sensor networks. This review makes a comprehensive summary of the significance and physical application of pyroelectric materials including single crystal, inorganic films, ceramics, organic materials, polymers, and composites as energy harvesting devices for scavenging thermal energy from surrounding for sensing devices. Finally, the perspective for next-generation self-powered sensor technologies is described.     

压电复合材料的共线周期性裂纹平面问题的电弹性场分析

利用复变函数知识、半逆解法及待定系数法, 研究了压电复合材料的共线周期性裂纹问题, 给出了在电不可渗透边界条件下的应力、电位移、应力强度因子、电位移强度因子和机械应变能释放率的解析解。当裂纹间距趋于无穷时, 共线周期性裂纹退化为一条单裂纹, 得到了压电复合材料一条单裂纹的结果。通过数值算例讨论了共线周期性裂纹的裂纹长度、裂纹间距和机电载荷对机械应变能释放率的影响规律。结果表明, 机械应变能释放率随着共线周期性裂纹的裂纹长度、共线周期性裂纹的裂纹间距、机械载荷和正电场的增大而增大, 随着负电场的增大而减小。     

Effective properties of three-phase electro-magneto-elastic composites

Coupling between the electric field, magnetic field, and strain of composite materials is achieved when electro-elastic (piezoelectric) and magneto-elastic (piezomagnetic) particles are joined by an elastic matrix. Although the matrix is neither piezoelectric nor piezomagnetic, the strain field in the matrix couples the electric field of the piezoelectric phase to the magnetic field of the piezomagnetic phase. This three-phase electro-magneto-elastic composite should have greater ductility and formability than a two-phase composite in which the electric field and the magnetic field are coupled by directly bonding two brittle materials. A finite element analysis (FEA) and micromechanics based averaging of a representative volume element (RVE) are performed in this work to determine the effective dielectric, magnetic, mechanical, and coupled-field properties of an elastic matrix reinforced with piezoelectric and piezomagnetic fibers as functions of the phase volume fractions, the fiber arrangements in the RVE, and the fiber material properties with special emphasis on the poling directions of the piezoelectric and piezomagnetic fibers. The effective magneto-electric moduli of this three-phase composite are found to be less than the effective magneto-electric moduli of a two-phase piezoelectric/piezomagnetic composite, because the elastic matrix is not stiff enough to transfer significant strains between the piezomagnetic and piezoelectric fibers.     

Elliptical Inclusion Problem in Antiplane Piezoelectricity: Stress Concentrations and Energy Release Rates

An elliptical piezoelectric inclusion embedded in an infinite piezoelectric matrix is analyzed in the framework of antiplane piezoelectricity. The stress distribution patterns for different elliptical inclusion and cavity shapes with different material constants are discussed based on the closed-form solution obtained by the authors. It is found that the stress concentration at the interface of the inclusion and the matrix becomes significantly high when piezoelectric constants of the inclusion and matrix have opposite sign. The variation in the energy release rates of selfsimilarly expanding and rotating defects, expressed by the M-and L-integrals, respectively, are discussed as a function of the applied electric field. Information on the stress concentration and the energetics of such a system can be quite useful in predicting failures, hence, aid in properly designing piezoelectric electromechanical systems.     

Impact and vibration detection in composite materials by using intermodal interference in multimode optical fibers

An optical fiber sensor based on the intermodal interference principle is integrated in a composite material to detect impacts and vibrations. Six fibers are integrated at the top of a carbon/epoxy composite panel so as to form a grid into the structure. Spectral and temporal responses to impacts and acoustic vibrations of the sensor are compared with a piezoelectric accelerometer. The tests proved the facility of integration and the high sensitivity of the device. The location of impacts is performed with this arrangement by measuring the arrival times of the front waves to the fibers.     

Dynamic fracture mechanics study of an electrically impermeable mode III crack in a transversely isotropic piezoelectric material under pure electric load

The dynamic response of an electrically impermeable Mode III crack in a transversely isotropic piezoelectric material under pure electric load is investigated by treating the electric loading process as a transient impact load, which may be more appropriate to mimic the real service environment of piezoelectric materials. The stress intensity factor, the mechanical energy release rate, and the total energy release rate are derived and expressed as a function of time for a given applied electric load. The theoretical results indicate that a purely electric load can fracture the piezoelectric material if the stress intensity factor or the mechanical energy release rate is used as a failure criterion.     

A flex-compressive-mode piezoelectric transducer for mechanical vibration/strain energy harvesting

A piezoelectric transducer for harvesting energy from ambient mechanical vibrations/strains under pressure condition was developed. The proposed transducer was made of two ring-type piezoelectric stacks, one pair of bow-shaped elastic plates, and one shaft that pre-compresses them. This transducer works in flex-compressive (F-C) mode, which is different from a conventional flex-tensional (F-T) one, to transfer a transversely applied force F into an amplified longitudinal force N pressing against the two piezo-stacks via the two bowshaped elastic plates, generating a large electric voltage output via piezoelectric effect. Our experimental results show that without an electric load, an F-C mode piezo-transducer could generate a maximum electric voltage output of up to 110 Vpp, and with an electric load of 40 κΩ, it a maximum power output of 14.6 mW under an acceleration excitation of 1 g peak-peak at the resonance frequency of 87 Hz.     

Nano piezoelectric/piezomagnetic energy harvester with surface effect based on thickness shear mode

BackgroundEnergy harvesters with piezoelectric materials are widely discussed for the new kinds of smart structures. However, reports on the energy harvesters at the nano scale which have large potential applications in the future are rather limited.MethodsIt’s well known that the surface or interface stress can affect the mechanical properties of nanostructures. This work proposes the nano energy harvester with piezoelectric/piezomagnetic structure, in which the thickness-shear mode is considered by the surface stress model.ResultsThe vibration motion and output power density are derived and calculated. The peak value of the power density can be enlarged by increasing the residual surface stress and the surface effect on the nano-plate energy harvester can be influenced by both the surface piezoelectric and piezomagnetic elastic constants. Moreover, the harvesting ability can be improved by increasing the thickness of the piezoelectric layer.ConclusionThe capability of the energy harvester depends on the residual surface stress and the surface material constants. The proposed model provides the possibility of applying nano composite structures to the energy harvester.     

Fracture analysis of a piezoelectric layer with a penny-shaped and energetically consistent crack

The problem of an eccentric penny-shaped crack embedded in a piezoelectric layer is addressed by using the energetically consistent boundary conditions. The Hankel transform technique is applied to solve the boundary-value problem. Then two coupling Fredholm integral equations are derived and solved by using the composite Simpson’s rule. The intensity factors of stress, electric displacement, crack opening displacement and electric potential together with the energy release rate are further given. The effects of the thickness of a piezoelectric layer and the discharge field inside the penny-shaped crack on the fracture parameters of concern are discussed through numerical computations. The observations reveal that an increase of the discharge field decreases the stress intensity factor and the energy release rate. An eccentric penny-shaped crack is easier to propagate than a mid-plane one in a piezoelectric layer, and the geometry of the crack along with the layer thickness have significant influences on the electrostatic traction acting on the crack faces. The solutions for a penny-shaped dielectric crack in an infinite or a semi-infinite piezoelectric material can be obtained easily.     

Influence of pattern gradation on the design of piezocomposite energy harvesting devices using topology optimization

Piezoelectric materials can be used to convert oscillatory mechanical energy into electrical energy. Energy harvesting devices are designed to capture the ambient energy surrounding the electronics and convert it into usable electrical energy. The design of energy harvesting devices is not obvious, requiring optimization procedures. This paper investigates the influence of pattern gradation using topology optimization on the design of piezocomposite energy harvesting devices based on bending behavior. The objective function consists of maximizing the electric power generated in a load resistor. A projection scheme is employed to compute the element densities from design variables and control the length scale of the material density. Examples of two-dimensional piezocomposite energy harvesting devices are presented and discussed using the proposed method. The numerical results illustrate that pattern gradation constraints help to increase the electric power generated in a load resistor and guides the problem toward a more stable solution.