Nonlinear characteristics of circular-cylinder piezoelectric power harvester near resonance based on flow-induced flexural vibration mode

The nonlinear behaviors of a circular-cylinder piezoelectric power harvester （CCPPH） near resonance are analyzed based on the flow-induced flexural vibration mode. The geometrically-nonlinear effect of the cylinder is studied with considering the in-plane extension incidental to the large defection. The boundary electric charges generated from two deformation modes, flexure and in-plane extension, were distinguished with each other because the charge corresponding to the latter mode produces no contribution to the output current. Numerical results on output powers show that there are multi- valuedness and jump behaviors.

Analysis of Vibration Frequencies of Piezoelectric Ceramic Rings as Ultrasonic Transducers in Welding of Facial Mask Production

The explosive demands for facial masks as vital personal protection equipment(PPE)in the wake of Covid-19 have challenged many industries and enterprises in technology and capacity,and the piezoelectric ceramic(PZT)transducers for the production of facial masks in the welding process are in heavy demand.In the earlier days of the epidemic,the supply of ceramic transducers cannot meet its increasing demands,and efforts in materials,development,and production are mobilized to provide the transducers to mask producers for quick production.The simplest solution is presented with the employment of Rayleigh-Ritz method for the vibration analysis,then different materials can be selected to achieve the required frequency and energy standards.The fully tailored method and results can be utilized by the engineers for quick development of the PZT transducers to perform precise function in welding.

Nonlinear thickness-shear vibration of an infinite piezoelectric plate with flexoelectricity based on the method of multiple scales

This paper presents a nonlinear thickness-shear vibration model for onedimensional infinite piezoelectric plate with flexoelectricity and geometric nonlinearity.The constitutive equations with flexoelectricity and governing equations are derived from the Gibbs energy density function and variational principle.The displacement adopted here is assumed to be antisymmetric through the thickness due to the thickness-shear vibration mode.Only the shear strain gradient through the thickness is considered in the present model.With geometric nonlinearity,the governing equations are converted into differential equations as the function of time by the Galerkin method.The method of multiple scales is employed to obtain the solution to the nonlinear governing equation with first order approximation.Numerical results show that the nonlinear thickness-shear vibration of piezoelectric plate is size dependent,and the flexoelectric effect has significant influence on the nonlinear thickness-shear vibration frequencies of micro-size thin plates.The geometric nonlinearity also affects the thickness-shear vibration frequencies greatly.The results show that flexoelectricity and geometric nonlinearity cannot be ignored in design of accurate high-frequency piezoelectric devices.

Effects of surface impedance on current density in a piezoelectric resonator for impedance distribution sensing

We study the relationship between the surface mechanical load represented by distributed acoustic impedance and the current density distribution in a shear mode piezoelectric plate acoustic wave resonator.A theoretical analysis based on the theory of piezoelectricity and trigonometric series is performed.In the specific and basic case when the surface load is due to a local mass layer,numerical results show that the current density concentrates under the mass layer and is sensitive to the physical as well as geometric parameters of the mass layer such as its location and size.This provides the theoretical foundation for predicting the surface impedance pattern from the current density distribution,which is fundamental to the relevant acoustic wave sensors.

DYNAMIC ANTI-PLANE PROBLEMS OF PIEZOCERAMICS AND APPLICATIONS IN ULTRASONICS—A REVIEW

We review theoretical results on anti-plane motions of polarized ceramics based on the linear theory of piezoelectricity. Solutions to dynamic problems of the propagation of bulk acoustic waves （BAW） and surface acoustic waves （SAW）, vibrations of finite bodies, and applications to various piezoelectric devices including piezoelectric waveguides, resonators, mass sensors, fluid sensors, actuators, nondestructive evaluation, power harvesters （generators）, transformers, and power transmission through an elastic wall by acoustic waves are discussed. Complications due to material inhomogeneity, initial stress, electromagnetic coupling, electric field gradient and semiconduction are also discussed. The paper cites 82 references.

PARALLEL FINITE ELEMENT ANALYSIS OF HIGH FREQUENCY VIBRATIONS OF QUARTZ CRYSTAL RESONATORS ON LINUX CLUSTER

Quartz crystal resonators are typical piezoelectric acoustic wave devices for frequency control applications with mechanical vibration frequency at the radio-frequency （RF） range. Precise analyses of the vibration and deformation are generally required in the resonator design and improvement process. The considerations include the presence of electrodes, mountings, bias fields such as temperature, initial stresses, and acceleration. Naturally, the finite element method is the only effective tool for such a coupled problem with multi-physics nature. The main challenge is the extremely large size of resulted linear equations. For this reason, we have been employing the Mindlin plate equations to reduce the computational difficulty. In addition, we have to utilize the parallel computing techniques on Linux clusters, which are widely available for academic and industrial applications nowadays, to improve the computing efficiency. The general principle of our research is to use open source software components and public domain technology to reduce cost for developers and users on a Linux cluster. We start with a mesh generator specifically for quartz crystal resonators of rectangular and circular types, and the Mindlin plate equations are implemented for the finite element analysis. Computing techniques like parallel processing, sparse matrix handling, and the latest eigenvalue extraction package are integrated into the program. It is clear from our computation that the combination of these algorithms and methods on a cluster can meet the memory requirement and reduce computing time significantly.

Influence of spherical inclusions on effective thermoelectric properties of thermoelectric composite materials

A homogenization theory is developed to predict the influence of spherical inclusions on the effective thermoelectric properties of thermoelectric composite materials based on the general principles of thermodynamics and Mori-Tanaka method.The closed-form solutions of effective Seebeck coefficient,electric conductivity,heat conductivity,and figure of merit for such thermoelectric materials are obtained by solving the nonlinear coupled transport equations of electricity and heat.It is found that the effective figure of merit of thermoelectric material containing spherical inclusions can be higher than that of each constituent in the absence of size effect and interface effect.Some interesting examples of actual thermoelectric composites with spherical inclusions,such as insulated cavities,inclusions subjected to conductive electric and heat exchange and thermoelectric inclusions,are considered,and the numerical results lead to the conclusion that considerable enhancement of the effective figure of merit is achievable by introducing inclusions.In this paper,we provide a theoretical foundation for analytically and computationally treating the thermoelectric composites with more complicated inclusion structures,and thus pointing out a new route to their design and optimization.

Extended Kantorovich method for local stresses in composite laminates upon polynomial stress functions

The extended Kantorovich method is employed to study the local stress concentrations at the vicinity of free edges in symmetrically layered composite laminates subjected to uniaxial tensile load upon polynomial stress functions. The stress fields are initially assumed by means of the Lekhnitskii stress functions under the plane strain state. Applying the principle of complementary virtual work,the coupled ordinary differential equations are obtained in which the solutions can be obtained by solving a generalized eigenvalue problem. Then an iterative procedure is established to achieve convergent stress distributions. It should be noted that the stress function based extended Kantorovich method can satisfy both the traction-free and free edge stress boundary conditions during the iterative processes. The stress components near the free edges and in the interior regions are calculated and compared with those obtained results by finite element method（FEM）. The convergent stresses have good agreements with those results obtained by three dimensional（3D） FEM. For generality, various layup configurations are considered for the numerical analysis. The results show that the proposed polynomial stress function based extended Kantorovich method is accurate and efficient in predicting the local stresses in composite laminates and computationally much more efficient than the 3D FEM.

Effects of mode coupling on the admittance of an AT-cut quartz thickness-shear resonator

We study the effects of couplings to flexure and face-shear modes on the admittance of an AT-cut quartz plate thickness-shear mode resonator. Mindlin’s two-dimensional equations for piezoelectric plates are employed. Electrically forced vibration solutions are obtained for three cases： pure thickness-shear mode alone; two coupled modes of thickness shear and flexure; and three coupled modes of thickness shear, flexure, and face shear. Admittance is calculated and its dependence on the driving frequency and the length/thickness ratio of the resonator is examined. Results show that near the thickness-shear resonance, admittance assumes maxima, and that for certain values of the length/thickness ratio, the coupling to flexure causes severe admittance drops, while the coupling to the face-shear mode causes additional admittance changes that were previously unknown and hence are not considered in current resonator design practice.

A nonlinear analysis of surface acoustic waves in isotropic elastic solids

With the fast evolution of wireless and networking communication technology,applications of surface acoustic wave(SAW),or Rayleigh wave,resonators are proliferating with fast shrinking sizes and increasing frequencies.It is inevitable that the smaller resonators will be under a strong electric field with induced large deformation,which has to be described in wave propagation equations with the consideration of nonlinearity.In this study,the formal nonlinear equations of motion are constructed by introducing the nonlinear constitutive relation and strain components in a standard procedure,and the equations are simplified by the extended Galerkin method through the elimination of harmonics.The wave velocity of the nonlinear SAW is obtained from approximated nonlinear equations and boundary conditions through a rigorous solution procedure.It is shown that if the amplitude is small enough,the nonlinear results are consistent with the linear results,demonstrating an alternative procedure for nonlinear analysis of SAW devices working in nonlinear state.

Coupled extension and thickness-twist vibrations of lateral field excited AT-cut quartz plates

In this paper, the coupled extension and thickness- twist vibrations are studied for AT-cut quartz plates under Lateral Field Excitation （LFE） with variations along the x1- direction. Mindlin＇s two-dimensional equations are used for anisotropic crystal plates. Both free and electrically forced vibrations are considered. Important vibration characteristics are obtained, including dispersion relations, frequency spectra, and motional capacitances. It is shown that, to avoid the effects of the couplings between extension and thickness-twist vibrations, a series of discrete values of the length/thickness ratio of the crystal plate need to be excluded. The results are of fundamental significance for the design of LFE resonators and sensors.

ELECTRICALLY FORCED THICKNESS-SHEAR VIBRATIONS OF QUARTZ PLATE WITH NONLINEAR COUPLING TO EXTENSION

We study electrically forced nonlinear thickness-shear vibrations of a quartz plate resonator with relatively large amplitude. It is shown that thickness-shear is nonlinearly coupled to extension due to the well-known Poynting effect in nonlinear elasticity. This coupling is relatively strong when the resonant frequency of the extensional mode is about twice the resonant frequency of the thickness-shear mode. This happens when the plate length/thickness ratio assumes certain values. With this nonlinear coupling, the thickness-shear motion is no longer sinusoidal. Coupling to extension also affects energy trapping which is related to device mounting. When damping is 0.01, nonlinear coupling causes a frequency shift of the order of 10^-6 which is not insignificant,and an amplitude change of the order of 10^-8. The effects are expected to be stronger under real damping of 10^-5 or larger. To avoid nonlinear coupling to extension, certain values of the aspect ratio of the plate should be avoided.

The axisymmetric Rayleigh waves in a semi-infinite elastic solid

It is well-known that Rayleigh wave,also known as surface acoustic wave(SAW),solutions in semiinfinite solids are plane waves with signatory properties like the distinct velocity and exponentially decaying deformation in the depth.Applications of Rayleigh waves are focused on the deformation and energy in the vicinity of surface of solids and less loss in the propagation.A generalized model of Rayleigh waves in axisymmetric mode is established and solutions are obtained with cylindrical coordinates.It is found that the Rayleigh waves also propagate in the axisymmetric mode with slow decay in radius,confirming the existence of surface acoustic waves is irrelevant to coordinate system.On the other hand,the solutions can be treated as plane waves in regions far away from the source.Furthermore,the particle trajectory of axisymmetric SAW is a line with constant slope rather than the signatory ellipse in Cartesian coordinate case.

NONLINEAR ANALYSIS OF A 5-LAYER BEAM-LIKE PIEZOELECTRIC TRANSFORMER NEAR RESONANCE

The paper examines the weakly nonlinear behavior of a 5-layer beam-like piezo- electric transformer operating near resonance, where the main structure of the device consists of properly poled and electroded flexible piezoceramic four-layers separated by a central metallic layer. Nonlinear effects of the large deflection to induce the incidental implane extension near res- onance are considered, which is shown that on one side of the resonant frequency the output-input relation becomes nonlinear, and the other side output voltage experiences jumps.

An Analysis of Piezomagnetic-Piezoelectric Semiconductor Unimorphs in Coupled Bending and Extension under a Transverse Magnetic Field

We study the response of a composite beam(unimorph)with a piezomagnetic layer and a piezoelectric semiconductor layer under a transverse magnetic field.A one-dimensional model for coupled bending and extension of the beam is derived from the three-dimensional theory.A simple and analytical solution of the model is obtained,showing that various electromechanical fields develop in the beam through piezomagnetic and piezoelectric couplings as well as semiconduction.In particular,the mobile charges in the semiconductor layer redistribute themselves under the magnetic field.A coupling coefficient is defined to describe the strength of this magneto-semiconduction coupling.The effects of physical and geometric parameters on the fields and the coupling coefficient are examined.The results are fundamental to piezotronics when magnetic effects are involved.

Controllable Delamination of CNT-Reinforced Carbon Fiber Films by Harnessing Mechanical and Topological Characteristics of the Composites

Carbon nanotubes(CNTs)offer a remarkable reinforcement effect for the interlaminar toughness of laminated films,and optimizing the delamination of films through their toughening mechanism is of particular interest.Herein,we propose a theoretical model that combines the spatial evolution of aligned CNTs to describe the mode I fracture between opposing carbon fiber films.Our theoretical predictions quantitatively agree well with previous tests,and the influence of interfacial energy and modulus of films on toughness enhancement is considered.Our findings have demonstrated that aligned CNTs play a crucial role in enhancing delamination resistance,with the performance being highly sensitive to their volume fraction,mechanical properties,and geometric characteristics.We optimized interlaminar toughness by selecting appropriate strength and aspect ratio of CNTs based on two competitive failure modes.This work presents new concept for the topological design of composite laminates,bridging the properties of microfibers and macrostructures and ultimately achieving greater strength and toughness.

An analysis of surface acoustic wave propagation in a plate of functionally graded materials with a layered model

In a homogeneous plate, Rayleigh waves will have a symmetric and anti-symmetric mode regarding to the mid-plane with different phase velocities. If plate properties vary along the thickness, or the plate is of functionally graded material (FGM), the symmetry of modes and frequency behavior will be modified, thus producing dif-ferent features for engineering applications such as amplifying or reducing the velocity and deformation. This kind of effect can also be easily realized by utilizing a layered structure with desired material properties that can produce these effects in terms of velocity and displacements, since Rayleigh waves in a solid with gen-eral material property grading schemes are difficult to analyze with known methods. Solutions from layered structures with exponential and polynomial property grad-ing schemes are obtained from the layered model and comparisons with known analytical results are made to validate the method and examine possible applica-tions of such structures in engineering.

A two-dimensional analysis of surface acoustic waves in finite elastic plates with eigensolutions

It is generally known that surface acoustic waves, or Rayleigh waves, have different mode shapes in infinite plates. To be precise, there are both exponentially decaying and growing components in plates appearing in pairs, representing symmetric and antisymmentric modes in a plate. As the plate thickness increases, the combined modes will approach the Rayleigh mode in a semi-infinite solid, exhibiting surface acoustic wave deformation and velocity. In this study, the two-dimensional theory for surface acoustic waves in finite plates is extended to include the exponentially growing modes in the expansion function. With these extra equations, we study the surface acoustic waves in a plate with different thickness to examine the coupling of the exponentially decaying and growing modes. It is found that for small thick- ness, the two groups of waves are strongly coupled, showing the significance of including the effect of thickness in analysis. As the thickness increases to certain values, such as more than five wavelengths, the exponentially decaying modes alone will be able to predict vibrations of surface acoustic wave modes accurately, thus simplifying the equations and solutions significantly.

Thickness-Shear Frequencies of an Infinite Quartz Plate with Graded Material Properties Across the Thickness

For quartz crystal resonators of thickness-shear type,the vibration frequency and mode shapes reflect the basic material and structural properties of a quartz crystal plate and the variation with time under attack by erosive gases and liquids that can cause surface and internal degradation in a graded form.Such gradual effects,in turn,will change surface conditions through elastic constants and stiffness and more importantly the gradient of such properties across the thickness with certain depth.Now we study the thickness-shear vibrations of functionally graded material plates with properties of the popular AT-cut quartz crystal varying across the thickness in a general pattern represented by both sine and cosine components of the thickness.The vibration solutions are obtained through the Fourier expansion of the plate deformation.

Effects of mass layer imperfect bonding on the electrical impedance of a quartz crystal microbalance

We study electrically forced vibrations of a crystal plate of AT-cut quartz carrying a thin mass layer operating as a quartz crystal microbalance for mass sensing.The mass layer is imperfectly bonded to the crystal plate with their interface described by the so-called interface-slip model which allows a discontinuity of the tangential interface displacement.Mindlin’s equations for piezoelectric plates are used.An analytical solution is obtained.The electrical impedance is calculated.The effects of an elastic interface and a viscoelastic interface are examined.