PROPAGATION OF LOVE WAVES IN PRESTRESSED PIEZOELECTRIC LAYERED STRUCTURES LOADED WITH VISCOUS LIQUID

We investigate analytically the effect of initial stress in piezoelectric layered structures loaded with viscous liquid on the dispersive and attenuated characteristics of Love waves, which involves a thin piezoelectric layer bonded perfectly to an unbounded elastic substrate. The effects of initial stress in the piezoelectric layer and the viscous coefficient of the liquid on the phase velocity of Love waves are analyzed. Numerical results are presented and discussed. The analytical method and the results can be useful for the design of chemical and biosensing liquid sensors.     

BUCKLING ANALYSIS OF STRETCHABLE FERROELECTRIC THIN FILM ON ELASTOMERIC SUBSTRATES

The thin stiff films on pre-stretched compliant substrates can form wrinkles, which can be controlled in micro and nanoscale systems to generate smart structures. Recently, buck- led piezoelectric/ferroelectrie nanoribbons have been reported to show an enhancement in the piezoelectric effect and stretchability, which can be applied in energy harvesting devices, sensors and memory devices instead of polymeric polyvinylidine fluoride （PVDF）. This paper studies the buckling and post-buckling process of ferroelectric thin films bonded to the pre-stretched soft layer, which in turn lies on a rigid support. Nonlinear electromechanical equations for the buckling of thin piezoelectric plates are deduced and employed to model the ferroelectric film poled in the thickness direction. Two buckling modes are analyzed and discussed： partially de-adhered buck- ling and fully adhered buckling. Transition from one buckling mode to the other is predicted and the effect of piezoelectricity on the critical buckling condition of piezoelectric film is examined.     

A novel type of transverse surface wave propagating in a layered structure consisting of a piezoelectric layer attached to an elastic half-space

The existence and propagation of transverse surface waves in piezoelectric coupled solids is investigated, in which perfect bonding between a metal/dielectric substrate and a piezoelectric layer of finite-thickness is assumed. Dis- persion equations relating phase velocity to material con- stants for the existence of various modes are obtained in a simple mathematical form for a piezoelectric material of class 6mm. It is discovered and proved by numerical examples in this paper that a novel Bleustein-Gulyaev （B-G） type of transverse surface wave can exist in such piezoelectric cou- pled solid media when the bulk-shear-wave velocity in the substrate is less than that in the piezoelectric layer but greater than the corresponding B-G wave velocity in the same pie- zoelectric material with an electroded surface. Such a wave does not exist in such layered structures in the absence of pie- zoelectricity. The mode shapes for displacement and electric potential in the piezoelectric layer are obtained and discussed theoretically. The study extends the regime of transverse sur- face waves and may lead to potential applications to surface acoustic wave devices.     

Propagation behavior of elastic waves in one-dimensional piezoelectric/piezomagnetic phononic crystal with line defects

Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional （1D） piezoelectric/piezomagnetic （PE/PM） phononic crystals （PCs） with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the re- placement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly de- pendent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures.     

An eigen theory of waves in piezoelectric solids

Based on the standard spaces of the physical presentation, both the quasi-static mechanical approximation and the quasi-static electromagnetic approximation of piezoelectric solids are studied here. The complete set of uncoupled elastic wave and electromagnetic wave equations are deduced. The results show that the number and propagation speed of elastic waves and electromagnetic waves in anisotropic piezoelectric solids are determined by both the subspaces of electromagnetically anisotropic media and ones of mechanically anisotropic media. Based on these laws, we discuss the propagation behaviour of elastic waves and electromagnetic waves in the piezoelectric material of class 6 mm.     

PROPAGATION BEHAVIORS OF SHEAR HORIZONTAL WAVES IN PIEZOELECTRIC-PIEZOMAGNETIC PERIODICALLY LAYERED STRUCTURES

This paper investigates shear horizontal （SH） waves propagating in a periodically layered structure that consists of piezoelectric （PE） layers perfectly bonded with piezomagnetic （PM） layers alternately. The explicit dispersion relations are derived for the two cases when the propagation directions of SH waves are normal to the interface and parallel to the interface, respectively. The asymptotic expressions for dispersion relations are also given when the wave number is extremely small. Numerical results for stop band effect and phase velocity are presented for a periodic system of alternating BaTiO3 and Terfenol-D layers. The influence of volume fraction on stop band effect and dispersion behaviors is discussed and revealed.     

PROPAGATION OF SURFACE ACOUSTIC WAVES IN PRESTRESSED ANISOTROPIC LAYERED PIEZOELECTRIC STRUCTURES

The propagation of surface acoustic waves in layered piezoelectric structures withinitial stresses is investigated.The phase velocity equations are obtained for electrically free andshorted cases,respectively.Effects of the initial stresses on the phase velocity and the electrome-chanical coupling coefficient for the fundamental mode of the layered piezoelectric structures arediscussed.Numerical results for the c-axis oriented fihn of LiNbO_3 on a sapphire substrate aregiven.It is found that the fractional change in phase velocity is a linear function with the ini-tial stresses,and the electromechanical coupling factor increases with an increase of the absolutevalues of the compressive initial stresses.The results are useful for the design of surface acousticwave devices.     

APPLICABILITY OF THE CRACK FACE ELECTRICAL BOUNDARY CONDITIONS IN PIEZOELECTRIC MECHANICS

The electrical boundary conditions on the crack faces and their applicability in piezoelectric materials are discussed. A slit crack and a notch of ?nite thickness in piezoelectric materials subjected to combined mechanical and electrical loads is consi…     

Nonlinear active control of damaged piezoelectric smart laminated plates and damage detection

Considering mass and stiffness of piezoelectric layers and damage effects of composite layers, nonlinear dynamic equations of damaged piezoelectric smart laminated plates are derived. The derivation is based on the Hamilton＇s principle, the higher- order shear deformation plate theory, von Karman type geometrically nonlinear straindisplacement relations, and the strain energy equivalence theory. A negative velocity feedback control algorithm coupling the direct and converse piezoelectric effects is used to realize the active control and damage detection with a closed control loop. Simply supported rectangular laminated plates with immovable edges are used in numerical computation. Influence of the piezoelectric layers＇ location on the vibration control is in- vestigated. In addition, effects of the degree and location of damage on the sensor output voltage are discussed. A method for damage detection is introduced.     

Reflection and transmission of elastic waves at five types of possible interfaces between two dipolar gradient elastic half-spaces

Reflection and transmission of an incident plane wave at five types of possible interfaces between two dipo-lar gradient elastic solids are studied in this paper. First, the explicit expressions of monopolar tractions and dipolar trac-tions are derived from the postulated function of strain energy density. Then, the displacements, the normal derivative of displacements, monopolar tractions, and dipolar tractions are used to create the nontraditional interface conditions. There are five types of possible interfaces based on all possible combinations of the displacements and the normal derivative of displacements. These interfacial conditions with consid-eration of microstructure effects are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Further, the energy ratios of the reflection and transmission waves with respect to the incident wave are calculated. Some numerical results of the reflection and transmission coefficients are given in terms of energy flux ratio for five types of possible interfaces. The influences of the five types of possible interfaces on the energy parti-tion between the refection waves and the transmission waves are discussed, and the concept of double channels of energy transfer is first proposed to explain the different influences of five types of interfaces.     

COUPLED ANALYSIS FOR THE HARVESTING STRUCTURE AND THE MODULATING CIRCUIT IN A PIEZOELECTRIC BIMORPH ENERGY HARVESTER

The authors analyze a piezoelectric energy harvester as an electro-mechanically coupled system. The energy harvester consists of a piezoelectric bimorph with a concentrated mass attached at one end, called the harvesting structure, an electric circuit for energy storage, and a rectifier that converts the AC output of the harvesting structure into a DC input for the storage circuit. The piezoelectric bimorph is assumed to be driven into flexural vibration by an ambient acoustic source to convert the mechanical energies into electric energies. The analysis indicates that the performance of this harvester, measured by the power density, is characterized by three important non-dimensional parameters, i.e., the non-dimensional inductance of the storage circuit, the non-dimensional aspect ratio （length/thickness） and the non-dimensional end mass of the harvesting structure. The numerical results show that： （1） the power density can be optimized by varying the non-dimensional inductance for each fixed non-dimensional aspect ratio with a fixed non-dimensional end mass; and （2） for a fixed non-dimensional inductance, the power density is maximized if the non-dimensional aspect ratio and the non-dimensional end mass are so chosen that the harvesting structure, consisting of both the piezoelectric bimorph and the end mass attached, resonates at the frequency of the ambient acoustic source.     

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids.The propagation of three longitudinal waves is represented through three scalar potential functions.The lone transverse wave is presented by a vector potential function.The displacements of particles in different phases of the aggregate are defined in terms of these potential functions.It is shown that there exist three longitudinal waves and one transverse wave.The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated.For the presence of viscosity in pore-fluids,the waves refracted to the porous medium attenuate in the direction normal to the interface.The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a nonsingular system of linear algebraic equations.These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave.The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model.The conservation of the energy across the interface is verified.The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed.     

A comparative study of piezoelectric unimorph and multilayer actuators as stiffness sensors via contact resonance

Piezoelectric bar-shaped resonators were proposed to act as hardness sensors in the 1960 s and stiffness sensors in the 1990 s based on the contact impedance method.In this work, we point out that both multilayer and unimorph(or bimorph) piezoelectric actuators could act as stiffness/modulus sensors based on the principle of mechanical contact resonance. First, the practical design and the performance of a piezoelectric unimorph actuator–based stiffness sensor were presented. Then the working principle of piezoelectric multilayer actuator–based stiffness sensors was given and verified by numerical investigation. It was found that for these two types of resonance-based sensors, the shift of the resonance frequency due to contact is always positive, which is different from that of the contact impedance method. Further comparative sensitivity study indicated that the unimorph actuator–based stiffness sensor is very suitable for measurement on soft materials, whereas the multilayer actuator–based sensor is more suitable for hard materials.     

On aerodynamic noises radiated by the pantograph system of high-speed trains

Pantograph system of high-speed trains become significant source of aerodynamic noise when travelling speed exceeds 300 km/h. In this paper, a hybrid method of non-linear acoustic solver （NLAS） and Ffowcs Williams-Hawkings （FW-H） acoustic analogy is used to predict the aerodynamic noise of pantograph system in this speed range. When the simulation method is validated by a benchmark problem of flows around a cylinder of finite span, we calculate the near flow field and far acoustic field surrounding the pantograph system. And then, the frequency spectra and acoustic attenuation with distance are analyzed, showing that the pantograph system noise is a typical broadband one with most acoustic power restricted in the medium-high frequency range from 200 Hz to 5 kHz. The aerodynamic noise of pantograph systems radiates outwards in the form of spherical waves in the far field. Analysis of the overall sound pressure level （OASPL） at different speeds exhibits that the acoustic power grows approximately as the 4th power of train speed. The comparison of noise reduction effects for four types of pantograph covers demonstrates that only case 1 can lessen the total noise by about 3 dB as baffles on both sides can shield sound wave in the spanwise direction. The covers produce additional aerodynamic noise themselves in the other three cases and lead to the rise of OASPLs.     

Piezoelectric generator based on torsional modes for power harvesting from angular vibrations

Torsional vibration of a circular piezoelectric shell of polarized ceramics mounted on a rotationally vibrating base is analyzed. The shell is properly electroded and connected to a circuit such that an electric output is generated. The structure analyzed represents a piezoelectric generator for converting mechanical energy from angular vibrations to electrical energy. Analytical expressions and numerical results for the output voltage, current, power, efficiency and power density are given.     

Power transmission through double-walled laminated composite panels considering porous layer-air gap insulation

The acoustic behavior of double-walled laminated composite panels consisting of two porous and air gap middle layers is studied within the classical laminated plate theory （CLPT）. Thus, viscous and inertia coupling in a dynamic equation, as well as stress transfer, thermal and elastic coupling of porous material ave based on the Biot theory. In addition, the wave equations are extracted according to the vibration equation of composite layers. The transmission loss （TL） of the structure is then calculated by solving these equations simultaneously. Statistical energy analysis （SEA） is developed to divide the structure into specific subsystems, and power transmission is extracted with balancing power flow equations of the subsystems. Comparison between the present work and the results reported elsewhere shows excellent agreement. The results also indicate that, although favorable enhancement is seen in noise control particularly at high frequencies, the corresponding parameters associated with fluid phase and solid phase of the porous layer are important on TL according to the boundary condition interfaces. Finally, the influence of composite material and stacking sequence on power transmission is discussed.     

Analytical modeling of sandwich beam for piezoelectric bender elements

Piezoelectric bender elements are widely used as electromechanical sensors and actuators.An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory(FSDT),which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers,and corrects the effect of transverse shear strain on the electric displacement integration.Free vibration analysis of simply- supported bender elements was carried out and the numerical results showed that,solu- tions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions,which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.     

The wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges

In this paper,wave and vibratory power transmission in a finite L-shaped Mindlin plate with two simply supported opposite edges are investigated using the wave approach.The dynamic responses,active and reactive power flow in the finite plate are calculated by the Mindlin plate theory (MPT) and classic plate theory (CPT).To satisfy the boundary conditions and continuous conditions at the coupled junction of the finite L-shaped plate,the near-field and far-field waves are entirely contained in the wave approach.The in-plane longitudinal and shear waves are also considered.The results indicate that the vibratory power flow based on the MPT is different from that based on the CPT not only at high frequencies but also at low and medium frequencies.The influence of the plate thickness on the vibrational power flow is investigated.From the results it is seen that the shear and rotary inertia correction of the MPT can influence the active and reactive power at the junction of the L-shaped plate not only at high frequencies but also at low and medium frequencies.Furthermore,the effects of structural damping on the active and reactive power flow at the junction are also analyzed.     

THE PROPAGATION OF SOLITARY WAVES IN A NONLINEAR ELASTIC ROD

In this paper, the inverse scattering method is used to analyse strain solitary waves in a nonlinear elastic rod[1]. Properties of solitary waves and their influence on solid structures are discussed in detail. Some quantitative results are given.     

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.