MULTIDIMENSIONAL COUPLED VIBRATIONS OF PIEZOELECTRIC VIBRATORS——PURE PIEZOELECTRIC VIBRATORS

In this paper,the fundamental modes of two- and three-dimensional coupled vibrations ofvarious piezoelectric ceramic vibrators,including the rectangular cross-sectional bar,the rectangularplate,the finite solid cylinder and hollow cylinder,are analyzed by using the apparent elasticitymethod,and some quite simple analytic formulae for the resonant frequencies of the above-men-tioned various piezoelectric vibrators are obtained,These formulae have been used to calculatethe variations of frequency constants with the geometric size of the vibrators,and the calculatedresults are in satisfactory agreement with the published experimental results and results calculatedby using various other methods,including the finite difference method,finite element method andRitz variational method.These formulae are quite simple,and the resonant frequencies or the geo-metric size of the vibrators can be rapidly calculated by using a scientific calculator instead of acomputer,so this method is more convenient for engineering     

A SUSCEPTANCE METHOD TO MEASURE PARAMETERS OF PIEZOELECTRIC VIBRATORS

By way of theoretical analyses of the admittance locus of piezoelectric vibrators,a susceptancemethod for measurement of piezelectric vibrators is suggested.By use of the method,we measuredthe relevant elastic,piezoelectric constants and electromechanical coupling coefficients of LiTaO_3crystal.     

MULTIDIMENSIONAL ANALYSIS OF PERCEPTIONAL CONFUSION OF CHINESE CONSONANTS

The perceptional features of Chinese consonants has been analysed in multidimensional scalingby means of optimizing the fitting to the confusion probabilities of consonants as observed in articula-tion tests.The dependence of minimum Stress as criterion for fitting on dimensions has beenobtained. In this paper,a method of multidimensional scaling is described briefly.A program for perform-ing calculations on a programmable calculator and the questions of handling the blank data as wellas setting the starting configurations are discussed.Some typical results of calculation are given.     

ON VARIATIONAL PRINCIPLES OF A PIEZOELECTRIC BODY

The consonance of state variables of a piezoelectric body is explored and four variational princi-ples of a piezoelectric body are systematically proposed.The Lagrangian function of each of theseprinciples is the difference between a corresponding thermodynamic function and the kinetic energy.These principles correspond to different physical conditions and are to be used in different problems.Their applications are discussed.     

PRINCIPLE OF PIEZOELECTRIC DAMPING OF VIBRATION:AN EXPERIMENTAL INVESTIGATION

Since the vibration behaviours of a piezoelectric vibration system change with an electrical load,thevibration of such a system will be damped,when the electrical load includes a resistance component.Basedon this effect,a principle of piezoelectric damping of vibration is developed.In this paper piezoelectric damping configurations for both thickness and longitudinal vibrations areexperimentally studied.The results show that the piezoelectric material may become a new type of materialfor damping and the piezoelectric vibrator can be used as a new type of damper.The piezoelectric damping adjustment is convenient and can be carried out continuously andinstantaneously.     

MEASUREMENT METHOD OF MATERIAL CONSTANTS OF THIN PIEZOELECTRIC CYLINDRICRL TUBES

This paper reports a new measurement method of the constants of piezoelectric ceramics.Themethod can be used for measuring the material constants of the radially polarized thin piezoelectricceramic cylindrical tubes.The mathematical formulas only contain very simple algebraic operationand the measurement equipments in use is usual electrical ones.Using developed method,we candetermine Poisson's ratio σ,the elastic compliances_(11)~E at constant electric field,the planar electrome-chanical coupling factor k_p,the transverse electromechanical coupling factor k_(31),the mass density p and the dielectric constant ε_(33)~T/ε_0 at constant stress.The material constants obtained from theradially polarezed thin cylindrical tubes by our method are in good agreement with the results ob-tained by using the method in IRE Standards on Piezoelectric Crystals.     

RECONSTRUCTIONS OF PHASE SPECTRUM AND TRANSIENT RESPONSES OF SPHERICAL PIEZOELECTRIC TRANSDUCER

In this paper,a simple method deriving the transfer function of a spherical piezoelectric transducerhas been given.Transient responses have been obtained from the analytical expression of transferfunction by using FFT.Calculated results show that the impulse response of the spherical piezoelectrictransducer also exhibits the minimum phase behaviour and so the phase spectrum of its transfer func-tion can be reconstructed from the amplitude spectrum by using the Hilbert transform,the reconstruct-ed phase spectrum is in good agreement with that calculated from the analytical expression of transferfunction directly. Based on above-mentioned results,the phase spectrum of transfer function of a F42-c spherical pic-zoelectric transducer has been reconstructed from the measured values of its amplitude spectrum for thefirst time.The reconstructed phase spectrum is basically consistent with the measured values of phasespectrum. In addition,the impulse response and step response of F42-c spherical piezoelectric tra     

SCATTERING OF PLANE WAVE BY PIEZOELECTRIC CYLINDER——TRANSFER FUNCTION,TRANSIENT RESPONSES AND PHASE RECONSTRUCTION OF TRANSDUCER

In this paper,under Kirchhoff's assumptions,a theory of the thin shell of radially-Polarizedpiezoelectric ceramic cylinder has been developed.Using the methods of Green's function and separa-tion of variables the scattering of a plane wave by the cylinder has been solved.The normal modeseries expressions of the velocity distribution of the surface of the cylinder and of the total soundfield have been obtained and from those an exact analytic expression of the transfer function of thecylinder as a sound receiver has been give.Arbitrary transient response of the cylinder can be cal-culated from the transfer function by using FFT. For PZT-5 piezoelectric ceramic cylinder,the transfer function,impulse response and step responsehave been calculated.The results show that the impulse response displays a typical minmum phasebehaviour and the cylindrical piezoelectric receiver belongs to the minimum phase system.Therefore,the phase spectrum of transfer function of the receiver can be reconstructed from its amplit     

ANALYSIS OF SURFACE EXCITATION OF ELASTIC WAVE FIELD IN A HALF SPACE OF PIEZOELECTRIC CRYSTAL——GENERAL FORMULAE OF SURFACE EXCITATION OF ELASTIC WAVE FIELD

This paper developes the general theory of the surface excitation of elastic wave field in a halfspace of piezoelectric crystal for both free and metallized surfaces.It is shown that the general elas-tic wave field U is equal to the convolution of the generalized Green's functions G and the general-ized forces T, U = G Twhere symbol,expresses dot-product-convolution. The generalized Green's functions are independent of excitation conditions and only dependenton material parameters and orientation. For the piezoelectric crystal,not only a mechanical source distribution at the surface,but anelectrical source distribution can also excite the elastic wave fields.Complete expressions of thegeneralized forces representing mechanical and electrical source distribution respectively are given.Especially for the free surface,the surface electrical sources can be composed of the discontinuityof normal electric displacement at the surface,and of the discontinuity of the tangential electric fieldas well.     

COMPLETE EQUIVALENT CIRCUIT FOR RADIAL MODE OF PIEZOELECTRIC DISKS

Radial mode resonator of a piezoelectric disk is extensively applied to piezoelectric measure-ment;it has been a major subject of piezoelectric measurement in international standardization.Mason investigated this mode at first,and he derived the electrical admittance formula and approximateequivalent circuit that is only correct to the vicinity of the fundamental frequency.In this article,based on the admittance formula derived by Mason and using the Mittag-Leffler's theorem the completeequivalent circuit has been derived that is applicable to any frequency.It is proved that the completeequivalent circuit corresponds to the strict analytic solution derived from wave equation.     

THEORETICAL ANALYSIS OF REAL-TIME AIR-GAP COUPLED SAW CONVOLVERS

In this paper,a new theory is developed for the analysis of real-time air-gap coupled SAWconvolvers.There are two important features about the theory proposed here.Firstly,we rigorouslyconsider the role of the surface states of semiconductors in acoustoelectric nonlinear interactions.Secondly,by means of a new equivalent circuit for such a convolver,we derive various new analyticalexpressions which describe the linear coupling coefficient for air-gap,nonlinear coupling coefficientfor acoustoelectric nonlinear interactions,and convolution output(or figure of merit);these expres-sions exhibit obvious dependence on bias.The frequency response of the surface states is also ana-lyzed. The theory presented here is a general formula applicable to dealing with the situation when thesemiconductor surface is accumulated,at flat-band,depleted,or inverted. The presented theory can essentially explain experimental results of SAW acoustoelectric non-linear interactions which were carried out by the author and others.     

GENERALIZED GREEN''''S FUNCTIONS OF SURFACE EXCITATION OF ELASTIC WAVE FIELDS IN A PIEZOELECTRIC HALF-SPACE

Since the generalized Green's functions,which correspond to surface excitation of elastic wavefields in a half-space of piezoelectric crystal,are independent of excitation conditions and only depen-dent on material parameters and orientation,they can be investigated in advance and independently. It is shown that the generalized Green's functions can be written as a sum of three parts repre-senting separately a surface wave,a bulk wave and an electrostatic effect. We also confirm that the surface wave part and the bulk wave part at the far field of the generalizedGreen's functions can be expressed by analytical expressions,and thus,the surface wave field and thefar field of bulk wave among the excited elastic wave fields can be evaluated exactly. Finally,as an example,the generalized Green's functions for the 6 mm crystal are given.     

ANALYSIS OF THE LOWER MODES OF FREE VIBRATION OF A PIEZOELECTRIC CERAMIC DISK POLARIZED IN THE THICKNESS DIRECTION

By means of the adjoints method of solving the differential equations of two-point boundaryvalue problems,the equations of motion of a boundary stress-free ceramic disk vibrator polarizedin the thickness direction are solved by numerical integration.The resonance frequencies of the lowermodes of radial vibration under the influence of motion in the thickness direction and the particledisplacement distribution patterns are obtained for disks whose thickness-diameter ratios are less than0.45.Correction curves for thickness effect on fundamental frequencies are given.Curves showing.the effect of Poisson ratio on the relation between the second harmonic-fundamental ratio and thethickness-diameter ratio are also given. In the numerical calculations,piezoelectric ptoperties of the ceramic disks are fully taken intoconsideration and no restrictions are set for the dimensions of the disks.Experimental results agreewell with those obtained by calculation.     

VIBRATION OF IMMERSED RECTANGULAR COMPOSITE PLATE EXERTED BY UNDERWATER SOUND

Based on the theory of elastisity,according to the principle of least elastic energy and variationalmethod,the position of neutral surface of the elastic composite plate system is determined.And then,the governing equation for the flexural vibration of composite plate system is derived.After intro-ducing the equivalent rigidity,Poisson's ratio and surface mass density,the governing equation andboundary conditions of this plate system may be deduced in the form similar to those of thin platewith same boundary conditions.The governing equation for bending motion of elastic-viscoelasticcomposite plate system is derived from the theory of viscoelasticity.Then,the effective damping con-stant of plate system may be calculated by dynamic constants of material of these plates.A generalsolution for the bending motion of plate system is given by the method of normal mode analysis andFourier analysis.As an example,a simply-supported rectangular composite plate system is concerned.The equivalent rigidity,Poisson's r     

THE ENERGY SPECTRUM AND WAVEFUNCTION OF NUCLEUS 31Si——A TEST ON THE COMPOSITE PARTICLE REPRESENTATION THEORY

The nuclecus ³¹Si₁₇ is studied by the composite particle representation theory and compared with the shell model calculations. It is shown that the entire energy spectrum agrees with the shell model results very well, and the wave function is equivalent to the shell model wavefunction exactly. Therefore it strongly supports the composite particle representation theory.     

THE EFFECT OF ELECTRIC LOAD ON THE CHARACTERISTICS FOR PIEZOELECTRIC VIBRATIONAL SYSTEM

The effect of electric load on the piezoelectric vibrational system due to electroacoustic coupling isanalytically investigated.The analytical results show that:(1)when load impedance continuallychanges from ∞to+∞,the mechanical resonant frequency of the system would fill all frequencydomain from 0 to ∞;(2)the displacement and stress distributions also would change,even the dis-placement may be zero at both free ends(i.e.at points where stress is equal to zero). Finally,the experiments for longitudinal vibration of piezoelectric strip of lateral polarizationare given and compared with theoretical results.     

THE DESIGN OF A SENSITIVE LOW FREQUENCY COUPLED RESONANT PHOTOACOUSTIC CELL

This paper describes the structure and characters of a coupled resonant photoacoustic cell whichhas a smaller volume and operates at the modulation frequency of several hundred Hz.By the adop-tion of transverse exciting light and differential receiving the detection SNR is increased.Its detec-tion sensitivities for concentration of CH_3OH and C_2H_4 have reached 1.2×10~(-9)/W Hz~(1/2) and4.2×10~(-9)/W Hz~(1/2) respectively.     

SCATTERING NEAR FIELD OF A RECTANGULAR COMPOSITE PLATE IMMERSED IN WATER

According to the extensive theory of flexural vibration of elastic-viscoelastic composite platesystem in a previous paper,the vibration and scattering sound near field of an immersed rectangularelastic-viscoelastic composite plate in an underwater sound are studied.The solution for deflectionof the composite plate is expanded into a series in terms of normal mode,whatever plate is vibratingin water under the influence of incident sound wave.The interaction between normal modes owingto sound field coupling is taken into consideration.As a function of(kl_1,r;m,n;p,q),the couplingcoefficients between(m,n);(p,q)modes of vibration are calculated numerically.Whith these coef-ficients,the vibration of composite plate and the sound irradiation from which may be characterized(where k is wave number,l_1,is length of one parallel edges,r=1_2/l_1 is parametric variable,l_2 is lengthof another parallel edges).And then,the complex values of amplitude of normal modes for flexuralmotion of a Steel-Rubber bilaminar plate     

COMPOSITE NATURAL ORBITAL METHOD—A TEST ON BIPYRROLH

A scheme for construction of virtual orbitals for use in a config-uration interaction(CI)method is described and is applide to the2,2＇-bipyrrole molecule.     

COMPOSITE NATURAL ORBITAL METHOD—A TEST ON BIPYRROLE

A scheme for construction of virtual orbitals for use in a configuration interaction(CI) method is described and is applied to the 2,2‘-bipyrrole moecule.