摘要:

The power extracted from a piezoelectric surface wave in quartz by an arrangement of electrodes on the surface is determined by a perturbation technique, which is extremely accurate for low‐coupling materials. The mechanical portion of the surface wave is found by neglecting the piezoelectric coupling, which is very small in quartz. The elastic solution then yields both volumetric and surface source terms, which are generated by the piezoelectric coupling and drive the steady‐state electrostatic solution. A technique is introduced for reducing the remaining electrostatic problem to Laplace's equation, subject to such boundary conditions that the solution is amenable to conformal mapping techniques for several interesting, and possibly useful, electrode arrangements. Surface waves propagating along the digonal axis for all rotatedYcuts are considered, as well as those propagating in all directions along the surface of anX‐cut crystal. A reciprocal relation between the excitation and detection problems is derived, and is used to determine the amplitude of a surface wave generated by the application of an alternating voltage to the surface electrodes when the solution to the detection problem for the same arrangement of electrodes is known.

ISSN:0001-4966    

DOI:10.1121/1.1910447

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

Mathematical techniques are discussed whereby one may analyze a thin piezoelectric plate with arbitrary electrodes, external electrical loads, and external mechanical tractions. These techniques include tensor Green's‐function operations, Fourier‐eigenmode expansions, and circuit‐theory manipulations. Application of these techniques leads to admittance matrices interrelating the linear responses of the various mechanical terminals (i.e., the sites of external‐force application) and electrical terminals (i.e., electrodes). It is demonstrated that these admittance matrices may be represented by quite simple equivalent circuits. External mechanical forces may be applied either at a point or over a distributed area. These two types are represented best by separate methods, both of which are discussed here. Two specific, nontrivial examples of actual piezoelectric devices are analyzed at the conclusion of this work, and results are compared with experimental observations. These examples are a symmetrically electroded ferroelectric ceramic disk bonded to a substrate and an asymmetrically electroded, mechanically free, ferroelectric ceramic disk. Effects due to loss, nonuniform density, and nonuniform material coefficients (elastic, dielectric, and piezoelectric) have been included in this work. However, finite‐plate‐thickness effects, such as electrical fringing and particle accelerations perpendicular to the plane of the plate, are not included.

ISSN:0001-4966    

DOI:10.1121/1.1910448

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

An electromechanical bandpass filter that is suitable for low frequencies is described. The mechanical filter consists of two transducer‐resonators and two couplers, of which the transducer‐resonators vibrate transversely and are coupled at their nodal points with the torsionally vibrating couplers. Each transducer‐resonator consists of two pieces of electrostrictive material with a basis reed sandwiched between them. Also, in this paper, the effects of impedance of electrostrictive material on the basis reed are analyzed. In order to analyze the mechanical vibrating system, mechanical network theory is adopted.

ISSN:0001-4966    

DOI:10.1121/1.1910449

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

The thickness/twist vibrations of a truncated, linearly tapered, quartz‐crystal strip are investigated. The frequency equation is expressed in terms of Bessel functions, with the order, in general, a large irrational number. Frequencies and mode shapes depend on two geometric parameters expressing the taper and a length/thickness ratio. Numerical values for several modes and a range of the geometric parameters are given forAT‐cut quartz to illustrate typical results. Frequencies are only slightly higher than for a corresponding uniform strip, and depend mainly on the maximum thickness of the tapered strip. Motion of the strip is concentrated at the thick end, even for very slight taper, but spreads gradually across the strip as the taper is reduced, approaching in the limit the response of a uniform strip.

ISSN:0001-4966    

DOI:10.1121/1.1910450

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

Two methods are described for calculating Bechmann's number for harmonic overtones of thickness/twist modes in rotatedY‐cut quartz plates: one based on an exact solution of the equations of elasticity and the other based on an asymptotic form of the exact solution. The latter leads to an explicit formula for Bechmann's number and it is shown to give results very close to the former—which requires extensive computations.

ISSN:0001-4966    

DOI:10.1121/1.1910451

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

Electrical characteristics of a lossless ceramic resonator with a fully covered electrode can be expressed by three basic parameters: clamped capacitance, electromechanical coupling factor, and the gravest resonant frequency or antiresonant frequency. Unified formulas are derived for various modes of vibration with longitudinal and transverse electric fields. The formulas are valid for a very wide range of frequency, but it is not easy to use them for calculation in most cases because of the transcendental functions involved. Hence, approximate formulas are derived that are simple and easy to calculate but accurate enough for practical uses. The accuracy of the approximation is far better than the accuracy of conventional lumped‐constant equivalent‐circuit representation. A novel method for determining three basic parameters of a ceramic resonator with transverse electric field is developed, based on the present approximate formulas. The method requires only the measurement of resonant frequencies, before and after the insertion of a series capacitance, and eliminates the need for both the measurement of antiresonant frequency and the measurement of low‐frequency capacitance, which are required in a conventional practice.

ISSN:0001-4966    

DOI:10.1121/1.1910452

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

The behavior of thickness/shear‐mode quartz resonators is explained both mathematically and experimentally in terms of lateral standing‐wave trapped‐energy modes. A cutoff phenomenon, similar to that occurring in optical total internal reflection, results in energy trapping or the restriction of vibratory energy almost exclusively to the electroded region of a resonator, with an energy distribution decreasing exponentially with distance from the electrode edge. Consideration of boundary conditions at the electrode edges of an idealized two‐dimensional model yields an expression for the eigenfrequencies of symmetric inharmonic overtone modes (lateral standing waves) that can exist in the electroded region of fundamental‐ and harmonic‐mode resonators. Design formulas for the suppression of these unwanted modes are included. They show that electrode thickness and lateral dimensions can be traded off against one another to obtain a wide range of motional parameters. Previously, unwanted responses were eliminated by restricting the electrode diameter to empirically established values. The present understanding has led to a reduction in resonant resistance and an increase in motional capacitance by at least a factor of four with hf and vhf fundamental‐ and harmonic‐mode filter crystals. Experimental data that verify results predicted by energy‐trapping theory are given, and application to design of single‐ and multi‐electrode resonators is considered. Specific examples in the 10‐ to 180‐MHz frequency range are given.

ISSN:0001-4966    

DOI:10.1121/1.1910453

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

The frequency versus length‐to‐thickness ratios for the thickness/shear and thickness/twist modes inBT‐cut quartz plates are given. TheC44thickness/shear frequency is calculated and this mode is identified in contoured circularBTplate by x‐ray‐diffraction topography. The electrode‐length to plate‐thickness ratios for suppressing the anharmonic overtones in bothATandBTplates as a function of electrode thickness are derived and compared with those measured on partially electroded quartz plates. The use ofBTplates as singly resonant and coupled‐mode resonators is discussed.

ISSN:0001-4966    

DOI:10.1121/1.1910454

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

The geometry of the human vocal tract from the glottis (vocal cords) to the lips is one of the determining factors in human speech production and basic to a better understanding of articulation. Measurement of the vocal‐tract geometry is difficult, especially that of its time‐dependent behavior during connected speech utterances. Practically the only tools that have been available in the past for such measurements are radiography and cinéradiography. Unfortunately, radiographic measurements and their evaluation are laborious. In addition, adequate cinéradiography for longer utterances poses severe problems owing to dosage limitations. Alternative methods of obtaining information on the vocal‐tract geometry have therefore always remained a desideratum. In this paper, it is shown that some of the desired vocal‐tract‐shape information can be obtained by purely acoustic measurements. Two kinds of acoustic methods are discussed in some detail: measurement of the eigenfrequencies (formants) of the vocal tract and measurement of the acoustic impedance at the lips. Both measurements allow the determination of an approximation to the cross sectional area of the vocal tract as a function of distance along its axis. More specifically, if the logarithm of the area function is described by a Fourier series, these measurements allow the determination of certain terms of the Fourier series. The number of terms, and therefore the spatial resolution of the approximation, increases with the number of measured eigenfrequencies of the tract or with the number of measured singularities of the impedance function. Both methods are applicable to dynamic measurements during nonstationary utterances and hold promise for supplying large amounts of area data necessary for specifying or refining articulatory models of speech production. The results can be portrayed by computer‐drawn single frames or motion pictures of the acoustically derived area functions.

ISSN:0001-4966    

DOI:10.1121/1.1910429

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP

摘要:

Some techniques for bonding piezoelectric transducers to various materials at cryogenic temperatures are discussed. A number of bond materials are mentioned from the literature, along with a new material, di‐2‐ethylhexylsebacate (Plexol®). Factors involving the choice of transducer ‐i.e., expansivtiy, thickness, and finish—are discussed. Experimental data on the mechanical impedance of some of the materials are presented.

ISSN:0001-4966    

DOI:10.1121/1.1910430

出版商:Acoustical Society of America    

年代:1967

数据来源: AIP