Piezoelectric ceramic rectangular transducers in flexural vibration

Based on the equivalent elastic method and coupled vibration theory, an analytic method is presented to study the flexural vibration of rectangular transducers consisting of piezoelectric ceramic thin plates. By introducing a mechanical coupling coefficient, the flexural vibration of the piezoelectric ceramic rectangular thin plate is reduced to two simple, one-dimensional flexural vibrations of narrow piezoelectric ceramic strips. The resonance frequency equations for the piezoelectric ceramic rectangular thin-plate transducers in flexural vibration are derived under the free and simply supported boundary conditions analytically. The relationship between the resonance frequency and the flexural vibrational order, the geometrical shape, and the dimensions of the piezoelectric ceramic rectangular thin-plate transducer is analyzed. It is demonstrated that the one-dimensional vibrational theory for the flexural vibration of a narrow piezoelectric ceramic strip and the stripe-mode flexural vibrational theory for the piezoelectric ceramic rectangular thin plate can be derived directly from the theory obtained in this paper. Experimental results show that the measured resonance frequencies of the piezoelectric ceramic rectangular thin-plate transducers in flexural vibration under free-boundary conditions are in good agreement with the calculated results. The method presented in this paper can be used in the resonance frequency analysis of vibrating systems in coupled vibration.     

A concentric-ring equivalent phased array method to model fields of large axisymmetric ultrasound transducers

An equivalent concentric-ring ultrasound phased array method was developed to estimate ultrasonic continuous wave fields generated by axisymmetric single-source transducers. The method models a given source as a concentric-ring phased array by mathematically segmenting it into many rings and subsequently finding the amplitude and phase for each ring that produces an acoustic field similar to the field of the single-source transducer. The excitation source of each ring was calculated using an inverse technique based on complex pressure measurements along a radial line close to the source. The predicting abilities of the method are evaluated by comparing measured and estimated ultrasound fields for six different transducers. The results show that the concentric-ring equivalent phased array method (CREPAM) is able to estimate quantitatively the ultrasound fields generated by large axisymmetric planar and focused transducers.     

On the development and testing of a guided ultrasonic wave array for structural integrity monitoring

The prototype of a guided ultrasonic wave array for the structural integrity monitoring of large, plate-like structures has been designed, built, and tested. The development of suitably small transducers for the excitation and measurement of the first antisymmetric Lamb wave mode Ao is described. The array design consists of a ring of 32 transducers, permanently bonded to the structure with a protective membrane, in a compact housing with the necessary multiplexing electronics. Using a phased addition algorithm with dispersion compensation and deconvolution in the wavenumber domain, a good dynamic range can be achieved with a limited number of transducers. Limitations in the transducer design and manufacture restricted the overall dynamic range achieved to 27 dB. Laboratory measurements for a steel plate containing various defects have been performed. The results for standard defects are compared to theoretical predictions and the sensitivity of the array device for defect detection has been established. Simulated corrosion pitting and a defect cut with an angle grinder simulating general corrosion were detected.     

Omni-directional guided wave transducer arrays for the rapid inspection of large areas of plate structures

Omni-directional guided wave array transducers contain a circular pattern of elements that individually behave as omni-directional point transmitters or receivers. The data set acquired from such an array contains time-domain signals from each permutation of transmitter and receiver. A phased addition algorithm is developed that allows an omni-directional, B-scan image of the surrounding plate to be synthesized from any geometry of array. Numerically simulated data from a single reflector is used to test the performance of the algorithm. The results from an array containing a fully populated circular area of elements (Type I array) are found to be good, but those from an array containing a single ring of elements (Type II array) contain many large side-lobes. An enhancement to the basic phased addition algorithm is presented that uses deconvolution to suppress these side-lobes. The deconvolution algorithm enables a Type II array to equal the performance of a Type I array of the same overall diameter. The effect of diameter on angular resolution is investigated. Experimental data obtained from a guided wave array containing electromagnetic acoustic transducers (EMAT) elements for exciting and detecting the S/sub 0/ Lamb wave mode in a 5-mm thick aluminium plate are processed with both algorithms and the results are discussed.     

Electromagnetic wave propagation in rectangular waveguides filled with Omega-medium

A time-harmonic electromagnetic plane wave propagating in a uniaxial bianisotropic medium, the so-called Omega medium, is considered. Plane waves are identified together with their dispersion equations with the help of an appropriate coordinate system. The plane wave solution is then used to study in a rigorous way the coupled-mode equations satisfied by the electromagnetic field in a rectangular waveguide filled with such a material and bounded by perfect electrically conducting walls. The features of this approach are demonstrated and an application to rectangular waveguides is discussed. Numerical results are also presented as a function of the material parameters.     

Analysis of piezoelectric ultrasonic transducers attached to waveguides using waveguide finite elements

A finite-element modeling procedure for computing the frequency response of piezoelectric transducers attached to infinite constant cross-section waveguides, as encountered in guided wave ultrasonic inspection, is presented. Two-dimensional waveguide finite elements are used to model the waveguide. Conventional three-dimensional finite elements are used to model the piezoelectric transducer. The harmonic forced response of the waveguide is used to obtain a dynamic stiffness matrix (complex and frequency dependent), which represents the waveguide in the transducer model. The electrical and mechanical frequency response of the transducer, attached to the waveguide, can then be computed. The forces applied to the waveguide are calculated and are used to determine the amplitude of each mode excited in the waveguide. The method is highly efficient compared to time integration of a conventional finite-element model of a length of waveguide. In addition, the method provides information about each mode that is excited in the waveguide. The method is demonstrated by modeling a sandwich piezoelectric transducer exciting a waveguide of rectangular cross section, although it could be applied to more complex situations. It is expected that the modeling method will be useful during the optimization of piezoelectric transducers for exciting specific wave propagation modes in waveguides.     

Broadband Poly(vinylidene fluoride-trifluoroethylene) Ultrasound Focusing Transducers for Determining Elastic Constants of Coating Materials

This paper develops broadband Poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] focusing transducers and its surface wave measurement system for determining the elastic constants of coating layers. The measurement is based on a defocussing measurement method and V(f,z) analysis of the focusing transducers. Few P(VDF-TrFE) focusing transducers are successfully fabricated in laboratory and the wave measurements can cover a wide frequency range of 4–120 MHz with great accuracy. Brass and glass substrates electroplated with nickel coating layer with thickness ranging from 15 to 60 μm are tested in this work. Dispersion curves sensitivity analysis is carried out to decide the best approach for inversely determination of coating elastic properties. A searching method based on the downhill simplex algorithm and numerical calculation on waves in a layered half-space model is used for inversely determining the elastic constants of coating layer. The results show good agreement with reported data. Measurement accuracy and potential applications for other types of nondestructive evaluation of the focusing transducers and measurement system are addressed.     

Guided Waves in Functionally Graded Rods with Rectangular Cross-Section under Initial Stress

The characteristics of the guided waves propagation in functionally graded rods with rectangular cross-section (finite width and height) under initial stress are investigated in this paper based on Biot’s theory of incremental deformation. An extended orthogonal polynomial approach is present to solve the coupled wave equations with variable coefficients. By comparisons with the available results of a rectangular aluminum rod, the validity of the present approach is illustrated. The dispersion curves and displacement profiles of various rectangular functionally graded rods are calculated to reveal the wave characteristics, and the effects of different width to height ratios and initial stress and gradient functions on the guided waves are discussed in detail.     

Numerical analysis of the radiated fields of ultrasonic transducers

A finite element model is implemented for simulating the radiated fields of both planar and curved transducers in acoustic media. The approach is based on general finite element analysis developed for solving the governing equations of elastic wave propagation. The distributions of the wave fields are presented for both the nearfield and farfield regions of the transducer. Three excitation pulses with the same center frequency but different bandwidths are examined and the accuracy is indicated by a comparison of the simulation results for the axial and transverse fields with the analytical results for continuous wave excitation.     

基于超声导波的钢梁结构损伤大小识别研究

本研究探讨了应用超声导波检测技术在较厚结构中对结构损伤大小识别的可行性。基于优化的激励波形和PZT换能器布局,应用商业有限元软件Abaqus对导波在结构中的传播进行了仿真;同时对无损伤及有损伤的仿真模型进行了实验验证,实验信号与仿真波形具有很好的吻合度。仿真结果表明：随损伤深度或者损伤厚度的增加,损伤反射波波包、透射波波包的到达时间和信号幅值都会随之呈现一定规律的变化,从中提取变化较大的信号特征可用于损伤大小的识别。     

Inductive and Transformative Transducers with Short-Circuiting Ring

An ideal short-circuiting ring (R = 0) represents an infinite magnetic resistance for magnetic flux. A core of suitable shape allows an influence to be exercised upon the path of magnetic flux in a ferromagnetic circuit by displacing a short-circuiting ring. This fact may be utilized to construct transformative or inductive transducers. Two practical arrangements are described, and the effects on the characteristics of various parameters such as short-circuit resistance, core geometry, frequency of the energizing current, etc., are explained. The transducers examined attain a linearity error of 0.3 percent for displacement of 10 cm. The transducers, as described, do not show any wear, and the force of the short-circuiting ring exerted on the object of measurement remains a factor of 1000 below the force of the transducer used previously. Consequently, transducers (for linear travel or angular rotation) with short-circuiting rings are suitable both for use as rugged shop instruments and for precision transducers in metrology and control.     

An ultrasonic linear motor using ridge-mode traveling waves

A new type of ultrasonic linear motor is presented using traveling waves excited along a ridge atop a substrate. The ridge cross section was designed to permit only the fundamental mode to be excited during operation of the motor, with a Langevin transducer used as the source of vibration in this study. The ridge waveguide was first made of lossy media to avoid reflecting vibration energy back toward the vibration source, forming a traveling wave. A 5-mm-wide, 15-mm-tall rectangular acrylic ridge was used to move a slider placed upon it toward the vibration source, in opposition to the direction of the traveling wave transmitted along the waveguide ridge. Using a low-loss 3 x 6-mm aluminum rectangular ridge combined with a damper clamped onto the far end of the waveguide, similar results were obtained. To obtain bidirectional operation, the damper was replaced with a second Langevin transducer, giving a pair of transducers located perpendicularly to the ends of the ridge and driven with an appropriate phase difference. The moving direction of the slider was reversed by shifting this phase difference by about 180 degrees. With this simple configuration, it may soon be possible to fabricate a linear micromotor system on a silicon substrate or other semiconductor wafer adjacent to other electronic and optoelectronic devices.     

Evaluation of wafer bonded CMUTs with rectangular membranes featuring high fill factor

Increasing fill factor is one design approach used to increase average output displacement, output pressure, and sensitivity of capacitive micromachined ultrasonic transducers (CMUTs). For rectangular cells, the cell-to-cell spacing and the aspect ratio determine the fill factor. In this paper, we explore the effects of these parameters on performance, in particular the nonuniformity of collapse voltage between neighboring cells and presence of higher order modes in air or immersed operation. We used a white light interferometer to measure nonuniformity in deflection between neighboring cells. We found that reducing the cell-to-cell spacing could cause bending of the center support post, which amplifies nonuniformities in collapse voltage to 18.4% between neighboring cells. Using a 2-D finite element model (FEM), we found that for our designs, increasing the support post width to 1.67 times the membrane thickness alleviated the post bending problem. Using impedance and interferometer measurements to observe the effects of aspect ratio on higher order modes, we found that the (1,3) modal frequency approached the (1,1) modal frequency as the aspect ratio of the rectangles increased. In air operation, under continuous wave (CW) excitation at the center frequency, the rectangular cells behaved in the (1,1) mode. In immersion, because of dispersive guided modes, these cells operated in a higher order mode when excited with a CW signal at the center frequency. This contributed to a loss of output pressure; for this reason our rectangular design was unsuitable for CW operation in immersion.     

Optimization of broadband withdrawal weighted interdigital transducers for high selective SAW filters

The problem under discussion is the design of highly selective broadband surface acoustic wave (SAW) interdigital transducers (IDT) with uniform electrodes. In most SAW filters, such transducers are used with apodized IDTs or instead of them. The proposed optimization algorithms are intended for improvement of IDT selectivity by means of a withdrawal weighting (WW) technique. Unlike the familiar methods of WW transducer optimization, these algorithms choose the best IDT structure on the basis of how well it meets the specifications, not in the time but in frequency domain directly. This approach is more effective for broadband WW transducers. A number of SAW filters have been designed using the described algorithms. Their experimental characteristics follow: bandwidths of 0.5 to 15%, stopband rejection of 40 to 50 dB, 3 dB/40 dB shape factors of 1.07 to 1.3.     

Ring vibrations in an acoustic medium as a source of ultrasonic radiation

In this paper, the vibrational characteristics of ultrasonic transducers consisting of a ceramic ring filled with a plastic disk are considered. For axially symmetric resonances, the vibrational amplitude on the surface of the plastic core is approximately described by a truncated Bessel function of zero order and first kind J(0), leading to an ultrasonic beam which is nondiffracting near the transducer. The near- and far-field pressure distributions of such transducers are measured and compared with model predictions. In the near zone, the width of the measured main lobe is narrow, which is in accordance with the theoretical results for circular transducers with a truncated Bessel function amplitude distribution. By changing the inner diameter of the ring, it is possible to control the resonance frequency of the plastic core. On the other hand, the resonance frequency of the ring may be regulated by varying its width. The existing coupling of resonant vibrations of the ceramic ring and plastic core enables variations of the bandwidths of the considered circular transducers.     

Optimal wave with respect to efficiency in percussive drilling with integral drill steel

The problem considered is that of finding the optimum wave of given finite duration that maximizes the efficiency of conversion of wave energy into work in percussive drilling with integral drill steel (drill rod with integrated bit). A 1D model is used for the drill rod, and the bit-rock interaction is represented by a piecewise linear force versus penetration relation with different penetration resistances for primary loading and for unloading/reloading. A functional expressing the dependence of the efficiency on the incident wave is derived and maximized. The optimal incident wave has exponential shape with time constant for the growth rate equal to the characteristic response time of the percussive drill system, including the rock. The maximal efficiency increases monotonously with the duration of the optimal wave. It approaches zero for very short waves and unity for very long waves. Optimal waves of short duration are close to rectangular while those of long duration approach the semi-infinite exponential wave derived by Long in the 1960s. Optimal waves of medium or longer duration give significantly higher efficiencies than commonly used rectangular waves of the same duration.     

Wave propagation in multilayered piezoelectric spherical plates

This paper proposes an improvement of the Legendre polynomial series method to solve the harmonic wave propagation in multilayered piezoelectric spherical plates, which are used in point-focusing transducers. The conventional Legendre polynomial method can deal with the multilayered structures only when the material properties of two adjacent layers do not change significantly and cannot obtain correctly normal stress and normal electric displacement shapes unlike the proposed improved orthogonal polynomial approach which overcomes these drawbacks. Detailed formulations are given to highlight its differences from the conventional Legendre polynomial approach. Through the comparisons of numerical results given by an exact solution (obtained from the reverberation-ray matrix method), and by the conventional polynomial approach and the improved polynomial approach, the validity of the proposed approach is illustrated. The influences of the radius-to-thickness ratio on dispersion curves, stress and electric displacement distributions are discussed. It is found that three factors determine the distribution of mechanical energy and electric energy at higher frequencies: radius-to-thickness ratio, wave speed, and position of the component material.     

Focusing of Rayleigh waves: simulation and experiments

A linear array of surface wave transducers has been developed to generate focused surface wave motion. A novel theoretical approach, whereby time-harmonic surface wave motion is represented by a carrier wave that satisfies a reduced wave equation on the surface of the body and supports the subsurface motion, is used to model the beam generated by a single element of the array. Comparison of theoretical and experimental results show that, for a single element, the opening angle of the beam is about 20 degrees and its cross-section can be represented by a Gaussian distribution of the normal displacements. For an eight-element array, the focused beam is subsequently obtained by superposition considerations. For the focused beam comparisons of theoretical and experimental results, in which the latter have been obtained by the use of a laser interferometer, show excellent agreement both for the normal displacements along a radial line and across the width of the beam. The array can be used for self-focusing of surface waves on a surface defect.     

Scattering of waves by flaws in anisotropic laminated plates

The strip element method (SEM) is used to investigate wave scattering by rectangular flaws in anisotropic laminated plates. The plates containing flaws are divided by junctions into domains in which the SEM is applied. For each domain, SEM equations are obtained which give a relationship between the traction and displacement vector on the vertical boundaries. A set of equations which gives a relationship between the traction and displacement vector on the junctions is then obtained by assembling the SEM equations for all the domains. This set of equations is solved by using the conditions on the junctions. Scattered wave fields in the frequency domain for isotropic and composite plates with rectangular flaws are computed and discussed in comparison with results for corresponding plates without flaws. A technique for determining the length of a rectangular flaw in a plate is also presented. The results presented in this paper are of importance and could be used in the characterization of flaws in anisotropic laminated plates.