Dynamics of an ultrasonic transducer used for wire bonding

The vibration displacement distributions along a transducer used in ultrasonic wire bonding were measured using a heterodyne interferometer, and many nodes and anti-nodes were found. A mechanical finite element method (FEM) was used to compute the resonant frequencies and vibration mode shapes. The displacement distributions of the dominant 2nd axial mode agreed well with the measured values. Undesirable nonaxial modes, including the higher order flexural and torsional modes, also were excited at frequencies very close to the working frequency (2nd axial mode) of the transducer. Hence, the measured displacements were the resultant of all the allowable modes being excited. However, the excitation of these nonaxial modes were small enough not to affect the formation of consistent and high quality wire bonds. Results of the present study were used to determine a suitable location for installing a piezoelectric sensor to monitor the bond quality.     

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.     

An alternative approach of acousto-ultrasonic technique formonitoring material anisotropy of fiber-reinforced composites

An alternative acousto-ultrasonic (AU) technique has been developed for nondestructive evaluation (NDE) of fiber-reinforced composites. The technique measures the time of flight (TOF) of AU waves, instead of the stress wave factor, by two low-frequency (0.5 MHz) transducers and relates TOF to material properties and fiber orientation. As the transducer separation increases, the measured time-domain AU signals clearly separate into two groups, since the excitation is under the first critical frequency, which correspond to the first two fundamental modes of the Lamb waves. One is an antisymmetric mode with slower propagation velocity and is highly dispersive, while the other is a symmetric mode with faster propagation velocity, which is very close to that of the longitudinal bulk wave, and is nearly nondispersive. The phase velocity in the composites can be accurately determined from the slopes of the TOF curves, and depends strongly on the azimuthal angle, frequency, and plate thickness. If the wave propagates away from the fiber direction, a slower but more attenuated wave is observed. Phase-velocity curves in azimuthal angles were obtained for E-glass/polyester, S-2-glass/epoxy, and Kevlar 49 composites. The theoretical solutions, for the longitudinal bulk wave and Lamb wave, are obtained by solving an eigenproblem once the material mechanical properties are defined. Good agreement is obtained between the measurements and the theoretical calculations     

An alternative method for suppressing undesired transverse modes inlongitudinally coupled SAW resonator filters

As known, perturbing transverse modes arising from the waveguide properties of the interdigital transducers and reflectors can appear in SAW resonator filters. Usually, these undesired modes are suppressed by transducer apodization. This method has the disadvantage of increasing the transducer impedance. We propose a longitudinally coupled resonator filter, the basic elements of which are able to guide the two slowest waveguide modes alone, but to excite and receive the first mode only. The basic elements are arranged side by side forming the complete filter permitting coupling with each other weak enough to fulfill the filter specification. The suppression of undesired modes by the construction is demonstrated by transmission measurements     

Guided acoustic wave propagation for porcelain coatingcharacterization

In this paper a measurement technique to obtain dispersion curves for guided acoustic modes in porcelain-coated steel is described. The measurement is performed with two angled ultrasonic longitudinal transducers in a pitch catch configuration by employing an immersion technique. Phase velocities for the guided modes are selected through the variation of the angle formed by the transmitter beam with the surface normal vector. The excitation signal of the transmitting transducer is a narrow band pulse. For each phase velocity, the guided mode frequencies are recovered by evaluating the frequency minima of the reflection coefficient     

Propagation and coupling of hybrid modes in twisted fibers

The first-order paraxial approximation is used to obtain the distributions of the electric and magnetic fields for the core and cladding hybrid fiber modes. The coupling coefficients of these modes are found for fibers subject to twist. The longitudinal electric field component determines the mode coupling in twisted fibers. It is shown that in the first-order paraxial approximation the cladding hybrid modes propagating in a twisted fiber rotate along the direction of the twist at the same rate as the core mode, independently of the azimuthal and radial mode numbers. Four hybrid modes constituting one linearly polarized mode have different longitudinal components, and the corresponding cladding-mode resonances of a long-period fiber grating undergo different shifts owing to different mode self-coupling coefficients. This results in the removal of mode degeneracy and splitting of resonances of long-period gratings in twisted fibers.     

双迭片弯曲压电陶瓷换能器及振动模态分析测量

介绍了双迭片弯曲压电陶瓷换能器的制作及边缘固定金属压电陶瓷双迭片弯曲振动，并利用有限元分析了换能器的谐振模式，采用激光多普勒干涉仪对换能器的谐振特性以及振动速度和位移分布进行了测量和分析，结果表明：换能器空载性能良好，通过有限元分析与先进测量手段的结合，能够对换能器器件的制作与分析进行指导。     

A single probe spatial averaging technique for guided waves and its application to surface wave rail inspection

The nondestructive testing of structures using guided waves requires systems with high mode selectivity. Usually this is achieved with relatively complex probes comprising multiple transducer rings or arrays. For the rapid inspection of very long structures with only partial access to the waveguide, this may not be a viable solution. In this paper we present a very flexible alternative whereby a simple robust probe is scanned along the wave guide, and the acquired scan data is used for customizing the mode selectivity at the postprocessing stage. The characteristics of this spatial averaging method are discussed using a simple analytical model and compared to an existing linear array technique. The mode selectivity is found to be mainly limited by the uncertainty of the phase velocity assumed for the mode of interest. The method was successfully applied to surface wave rail inspection and was found to suppress unwanted modes very efficiently.     

Comparative study of mid-infrared fibers for modal filtering

We compare the filtering capabilities of two infrared fibers developed to achieve a high rejection ratio of the higher order modes in order to obtain compact modal filters devoted to stellar interferometry. Two types of double-clad fibers are studied: a fiber with a second thin absorbing cladding and a fiber with a second thick absorbing cladding closer to the fiber core; both are single mode around the CO(2) band (10.6 μm). We present the single-mode spectral domain and the nulling capabilities of both fibers for different fiber lengths, comparing simulations with experimental results. We show that the filtering capabilities are improved when the absorbing clad is closer to the fiber core, as the propagation distance needed to filter out these modes is shorter. Thus, to obtain high rejection ratios in compact devices, an absorbing cladding close to the core of the fiber is compulsory in order to suppress cladding modes that could eventually recouple into the waveguide. We present an empirical model that allows determining the minimum filter length, considering only one effective leaky mode with low attenuation, which considerably simplifies the theoretical studies.     

Simulation of piezoelectric excitation of guided waves using waveguide finite elements

A numerical method for computing the time response of infinite constant cross-section elastic waveguides excited by piezoelectric transducers was developed. The method combined waveguide finite elements (semi-analytical finite elements) for modeling the waveguide with conventional 3-D piezoelectric finite elements for modeling the transducer. The frequency response of the coupled system was computed and then used to simulate the time response to tone-burst electrical excitation. A technique for identifying and separating the propagating modes was devised, which enabled the computation of the response of a selected reduced number of modes. The method was applied to a rail excited by a piezoelectric patch transducer, and excellent agreement with measured responses was obtained. It was found that it is necessary to include damping in the waveguide model if the response near a "cut-on" frequency is to be simulated in the near-field.     

单向复合材料的应力集中系数

本文计算了实心纤维及空心纤维单向增强复合材料在横向、纵横剪切、纵向载荷形式下的应力集中系数,着重对单向增强复合材料受纵向载荷时的纵向应力集中现象进行了分析讨论。      

The centrally cracked Brazilian disc: closed solutions for stresses and displacements for cracks under opening mode

Closed-form solutions for the stress and displacement fields in a centrally cracked Brazilian disc are obtained. The disc is subjected to uniformly distributed radial pressure along two finite symmetric arcs on its perimeter. The solution is based on the complex potentials method introduced by Kolosov and Muskhelisvili, and advantage is taken of a recently introduced closed-form solution for the intact Brazilian disc. Special attention is paid to the displacements of the crack lips, since they dictate whether the lips are in an opening or closing mode. The solutions obtained are valid for configurations for which the crack lips are in an opening loading mode, where there are no contact forces along the crack flanks. As well as stresses and displacements, the stress intensity factors are also determined in closed form and are found to be in good agreement with the respective values obtained from existing approximate solutions. Preliminary experimental data obtained using the digital image correlation technique support the analytically deduced conclusions for the deformation and rotation of the crack flanks.     

复合管状结构中超声导波的位移分布

对超声纵向导波在复合管状结构中的传播特性进行了分析。然后分析了系统中的位移分布,以此确定了各模式检测管材的最佳频厚积范围和检测的最佳位置。结果表明,各模式的径向和轴向位移在管内壁上的值较大,而在管壁中间和管外壁上的值较小;当频厚积增大到一特定值后,管壁中间和管外壁上的径向和轴向位移都近似为零,此特定值随模式阶次的提高而增加。选取各模式检测的频厚积时,应尽可能的选径向位移较小而轴向位移较大的频厚积点。     

Analysis of optical waveguide structures by use of a combined finite-difference/finite-difference time-domain method

We present a method for full-wave characterization of optical waveguide structures. The method computes mode-propagation constants and cross-sectional field profiles from a straight forward discretization of Maxwell's equations. These modes are directly excited in a three-dimensional finite-difference time-domain simulation to obtain optical field transmission and reflection coefficients for arbitrary waveguide discontinuities. The implementation uses the perfectly-matched-layer technique to absorb both guided modes and radiated fields. A scattered-field formulation is also utilized to allow accurate determination of weak scattered-field strengths. Individual three-dimensional waveguide sections are cascaded by S-parameter analysis. A complete 10(4)-section Bragg resonator is successfully simulated with the method.     

Broadband tonpilz underwater acoustic transducers based onmultimode optimization

Head flapping has often been considered to be deleterious for obtaining a tonpilz transducer with broadband, high power performance. In the present work, broadband, high power tonpilz transducers have been designed using the finite element (FE) method. Optimized vibrational modes including the flapping mode of the head are effectively used to achieve the broadband performance. The behavior of the transducer in its longitudinal piston mode and in its flapping mode is analysed for in-air and in-water situations. For the 37.8% bandwidth of the center frequency from 28.5 to 41.8 kHz, the amplitude variation of the transmitting voltage response (TVR) does not exceed ±2 dB and a maximum TVR of 146.8 dB (ref. 1 μPa/volt at 1 meter) is obtained. Reasonable agreement between the experimental results and the numerical results is achieved. A maximum sound pressure level of 214.8 dB can be expected. Further numerical calculation indicates that there is potential for increasing the bandwidth by varying other parameters in the design     

Experimental measurements and finite element analysis of the coupled vibrational characteristics of piezoelectric shells

Piezoelectric plates can provide low-frequency transverse vibrational displacements and high-frequency planar vibrational displacements, which are usually uncoupled. However, piezoelectric shells can induce three-dimensional coupled vibrational displacements over a large frequency range. In this study, three-dimensional coupled vibrational characteristics of piezoelectric shells with free boundary conditions are investigated using three different experimental methods and finite element numerical modeling. For the experimental measurements, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) is used to obtain resonant frequencies and radial, lateral, and angular mode shapes. This optical technique utilizes a real-time, full-field, non-contact optical system that measures both the natural frequency and corresponding vibration mode shape simultaneously. The second experimental technique used, laser Doppler vibrometry (LDV), is a pointwise displacement measurement method that determines the resonant frequencies of the piezoelectric shell. An impedance analyzer is also used to determine the resonant frequencies of the piezoelectric shell. The experimental results of the resonant frequencies and mode shapes for the piezoelectric shell are verified with a numerical finite element model. Excellent agreement between the experimental and numerical results is found for the three-dimensional coupled vibrational characteristics of the piezoelectric shell. It is noted in this study that there is no coupled phenomenon at low frequencies over which radial modes dominate. However, three-dimensional coupled vibrational modes do occur at high resonant frequencies over which lateral or angular modes dominate.     

Long-range surface plasmon polariton waveguides embedded in fluorinated polymer

Low-attenuation waveguides based on the propagation of long-range surface plasmon polaritons (LRSPPs) along thin Au stripes embedded in low absorption perfluorocyclobutane (PFCB) polymer are presented. A new low in propagation loss of <2.0 dB/cm was achieved for a 4 microm wide waveguide by optimizing the cladding material and fabrication process. The coupling efficiency between the LRSPP waveguide and the optical fiber is studied theoretically and experimentally for different widths of Au stripes and various cladding thicknesses. Lower coupling loss is found when the cladding thickness is close to the mode diameter of the butt-coupled fiber. Based on the 2D distribution of SPP modes calculated by a finite-difference mode solver, a symmetric structure of multilayer claddings with different refractive indices is proposed to optimize device insertion loss.     

Leaky guided wave propagation along imperfectly bonded fibers in composite materials

Leaky guided modes propagating along embedded fibers in a composite material can be used for characterizing the fiber-matrix interface. This principle can be applied to real composites containing small-diameter fibers by using laser interferometric detection of very fine lateral resolution on the order of a few microns. The main purpose of this paper is to develop the analytical tools needed to assess the sensitivity of guided wave inspection to interface properties in composite materials. Typically, the sound velocity is much lower in the matrix than in the fiber and the guided modes are strongly attenuated by leaking their energy into the matrix as they propagate. As a result, the velocity of the lowest-order axisymmetric longitudinal mode decreases while its attenuation increases with increasing interfacial stiffness between the fiber and the matrix. It is shown that loose fibers can be readily identified from early signals produced by fast guided modes. In the case of a well-bonded fiber-matrix interface, these guided modes are slowed down and strongly attenuated by the loading of the matrix depending on the fiber diameter and the interfacial stiffness of the interface. Interestingly, the relative difference between the well-bonded and free fibers is greater at low frequencies. Therefore, good sensitivity to the sought interfacial stiffness can be achieved at a few MHz, i.e., when the fiber diameter is still much smaller than the acoustic wavelength. Our analytical results show that the leaky guided mode technique is mainly sensitive to the transverse interfacial stiffness of the fiber-matrix interface. At typical ultrasonic frequencies between 1 and 20 MHz, the technique works best in the 10¹¹–10¹³ N/m³ interfacial stiffness range which is one or two orders of magnitude lower than the optimal sensitivity range of the more conventional bulk velocity and reflection methods.     

Use of Microwaves for the Detection of Water as a Cause of Corrosion Under Insulation

Corrosion under insulation is a significant cause of pipeline failure in the oil and gas industry. This paper describes the initial developmental stages of a technique which uses the structure of an insulated pipeline as a coaxial waveguide to support the propagation of microwaves. These microwaves are used to inspect the insulation layer for the presence of water, which will indicate the regions of the pipe at risk from corrosion. The practical requirements to achieve a low coherent noise level are identified, and the structures and dispersion characteristics of the modes which propagate in coaxial waveguides are examined to determine if these requirements can be met. An antenna array design proposed for pure mode excitation of the TEM mode and its effectiveness is demonstrated experimentally on a 12″ diameter coaxial waveguide. In particular, a signal-to-coherent-noise ratio as high as 39 dB is obtained with this arrangement. The sensitivity of the technique to the presence of water within the waveguide is investigated and it is found that water volumes with a cross-sectional area in the plane perpendicular to the waveguide axis of as little as 5% produce reflections that are readily detectable from the coherent noise floor.