Philip W. Loveday

Semi-analytical finite element analysis of elastic waveguides subjected to axial loads.

Predicting the influence of axial loads on the wave propagation in structures such as rails requires numerical analysis. Conventional three-dimensional finite element analysis has previously been applied to this problem. The process is tedious as it requires that a number of different length models be solved and that the user identify the computed modes of propagation. In this paper, the more specialised semi-analytical finite element method is extended to account for the effect of axial load. The semi-analytical finite element method includes the wave propagation as a complex exponential in the element formulation and therefore only a two-dimensional mesh of the cross-section of the waveguide is required. It was found that the stiffness matrix required to describe the effect of axial load is proportional to the mass matrix, which makes the extension to existing software trivial. The method was verified by application to an aluminium rod, where after phase and group velocities of propagating waves in a rail were computed to demonstrate the method.

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 ldquocut-onrdquo frequency is to be simulated in the near-field.

Modification of piezoelectric vibratory gyroscope resonator parameters by feedback control

A method for analyzing the effect of feedback control on the dynamics of piezoelectric resonators used in vibratory gyroscopes has been developed. This method can be used to determine the feasibility of replacing the traditional mechanical balancing operations, used to adjust the resonant frequency, by displacement feedback and for determining the velocity feedback required to produce a particular bandwidth. Experiments were performed on a cylindrical resonator with discrete piezoelectric actuation and sensing elements to demonstrate the principles. Good agreement between analysis and experiment was obtained, and it was shown that this type of resonator could be balanced by displacement feedback. The analysis method presented also is applicable to micromachined piezoelectric gyroscopes.

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.

Development of a Variable Stiffness and Damping Tunable Vibration Isolator

In this paper we report on the development of a variable stiffness and damping Liquid Inertia Vibration Eliminator (LIVE) vibration isolator. The result is the ability to shift the isolation frequency of the isolator and also to change the amplification at resonance. A practical variable stiffness spring was developed by using a compound leaf spring with circular spring elements. A wax actuator, controlled by a hot-air gun with a closed-loop displacement and velocity feedback control system, was used to separate the springs at the center. An experimental isolator was constructed and tested. The isolation frequency was shifted from 22.8 to 36.2 Hz by changing the stiffness of the spring by 270%. A transmissibility of less than 10% was achieved over the whole range. The viscous damping ratio was changed from 0.001 to 0.033 by increasing the flow losses in the system.

A Coupled Electromechanical Model of an Imperfect Piezoelectric Vibrating Cylinder Gyroscope

Coupled electromechanical equations of motion, describing the dynamics of a vibrating cylinder gyroscope, are derived using Hamiltons principle and the Rayleigh-Ritz method. The vibrating cylinder gyroscope comprises a thin walled steel cylinder which is closed at one end with discrete piezoceramic actuation and sensing elements bonded close to the open end. The operation of the gyroscope and the effect of imperfections are briefly described. The model allows direct comparison with experimental measurements in the form of electrical frequency response functions. The effects of ceramic location errors and mass imperfections were investigated. Comparisons with experimental measurements showed that the model could be used to predict the mass modifications required to reduce the effect of these typical imperfections in practical devices.

Guided wave propagation as a measure of axial loads in rails

Guided wave propagation has been proposed as a means to monitor the axial loads in continuously welded railway rails although no practical system has been developed. In this paper, the influence of axial load on the guided wave propagation characteristics was analyzed using the semi-analytical finite element method, extended to include axial loads. Forty modes of propagation were analyzed up to a maximum frequency of 100 kHz. The sensitivity of the modes to axial load or changes in elastic modulus was formulated analytically and computed. In practice, by using separation of signals in time it would only be possible to separate the mode with the greatest group velocity over a reasonable distance. It was found that the influence of axial load on the wavelength of such a mode should be measureable. However, the influence of changes in the elastic modulus due to temperature is expected to be an order of magnitude larger. In order to develop a practical measurement technique it would be necessary to eliminate or compensate for this and other influences.

Long range guided wave defect monitoring in rail track

A guided wave ultrasound system was previously developed for monitoring rail track used on heavy duty freight lines. This system operates by transmitting guided waves between permanently installed transmit and receive transducers spaced approximately 1km apart. The system has been proven to reliably detect rail breaks without false alarms. While cracks are sometimes detected there is a trade - off between detecting cracks and the possibility of false alarms. Adding a pulse-echo mode of operation to the system could provide increased functionality by detecting, locating and possibly monitoring cracks. This would require an array of transducers to control the direction and mode of propagation and it would be necessary to detect cracks up to a range of approximately 500 m in either direction along the rail. A four transducer array was designed and full matrix capture was used for field measurements. Post processing of the signals showed that a thermite weld could be detected at a range of 790m from the trans...

A piezoelectric deformable mirror for intra-cavity laser adaptive optics

This paper describes the development of a deformable mirror to be used in conjunction with diffractive optical elements inside a laser cavity. A prototype piezoelectric unimorph adaptive mirror was developed to correct for time dependent phase aberrations to the laser beam, such as those caused by thermal expansion of materials. The unimorph consists of a piezoelectric disc bonded to the back surface of a copper reflective mirror. The rear electrode of the piezoelectric ceramic disc is divided into segments so that a number of different control voltages can be applied to deform the mirror in a desired displacement distribution. The mirror is required to be able to deform in the shape of each of the lower order Zernike polynomials, which describe aberrations in optical systems. A numerical model of the device was used to determine a suitable electrode configuration. Finally, the device was constructed and the deformed shapes measured using a laser vibrometer.

Prediction of guided wave scattering by defects in rails using numerical modelling

A guided wave based monitoring system for welded freight rail, has previously been developed. The current arrangement consists of alternating transmit and receive stations positioned roughly 1 km apart, and is designed to reliably detect complete breaks in a rail. Current research efforts are focused on extending this system to include a pulse-echo mode of operation in order to detect, locate, monitor and possibly characterize damage, before a complete break occurs. For monitoring and inspection applications, it is beneficial to be able to distinguish between scattering defects which do not represent damage (such as welds) and cracks which could result in rail breaks. In this paper we investigate the complex interaction between selected propagating modes and various weld and crack geometries in an attempt to relate scattering behaviour to defect geometry. An efficient hybrid method is employed which models the volume containing the defect with conventional solid finite elements, while the semi-infinite in...