Eugene J. Danicki

Scattering by periodic cracks and theory of comb transducers

Abstract Combs are distributed ultrasonic transducers for the generation of Rayleigh waves in solids. Synchronously excited by subsequent comb teeth, the surface wave grows along its propagation path under the comb. Although sliding contact between the comb and a solid sample is frequently assumed, the mechanical coupling is not weak. This modifies the surface wave propagation conditions to such an extent that the Rayleigh wave no longer exists at the comb–sample interface. Instead, an interface mode propagates, collecting power from each subsequent comb tooth and delivering it to the comb edge to be eventually transformed into a Rayleigh wave outside the comb. Generation efficiency is evaluated for the optimized angle of incidence of the longitudinal wave onto the comb–sample interface.

Electrostatics of interdigital transducers

Interdigital transducers are systems of conducting strips on a piezoelectric halfspace; in some systems, the groups of strips repeat periodically over a transducer counting hundreds of strips that can be considered infinite. An infinite planar periodic system of groups of strips with adequate period, sufficiently large if necessary, is considered to model an electric field in the plane of strips. There are electric charge distributions on strips either resulting from an external voltage source applied to the strips or induced by a propagating surface acoustic wave in the piezoelectric substrate. The latter case is equivalent, in the electrostatic approximation applied in this paper, to strips embedded in an already existing, spatially variable electric field. A method is presented for evaluation of the spatial spectrum of charge distribution that is responsible for either the surface wave generation or the scattering by strips in weak piezoelectrics. It overcomes certain numerical difficulties arising when Fourier transform is computed from the already evaluated numerical representation of the square-root singular charge distribution at the strip edges.

Reflection of a saw from periodic shallow grooves

Tierstens perturbation boundary conditions are generalized to the case of a piezoelectric substrate with a sinusoidally corrugated surface. On the basis of these conditions the equations of coupled normal modes are derived, which in turn serve to calculate the coefficient of reflection of the surface acoustic wave from a single groove at an arbitrary angle of incidence of the wave. Both the mechanical and the electrical interactions are taken into account between the wave and the grooves having a free or metallized surface. The calculations indicate a considerable dependence of the coefficient of reflection of the wave upon the propagation directions of the incident and the reflected wave.

Evaluation of Planar Harmonic Impedance for Periodic Elastic Strips of Rectangular Cross Section by Plate Mode Expansion

A system of periodic elastic strips (each one considered as a piece of a plate) is characterized by a matrix relation between the Bloch series of displacement and traction at the bottom side of the system. Both these mechanical fields are involved in the boundary conditions at the contact plane between the strips and the substrate supporting a Rayleigh wave. The analysis exploits the mechanical field expansion over the plate modes, including complex modes; numerical results satisfy the energy conservation law satisfactorily. The derived planar harmonic Greens function provides an alternative tool for investigation of surface waves propagation under periodic elastic strips, with respect to pure numerical methods mostly applied in the surface acoustic wave devices literature. Perfect agreement of the presented theory with the experimentally verified perturbation model of thin strips is demonstrated.

Beam-Forming Electrostrictive Matrix

In this paper a two-dimensional ultrasound transducer comprising crossed periodic metal electrodes placed on both sides of electrostrictive layer and representing the matrix rows and columns is described. Such a system is capable of electronic beam-steering of generated wave both in elevation and azimuth. The wave-beam control is achieved by addressable driving of two-dimensional matrix transducer through proper voltage supply of electrodes on opposite surfaces of the layer. In this paper a semi-analytical method of analysis of the considered transducer is proposed, which is a generalization of the well-known BIS-expansion method. It was earlier exploited with great success in the theory of interdigital transducers of surface acoustic waves, theory of elastic wave scattering by cracks and certain advanced electrostatic problems. The paper presents evaluation of stress in the electrostrictive layer excited by potentials applied to electrodes. The corresponding nontrivial electrostatic problem is formulated. Some numerical examples showing the resulting generated electrostrictive stress in the dielectric layer are presented for a simple case of one upper strip excited by a uniform voltage and all bottom strips grounded.

Electrostatics of crossed arrays of strips [Correspondence]

The BIS-expansion method is widely applied in analysis of SAW devices. Its generalization is presented for two planar periodic systems of perfectly conducting strips arranged perpendicularly on both sides of a dielectric layer. The generalized method can be applied in the evaluation of capacitances of strips on printed circuits boards and certain microwave devices, but primarily it may help in evaluation of 2-D piezoelectric sensors and actuators, with row and column addressing their elements, and also piezoelectric bulk wave resonators.

An enhanced algorithm for evaluation of surface waves

A procedure based on the Stroh formalism is presented that yields the approximation for the planar harmonic Greens matrix function for piezoelectric half-space that is valid in the vicinity of the surface, or pseudosurface, wave number. This approximation can be directly exploited in the spectral-theoretical analysis of surface acoustic wave devices. Otherwise, the known characterization of the surface wave supporting substrate can be immediately inferred from it, like the wave velocity, piezoelectric coupling coefficient, the wave damping in the case of leaky pseudosurface waves, and the corresponding surface displacement velocities.

Synchronous Forward to Backward Surface Acoustic Wave Coupling in Reversing Multistrip Coupler

Surface acoustic wave (SAW) propagating on a surface of piezoelectric substrates is accompanied with a wave of electric potential on the surface. SAW can be excited by metal strips on the surface of a piezoelectric body when they are supplied with electric potential. Multistrip coupler is the directional coupler of two adjacent SAW channels where the coupling is provided by periodic metal strips covering both channels.

Correspondence: Interdigitated interdigital transducer for surface elastometry of soft damping tissue

Measurement of the shear elastic constant of soft and highly damping tissue of high Poisson ratio is quite a challenging task. It is proposed to evaluate shear wave velocity and damping of tissue by measuring the shear skimming bulk waves using one interdigitated interdigital transducer on a piezoelectric layer, such as polyvinylidene fluoride, applied to the surface of the small tissue sample.

Electrostatics of Planar Multielectrode Sensors with Application to Surface Elastometry

Systems of planar electrodes arranged on dielectric or piezoelectric layers are applied in numerous sensors and transducers. In this paper electrostatics of such electrode systems is presented and exploited in the analysis of distributed piezoelectric transducer dedicated to surface elastometry of biological tissues characterized by large Poisson modulus. The fundamental Matlab® code for analyzing complex planar multiperiodic electrode systems is also presented.