Rayleigh Waves in an isotropic Body with Deep Periodic Grooves

Bragg scattering of waves propagating in a periodically disturbed substrate is widely applied in optics and micro-acoustic systems. Here, it is studied for Rayleigh waves propagating on a periodically grooved elastic substrate. Practically applied groove depth in the Bragg grating reflectors does not exceed a few percent of the Rayleigh wavelength. Here, the analysis is carried out for periodic grooves of larger depth by applying the elastic plate model for the groove walls. The computed results show that the surface wave existence and reflection depends strongly on both the groove depth and period, and that there are limited domains of both for practical applications, primarily in comb transducers of surface waves

Kalibracja radarowego i akustycznego systemu antysnajperskiego

Antisniper systems exploit numerous sensors (acoustic or electromagnetic, EM) which spatial coordinates should be known with great accuracy, otherwise the system performance can be significantly deteriorated. Triangulation of many sensors is not, however, an easy task, particularly under possible enemy fire. Here, we propose a method exploiting a round of calibration shooting over the system, which measured by the sensors provide data for evaluation of the sensors' spatial positions. The method can be applied for calibration of the Doppler radar antisniper sensors presented here in certain basic arrangement, and the acoustic microphone system measuring the shock wave generated by supersonic bullet.Antysnajperskie systemy wykorzystują pewną liczbę czujników (akustycznych lub mikrofalowych), współrzędne, których winny być znane z dużą dokładnością, w przeciwnym razie ich skuteczność będzie znacznie ograniczona. Triangulacja wielu czujników nie jest prostym zadaniem, w szczególności, jeśli miałaby być dokonana pod nieprzyjacielskim ogniem. Tu proponujemy pewną metodę wykorzystującą serię wystrzałów kalibracyjnych ponad rozsianymi w polu czujnikami, których pomiary pozwalają na określenie ich położenia. Metoda może być wykorzystana dla kalibracji systemu opartego na radarach Dopplerowskich prezentowanych w pewnej podstawowej konfiguracji, albo w systemach akustycznych, mierzących falę uderzeniową generowaną przez naddźwiękowe pociski

On the solution of an integral equation arising in potential problems for circular and elliptic disks

This paper deals with a two-dimensional Fredholm integral equation of the first kind over the circular disk $S$, with a kernel of the form $g( \theta )/| {\bf r} - {\bf r}' | ,{\bf r} - {\bf r}' \in S$, where B is the angle between ${\bf r} - {\bf r}'$ and some reference direction. By expansions in Fourier series and in series involving Legendre functions, and by use of a new closed-form result for a Legendre-function integral, the integral equation is reduced to a system of linear equations for the expansion coefficients. It is shown that the system has a unique solution because of the Toeplitz structure of the system matrix. As an application, the electrostatic potential problem for a charged elliptic disk is discussed

Efficiency of Ultrasonic Comb Transducers

Comb transducers are applied in ultrasonic testing for generation of Rayleigh or Lamb waves by scattering of the incident bulk waves onto surface waves at the periodic comb-substrate interface. Hence the transduction efficiency, although rarely discussed in literature, is an important factor for applications determining the quality of the measured ultrasonic signals. This paper presents the full-wave theory of comb transducers concluded by evaluation of their efficiency for a couple of examples of standard and certain novel configurations

Full-wave Analysis of Periodic Baffle System in Beamforming Applications

Mixed boundary-value problem for periodic baffles in acoustic medium is solved with help of the method developed earlier in electrostatics. The nice feature of the method is that the resulting matrices are relatively easy for computations and that the results satisfy exactly the energy conservation law. Illustrative numerical examples present the wave-beam steering (in the far-field) in a baffle system that may be considered as a model of one-dimensional ultrasonic transducer array

On the solution of an integral equation arising in potential problems for circular and elliptic disks

This paper deals with a two-dimensional Fredholm integral equation of the first kind over the circular disk $S$, with a kernel of the form $g( \theta )/| {\bf r} - {\bf r}' | ,{\bf r} - {\bf r}' \in S$, where B is the angle between ${\bf r} - {\bf r}'$ and some reference direction. By expansions in Fourier series and in series involving Legendre functions, and by use of a new closed-form result for a Legendre-function integral, the integral equation is reduced to a system of linear equations for the expansion coefficients. It is shown that the system has a unique solution because of the Toeplitz structure of the system matrix. As an application, the electrostatic potential problem for a charged elliptic disk is discussed