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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.
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.
Content available Calibration of EM and acoustic antisniper systems
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.
A system of periodic elastic strips (each one considered as a fragment of a plate) is characterized by a matrix relation between the Bloch series of displacements and stress at the bottom side of the system, which will remain in contact with the substrate supporting a propagating Rayleigh wave. The theory exploits the mechanical field representation in a spectral domain. It was found advantageous in formulation of the scattering problem for an elastic plate with stress-free cross-section, allowing us to apply ordinary boundary conditions instead of the variational ones. The result satisfies the energy conservation law with great accuracy, provided that sufficient number of complex modes are included in the solution. An algorithm is presented for modes evaluation; asymptotic properties of modes can be applied as well for higher modes. Perfect agreement of the proposed model with the experimentally verified perturbation model of thin strips is demonstrated.
Interdigital transducers of surface acoustic waves are periodic or nearly periodic systems of strips. In several applications they work in the Bragg regime to obtain strong surface wave Bragg reflections. This paper presents generalization of the spectral, full-wave theory to the case of transducers exploiting periodic cells comprising many strips of arbitrary width and positions within the cell. A novel method is applied to solve the dynamic boundary-value problem by means of the generalized electrostatic analysis. The generalization is useful for two purposes: for analysis of transducers having substantially aperiodic strips (by applying large cell periods with respect to the transducer length), and for analysis, in the frame of spectral theory, of unidirectional transducers exploiting cells comprising several different strips and certain interconnections between them within each cell. The theory yields full characterization of such transducers, including the surface wave dispersion characterized by stopband frequencies, and the transducer directionality.
Content available remote Spectral theory of unidirectional transducers
A spectral theory of single-phase unidirectional transducers of the surface acoustic waves is presented. It helps to evaluate the stop-band width where the directionality takes place, and allows one to optimize the transducer structure in order to obtain its symmetric frequency response, with maximum directionality at the stop-band center.
Content available remote Acoustic sniper localization
Acoustic signals of small arm's fire, the muzzle blast and the shock wave generated by a supersonic bullet in air, are difficult to mask and can be exploited for localization of the hidden sniper. This paper presents the system of acoustic measurements, based on a number of both directional and omnidirectional microphones detecting the shock wave only, yielding exact solution for the sniper direction in spite of certain errors in the directional measurements. The system has a self-correcting ability concerning the sound directional measurements which contributes to the system technical feasibility. Auxiliary muzzle blast measurements would yield the sniper position.
Content available remote Piezoelectric guided wave propagation
A perfectly conducting strip embedded in a piezoelectric medium is considered. Waves propagating along the strip are investigated with the use of a surface impedance function which is suggested by the known surface impedance function for a perfectly conducting plane embedded in the medium. A dispersion equation for the waves is found and solved in the case of a narrow strip.
Content available remote Interaction of Rayleigh waves with periodic baffles
Rayleigh waves in two solids separated by an air gap containing two alternate periodic in-plane baffle systems are considered. A Bragg reflection of the waves occurs when the distance between the baffle planes and between baffles and solids are half wavelength long in air. This may support an idea of contactless application of comb transducers to generate Rayleigh waves. The analysis is carried out using the BIS expansion method to account for the wavefield singularity at the baffle edges.
Content available remote Electrostatic scattering by strips
A system of in-plane periodic perfectly conducting strips is considered embedded in an preexisting electric field which, in applications, can result from propagation of an elastic wave in a piezoelectric material supporting strips on its surface. The spatial spectrum of charge distribution in the plane of strips is of our primary interest. In spite of the functional dependence between the spectrum and the spatial distribution of charge by means of the Fourier transform, its direct application leads to a considerable numerical error caused by poor numerical representation of the singular field at the strip edges. Carrying out the analysis in the spectral domain instead of direct evaluation of the spatial charge distribution overcomes this difficulty.
There are paints on the slowness surface of anisotropic crystals which cannot be satisfactorily described with standard Gaussian curvatures. The paper presents complete sets of such points in quartz and lithium niobate, and also certain extraordinary points in Rochelle salt. The method of their evaluation and verification is presented briefly.
Content available remote Modeling of elastic slab with periodic breaks
An elastic slab having periodic breaks across its cross-section is loaded by space-harmonic forces applied to its surfaces. Due to the breaks, the slab displacement response to the load includes a series of space-harmonics. A method is proposed for evaluation of the slab harmonic response within a presumed spectral domain.
Content available remote Periodic crack-model of comb transducers: excitation of interface waves
A model for a comb transducer is proposed and analyzed. It is shown that interface waves are generated in the comb-sample contact area. The interface waves are leaky waves that transport acoustic energy along the interface towards the comb edges, where it is eventually converted into surface acoustic waves propagating outside the comb. By including piezoelectric effects in the comb and the sample materials, it is possible to analyze the incident bulk wave generated by embedded metal strips on both sides of the interface. Approximations for the scattered wavefield and the relationship describing the energy transfer along the interface are derived. Numerical examples are presented.
Content available remote Periodic crack-model of comb transducers: efficiency and optimization
A model for a comb transducer is investigated in which the comb-sample interface is modeled by a periodic system of cracks. Leaky interface crack waves are generated by a normal incident shear bulk wave beam or by an equivalent excitation of the comb teeth at the interface. The generation efficiency is analyzed in systems where both the comb and the sample halfspaces are from the same material, steel or aluminium, for different teeth width and period, and for the case of solid contact between the two halfspaces between cracks; the other case of sliding contact is discussed briefly. Numerical results show that up to 25% of the incident power can be transformed into interface crack waves by a comb tooth. Optimal number of comb teeth is estimated, and the transducer frequency response is discussed. Approximated relationships are presented that may help designing a comb.
Shortening of electric field results in certain smaller velocity of bulk waves in piezoelectric media. This provides the waveguiding mechanism for the waves studied in this paper, where the conducting strip shortens the electric field in its vicinity. The dispersive relation of the guided wave is derived for very narrow strips, and the conditions of existence of the wave are discussed.
Content available remote Bulk wave transmission by a multistrip coupler (MSC)
Multistrip coupler (MSC) is a component of SAW devices that couples surface acoustic waves (SAWs) propagating in two acoustic channels on piezoelectric substrate. Little is known in SAW literature about simultaneous transmission of bulk waves by MSC; it is beliewed that MSC efficiently suppress bulk wave spurious signals in SAW devices, and this is one of reasons of application of MSC in SAW devices. In this paper we investigate the efficiency of bulk wave transmission by MSC. New theory of MSC is developed that accounts for the fact that MSCs comprise finite number of conducting strips spanning over two acoustic channels. Numerical analysis based on FFT algorithm shows that bulk waves can be quite efficiently transmitted by MSC. This means particularly, that MSC can be applied to couple the surface skimming bulk waves which, having large velocity, are attractive for higher frequency SAW devices. In this case, MSCs would make it possible to shape the device frequency response by two apodized interdigital transducers (IDTs) converting electric signal to ultrasonic surface waves.
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