Dorel Homentcovschi

A method for two-dimensional characterization of animal vibrational signals transmitted along plant stems

Conventional approaches to measuring animal vibrational signals on plant stems use a single transducer to measure the amplitude of vibrations. Such an approach, however, will often underestimate the amplitude of bending waves traveling along the stem. This occurs because vibration transducers are maximally sensitive along a single axis, which may not correspond to the major axis of stem motion. Furthermore, stem motion may be more complex than that of a bending wave propagating along a single axis, and such motion cannot be described using a single transducer. Here, we describe a method for characterizing stem motion in two dimensions by processing the signals from two orthogonally positioned transducers. Viewed relative to a cross-sectional plane, a point on the stem surface moves in an ellipse at any one frequency, with the ellipse’s major axis corresponding to the maximum amplitude of vibration. The method outlined here measures the ellipse’s major and minor axes, and its angle of rotation relative to one of the transducers. We illustrate this method with measurements of stem motion during insect vibrational communication. It is likely the two-dimensional nature of stem motion is relevant to insect vibration perception, making this method a promising avenue for studies of plant-borne transmission.

A MEMS Low-Noise Sound Pressure Gradient Microphone With Capacitive Sensing

A silicon microelectromechanical systems microphone is described that detects sound pressure gradients. The diaphragm consists of a stiffened plate that rotates around a central axis in response to sound pressure gradients. The motion of the diaphragm is converted into an electronic signal through the use of interdigitated comb fins that enable capacitive sensing. Measured results show that the microphone achieves a substantially lower low-frequency sound pressure-referred noise floor than can be achieved using existing dual miniature microphone systems. Measured directivity patterns are shown to be very close to what is expected for sound pressure gradient receivers over a broad range of frequencies.

Analytical model for viscous damping and the spring force for perforated planar microstructures acting at both audible and ultrasonic frequencies

The paper presents a model for the squeezed film damping, the resistance of the holes, and the corresponding spring forces for a periodic perforated microstructure including the effects of compressibility, inertia, and rarefied gas. The viscous damping and spring forces are obtained by using the continuity equation. The analytical formula for the squeezed film damping is applied to analyze the response of an ultrasonic transducer. The inclusion of these effects in a model significantly improves the agreement with measured results. Finally, it is shown that the frequency dependence of the total damping and total spring force for a cell are very similar to those corresponding to a rectangular open microstructure without holes. A separate analysis reveals the importance of each particular correction. The most important is the compressibility correction; the inertia has to be considered only for determining the spring force and the damping force for sufficiently high frequencies.

A re-expansion method for determining the acoustical impedance and the scattering matrix for the waveguide discontinuity problem

The paper gives a new method for analyzing planar discontinuities in rectangular waveguides. The method consists of a re-expansion of the normal modes in the two ducts at the junction plane into a system of functions accounting for the velocity singularities at the corner points. As the new expansion has an exponential convergence, only a few terms have to be considered for obtaining the solution of most practical problems. To see how the method works some closed form solutions, obtained by the conformal mapping method, are used to discuss the convergence of the re-expanded series when the number of retained terms increases. The equivalent impedance accounting for nonplanar waves into a plane-wave analysis is determined. Finally, the paper yields the scattering matrix which describes the coupling of arbitrary modes at each side of the discontinuity valid in the case of many propagating modes in both parts of the duct.

Influence of viscosity on the diffraction of sound by a periodic array of screens.

The paper contains an analysis of the transmission of a pressure wave through a periodic grating including the influence of the air viscosity. The system of equations in this case consists of the compressible Navier-Stokes equations associated with no-slip boundary conditions on solid surfaces. The problem is reduced to two hypersingular integral equations for determining the velocity components along the slits. These equations are solved by using Galerkins method with some special trial functions. The results can be applied in designing protective screens for miniature microphones realized in the technology of micro-electro-mechanical systems (MEMS). In this case, the physical dimensions of the device are on the order of the viscous boundary layer so that the viscosity cannot be neglected. The microfluidic model of the screen consists of a periodic array of slits in a substrate. The analysis indicates that the openings in the screen should be on the order of 10 microm in order to avoid excessive attenuation of the signal.

An analytical-numerical method for determining the mechanical response of a condenser microphone

The paper is based on determining the reaction pressure on the diaphragm of a condenser microphone by integrating numerically the frequency domain Stokes system describing the velocity and the pressure in the air domain beneath the diaphragm. Afterwards, the membrane displacement can be obtained analytically or numerically. The method is general and can be applied to any geometry of the backplate holes, slits, and backchamber. As examples, the method is applied to the Bruel & Kjaer (B&K) 4134 1/2-inch microphone determining the mechanical sensitivity and the mechano-thermal noise for a domain of frequencies and also the displacement field of the membrane for two specified frequencies. These elements compare well with the measured values published in the literature. Also a new design, completely micromachined (including the backvolume) of the B&K micro-electro-mechanical systems (MEM) 1/4-inch measurement microphone is proposed. It is shown that its mechanical performances are very similar to those of the B&K MEMS measurement microphone.

A two-dimensional model of a directional microphone: Calculation of the normal force and moment on the diaphragm

It has been shown that the parasitoid fly Ormia Ochracea exhibits exceptional sound localization ability achieved through the mechanical coupling of its eardrums [R. N. Miles et al., J. Acoust. Soc. Am. 98, 3059-3070 (1995)]. Based on this biological system a new directional microphone has been designed, having as a basic element a special diaphragm undergoing a rocking motion. This paper considers a 2D model of the microphone in which the diaphragm is considered as a 2D plate having slits on the sides. The slits lead to a backing volume limited by an infinite rigid wall parallel to the diaphragm in its neutral position. The reflection and diffraction of an incoming plane wave by this system are studied to determine the resultant force and resultant moment of pressure upon the diaphragm. The results show that such a microphone will be driven better in the case of narrow slits and deep cavities.

Viscous scattering of a pressure wave: Calculation of the fluid tractions on a biomimetic acoustic velocity sensor

In the paper we give a method for calculating the tractions (local forces) of the fluid motion determined by an incoming plane pressure wave on an artificial hair cell transducer structure. The sensing element of the transducer is a standing high aspect ratio cilium in the shape of a narrow thin curved beam (tape-like), which can be easily fabricated in micro-/nanotechnology. The method is based on considering the system of partial differential equations describing the motion of the compressible viscous fluid in an acoustic linearized approximation, and representation of the velocity field as a viscous acoustic single-layer potential. The boundary conditions, stating the cancellation of the velocity components on the solid beam, yield a two-dimensional (2-D) system of three integral equations over the beams surface for the traction components. In the case of a narrow cilium, the system of integral equations furnishes a system of two 1-D integral equations over the symmetry curve of the structure for obtaining the tangential and normal components of the traction. This system is solved numerically by a finite (boundary) element method. The numerical code written for solving the problem was applied to some particular structures. The last structure is similar to the trichobothrium of a spider Cupiennius salei. The results obtained show that the curvature of the hair is enhancing sensitivity to flows directed normal to the main shaft of the hair confirming the assertion of Barth et al. [Philos. Trans. R. Soc. London, Ser. B 340, 445-461 (1993)].

High accuracy formulas for calculation of the characteristic impedance of microstrip lines

An analytical formula for determination of the characteristic impedance of a microstrip line assuming the quasi-TEM mode of propagation is presented. The new form of the final formulas contains only integrals which can be numerically performed by means of the Gauss-Laguerre quadrature. The method can be applied to multilayer lines and also to the case of anisotropic dielectrics. By using some suitable conformal mappings the formulas obtained can be used to determine the characteristic impedance of some cylindrical microstrip lines. We have compared the results given by the proposed formulas with the finite analytical solution available in a particular case and also with results obtained by the substrip method. All the performed tests indicate that the proposed formulas are highly accurate and efficient relations for determining the characteristic impedance of microstrip lines. >

An introduction to BEM by integral transforms

The paper provides a new method for obtaining the fundamental integral representation used in BEM. The method is based on integral transforms and can be applied to all linear differential equations with constant coefficients. Some explicit formulae pertaining to potential problems, linear elasticity and low Reynolds number flows are derived.