scholarly journals Mathematical modeling of monochromatic acoustic wave diffraction on a system of bodies and on flat screens

2021 ◽  
Vol 2142 (1) ◽  
pp. 012002
Author(s):  
S G Daeva ◽  
A L Beskin ◽  
N N Trokhachenkova
Keyword(s):  
Integral Equation ◽  
Acoustic Wave ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Sound Propagation ◽  
Hypersingular Integral Equation ◽  
Piecewise Constant ◽  
Solid Objects ◽  
Partial Filling ◽  
Complex Shapes

Abstract Some problems of diffraction of a monochromatic acoustic wave on surfaces of complex shapes are considered. To solve such problems, an approach is applied, in which the problem is reduced to a boundary hypersingular integral equation, where the integral is understood in the sense of a finite value according to Hadamard. Such approach allows solving diffraction problems both on solid objects and on thin screens. To solve the integral equation, the method of piecewise constant approximations and collocations, developed in the previous works of the author, is used. In the present study, examples of modeling the diffraction of an acoustic wave by bodies with partial filling are given. It is shown how the filling of bodies influences the acoustic pressure field, and the field direction patterns are given. An example of applying this approach to solving the problem of sound propagation in an urban area is also given: the diffraction of an acoustic wave from a point source on a system of buildings is considered. The presented results demonstrate that this method allows constructing reflected fields and analyze their characteristics on surfaces of complex shapes.

Acoustic Pressure Fields Generated With a High Frequency Acoustic Levitator

2017 ◽  
Author(s):  
Michael W. Sracic ◽  
Jordan D. Petrie ◽  
Henry A. Moroder ◽  
Ryan T. Koniecko ◽  
Andrew R. Abramczyk ◽  
...  
Keyword(s):  
Acoustic Wave ◽  
Acoustic Field ◽  
Vibration Amplitude ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Mechanical Vibration ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Pressure Magnitude ◽  
Acoustic Levitator

Acoustic levitation is an advantageous particle positioning mechanism currently employed for applications of x-ray spectroscopy and micro-material manufacturing[1], [2]. By levitating a particle using only acoustic pressure waves, one eliminates the need for a container or other physical structure which may contaminate the specimen. Unfortunately, the pressure field generated by a standing acoustic wave is susceptible to periodic instabilities, and a particle that is levitated in this field tends to vibrate. The amplitude of the vibration is largest in the directions that are orthogonal to the axis in which the acoustic wave is generated. Therefore, by generating additional acoustic waves in each orthogonal axis, the vibration amplitude of the levitated particle is significantly reduced. The authors have shown this phenomenon to be true in a previous study[3]. In this paper, the authors explore the details of the pressure field that is generated with the device. A single degree-of-freedom relationship is developed between the acoustic field pressure, the location of the levitated particle, and the mechanical vibration needed to produce levitation. In order to levitate a 100 micrometer diameter water droplet at 55 kilohertz, the calculations suggest that the transducer must achieve an average surface vibration amplitude of at least 6.43 micrometers. This mechanical vibration must produce a root means-squared pressure amplitude of 933 Pascal. Under these conditions, the particle will levitate approximately 0.4 millimeters below a zero pressure node. To validate the use of the single degree of freedom relationships and to explore the acoustic field for one, two, and three-axis levitation, the authors designed and prototyped an acoustic levitator capable of generating standing waves in three orthogonal directions. Using a simple electrical control circuit, the acoustic wave transducers of each axis can be turned on individually or simultaneously. An experiment was developed to measure the pressure of the acoustic field using a microphone. Preliminary pressure magnitude results were measured for one-axis levitation along the center of the vertical axis of the levitator. The measurements suggest that the theoretical development provides a valid first approximation for the pressure magnitude and required mechanical vibration amplitude.

scholarly journals Automated Insertion of Objects Into an Acoustic Robotic Gripper

Proceedings ◽  
2020 ◽  
Vol 64 (1) ◽  
pp. 40
Author(s):  
Marc Röthlisberger ◽  
Marcel Schuck ◽  
Laurenz Kulmer ◽  
Johann W. Kolar
Keyword(s):  
Acoustic Field ◽  
Acoustic Waves ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Acoustic Power ◽  
Industrial Applications ◽  
High Density ◽  
Analytical Models ◽  
Acoustic Levitation ◽  
Mechanical Contact

Acoustic levitation forces can be used to manipulate small objects and liquid without mechanical contact or contamination. To use acoustic levitation for contactless robotic grippers, automated insertion of objects into the acoustic pressure field is necessary. This work presents analytical models based on which concepts for the controlled insertion of objects are developed. Two prototypes of acoustic grippers are implemented and used to experimentally verify the lifting of objects into the acoustic field. Using standing acoustic waves and by dynamically adjusting the acoustic power, the lifting of high-density objects (>7 g/cm3) from acoustically transparent surfaces is demonstrated. Moreover, a combination of different acoustic traps is used to lift lower-density objects from acoustically reflective surfaces. The provided results open up new possibilities for the implementation of acoustic levitation in robotic grippers, which have the potential to be used in a variety of industrial applications.

scholarly journals Computation of Energy Release Rates for a Nearly Circular Crack

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Nik Mohd Asri Nik Long ◽  
Lee Feng Koo ◽  
Zainidin K. Eshkuvatov
Keyword(s):  
Integral Equation ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Linear Equations ◽  
Circular Crack ◽  
Plane Elasticity ◽  
Hypersingular Integral Equation ◽  
Hypersingular Integral ◽  
Energy Release Rates

This paper deals with a nearly circular crack, in the plane elasticity. The problem of finding the resulting shear stress can be formulated as a hypersingular integral equation over a considered domain, and it is then transformed into a similar equation over a circular region, , using conformal mapping. Appropriate collocation points are chosen on the region to reduce the hypersingular integral equation into a system of linear equations with unknown coefficients, which will later be used in the determination of energy release rate. Numerical results for energy release rate are compared with the existing asymptotic solution and are displayed graphically.

scholarly journals Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Daniel Omondi Onyango ◽  
Robert Kinyua ◽  
Abel Nyakundi Mayaka
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Plane Wave ◽  
Acoustic Pressure ◽  
Three Dimensional ◽  
The Other ◽  
Expansion Chamber ◽  
Central Tube ◽  
Simple Expansion ◽  
Plane Wave Propagation

The shape of the modal duct of an acoustic wave propagating in a muffling system varies with the internal geometry. This shape can be either as a result of plane wave propagation or three-dimensional wave propagation. These shapes depict the distribution of acoustic pressure that may be used in the design or modification of mufflers to create resonance at cut-off frequencies and hence achieve noise attenuation or special effects on the output of the noise. This research compares the shapes of acoustic duct modes of two sets of four pitch configurations of a helicoid in a simple expansion chamber with and without a central tube. Models are generated using Autodesk Inventor modeling software and imported into ANSYS 18.2, where a fluid volume from the complex computer-aided-design (CAD) geometry is extracted for three-dimensional (3D) analysis. Mesh is generated to capture the details of the fluid cavity for frequency range between 0 and 2000Hz. After defining acoustic properties, acoustic boundary conditions and loads were defined at inlet and outlet ports before computation. Postprocessed acoustic results of the modal shapes and transmission loss (TL) characteristics of the two configurations were obtained and compared for geometries of the same helical pitch. It was established that whereas plane wave propagation in a simple expansion chamber (SEC) resulted in a clearly defined acoustic pressure pattern across the propagation path, the distribution in the configurations with and without the central tube depicted three-dimensional acoustic wave propagation characteristics, with patterns scattering or consolidating to regions of either very low or very high acoustic pressure differentials. A difference of about 80 decibels between the highest and lowest acoustic pressure levels was observed for the modal duct of the geometry with four turns and with a central tube. On the other hand, the shape of the TL curve shifts from a sinusoidal-shaped profile with well-defined peaks and valleys in definite multiples of π for the simple expansion chamber, while that of the other two configurations depended on the variation in wavelength that affects the location of occurrence of cut-on or cut-off frequency. The geometry with four turns and a central tube had a maximum value of TL of about 90 decibels at approximately 1900Hz.

scholarly journals Diagonal scaling of stiffness matrices in the Galerkin boundary element method

2000 ◽  
Vol 42 (1) ◽  
pp. 141-150 ◽  
Author(s):  
Mark Ainsworth ◽  
Bill McLean ◽  
Thanh Tran
Keyword(s):  
Integral Equation ◽  
Stiffness Matrix ◽  
Numerical Experiments ◽  
Degrees Of Freedom ◽  
Boundary Integral ◽  
Piecewise Constant ◽  
Stiffness Matrices ◽  
Diagonal Scaling ◽  
Mesh Ratio ◽  
Galerkin Boundary Element Method

AbstractA boundary integral equation of the first kind is discretised using Galerkin's method with piecewise-constant trial functions. We show how the condition number of the stiffness matrix depends on the number of degrees of freedom and on the global mesh ratio. We also show that diagonal scaling eliminates the latter dependence. Numerical experiments confirm the theory, and demonstrate that in practical computations involving strong local mesh refinement, diagonal scaling dramatically improves the conditioning of the Galerkin equations.

scholarly journals Some Remarks Concerning Jones Eigenfrequencies and Jones Modes

2005 ◽  
Vol 12 (2) ◽  
pp. 337-348
Author(s):  
David Natroshvili ◽  
Guram Sadunishvili ◽  
Irine Sigua
Keyword(s):  
Exterior Domain ◽  
Thermal Stresses ◽  
Acoustic Pressure ◽  
Pressure Field ◽  
Three Dimensional ◽  
Boundary Surface ◽  
Isotropic Body ◽  
Oscillation Parameter ◽  
Uniqueness Of Solutions ◽  
Fluid Solid Interaction

Abstract Three-dimensional fluid-solid interaction problems with regard for thermal stresses are considered. An elastic structure is assumed to be a bounded homogeneous isotropic body occupying a domain , where the thermoelastic four dimensional field is defined, while in the unbounded exterior domain there is defined the scalar (acoustic pressure) field. These two fields satisfy the differential equations of steady state oscillations in the corresponding domains along with the transmission conditions of special type on the interface ∂Ω±. We show that uniqueness of solutions strongly depends on the geometry of the boundary ∂Ω±. In particular, we prove that for the corresponding homogeneous transmission problem for a ball there exist infinitely many exceptional values of the oscillation parameter (Jones eigenfrequencies). The corresponding eigenvectors (Jones modes) are written explicitly. On the other hand, we show that if the boundary surface ∂Ω± contains two flat, non-parallel sub-manifolds then there are no Jones eigenfrequencies for such domains.

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