Torsional Waves in an Infinite Elastic Solid Containing a Spheroidal Cavity

1972 ◽  
Vol 39 (4) ◽  
pp. 995-1001 ◽  
Author(s):  
S. K. Datta
Keyword(s):  
Shear Stress ◽  
Separation Of Variables ◽  
Low Frequency ◽  
Elastic Solid ◽  
Major Axis ◽  
Cavity Surface ◽  
Legendre Functions ◽  
Low Frequencies ◽  
Spheroidal Cavity ◽  
Torsional Waves

A low-frequency analysis is presented here for the axisymmetric problem of diffraction of torsional waves by an oblate spheroidal cavity in an isotropic homogeneous elastic medium. The method used gives a complete low-frequency expansion of the scattered field in terms of associated Legendre functions, instead of spheroidal wave functions that one gets by the method of separation of variables. This makes the numerical computation much simpler. Graphs and tables are presented for the displacement distribution on the cavity surface and the nonzero shear stress at the end of the major axis of the spheroid. It is found that for low frequencies and for the values of the ratio (b/a) of the minor and major axes of the spheroid considered here the absolute value of the ratio of the nonzero dynamic and static shear stress evaluated at the end of the major axis is independent of b/a for confocal spheroids. An estimate is also given for the radius of convergence of the low-frequency expansion.

ELASTIC WAVES ALONG A CYLINDRICAL BORE

Geophysics ◽  
1962 ◽  
Vol 27 (3) ◽  
pp. 327-333 ◽  
Author(s):  
J. E. White
Keyword(s):  
Elastic Waves ◽  
Low Frequency ◽  
Elastic Solid ◽  
Approximate Expression ◽  
Compressional Wave ◽  
Axially Symmetric ◽  
Low Frequencies ◽  
Phase Velocities ◽  
Pierre Shale ◽  
Limiting Case

This paper concerns axially symmetric solutions for waves propagating along a cylinder in an infinite elastic solid. Solutions are presented describing unattenuated propagation along the axis at phase velocities higher than shear and compressional speeds in the solid, in contradiction to earlier publications. Special attention is given to the limiting case of phase velocity equal to compressional speed in the solid, which at low frequencies very closely approximates the coupling of a fluid‐filled borehole to a plane compressional wave in the surrounding solid. Comparison with some experiments in a uniform section of Pierre shale show excellent agreement at low frequencies. In the low‐frequency limit, these solutions reduce to an approximate expression for borehole coupling published earlier by the author.

LOW-FREQUENCY ACOUSTIC SCATTERING OF A PLANE WAVE FROM A SOFT AND HARD TORUS

2007 ◽  
Vol 15 (02) ◽  
pp. 181-197 ◽  
Author(s):  
GEORGE VENKOV
Keyword(s):  
Separation Of Variables ◽  
Near Field ◽  
Scattering Problem ◽  
Acoustic Scattering ◽  
Low Frequency ◽  
Diagonal Form ◽  
Legendre Functions ◽  
Algebraic Equations ◽  
Analytical Technique ◽  
Linear Algebraic Equations

A plane acoustic wave is scattered by either a soft or a hard small torus. The incident wave has a wavelength which is much larger than the characteristic dimension of the scatterer and thus the low-frequency approximation method is applicable to the scattering problem. It is shown that there exists exactly one toroidal coordinate system that fits the given geometry. The R-separation of variables is utilized to obtain the series expansion of the fields in terms of toroidal harmonics (half-integer Legendre functions of first and second kind). The scattering problem for the soft torus is solved analytically for the near field, governing the leading two low-frequency coefficients, as well as for the far field, where both the amplitude and the cross-section are evaluated. The scattering problem for the hard torus appears to be much more complicated in calculations. The Neumann boundary condition on the surface of the torus leads to a three-term recurrence relation for the series coefficients corresponding to the scattered fields. Thus, the potential boundary-value problem for the leading low-frequency approximations is reduced to infinite systems of linear algebraic equations with three-diagonal matrices. An analytical technique for solving systems of diagonal form is developed.

Wave Function Expansions and Perturbation Method for the Diffraction of Elastic Waves by a Parabolic Cylinder

1967 ◽  
Vol 34 (4) ◽  
pp. 915-920 ◽  
Author(s):  
S. A. Thau ◽  
Yih-Hsing Pao
Keyword(s):  
Wave Function ◽  
Separation Of Variables ◽  
Low Frequency ◽  
Elastic Solid ◽  
Compressional Wave ◽  
Parabolic Cylinder ◽  
Infinite Matrix ◽  
Elastic Solids ◽  
Incident Plane ◽  
Scattered Fields

The dynamic response, including the stresses at the surface, of a rigid parabolic cylinder in an infinite elastic solid is studied for an incident plane compressional wave. The method of separation of variables in parabolic coordinates is used. With the wave function for one of the scattered waves expanded into a series of those for the other wave, the total scattered fields are then determined numerically by inverting a truncated infinite matrix. The same problem is solved also by a recently developed method of perturbation which describes the two waves in elastic solids in terms of wave functions with a common wave speed. With the latter method, the total scattered waves are determined analytically for the various orders of perturbation, and these results supplement the numerical wave function expansion results in the low-frequency range.

Fluid shielding of low frequency convected sources by arbitrary jets

1975 ◽  
Vol 70 (1) ◽  
pp. 17-36 ◽  
Author(s):  
T. F. Balsa
Keyword(s):  
Cross Section ◽  
Vertical Plane ◽  
Low Frequency ◽  
Major Axis ◽  
Arbitrary Cross Section ◽  
Mass Source ◽  
Low Frequencies ◽  
Noise Shielding ◽  
Radiative Power ◽  
Experimental Findings

A low frequency asymptotic theory is proposed for the shielding of noise by jets of arbitrary cross-section. The results of the theory provide a qualitative explanation for the appearance of the quiet and noisy planes of a slot jet. The arguments in favour of this explanation are derived from a model problem in which a pulsating mass source is convecting along the axis of an infinitely long column of fluid of arbitrary cross-section. The jet velocity is represented by a uniform velocity profile (i.e. slug flow). The method of matched asymptotic expansions is applied to derive expressions for the acoustic pressure and the radiative power of the source.The solution for the elliptic jet indicates that the radiative power in the horizontal plane (containing the major axis) is less than that in the vertical plane (containing the minor axis). This difference in power varies with source Strouhal number and jet Mach number. The effects of jet temperature are also included in the analysis. The theoretical results are in good qualitative agreement with experimental findings for slot nozzles. The theory indicates that the noise shielding offered by jets is negligible at low frequencies and low Mach numbers.

scholarly journals Earless toads sense low frequencies but miss the high notes

2017 ◽  
Vol 284 (1864) ◽  
pp. 20171670 ◽  
Author(s):  
Molly C. Womack ◽  
Jakob Christensen-Dalsgaard ◽  
Luis A. Coloma ◽  
Juan C. Chaparro ◽  
Kim L. Hoke
Keyword(s):  
High Frequency ◽  
Species Differences ◽  
Low Frequency ◽  
Auditory Brainstem ◽  
Low Frequencies ◽  
Hearing Sensitivity ◽  
Sensory Pathways ◽  
Airborne Sound ◽  
Vibrational Sensitivity ◽  
Species Specific

Sensory losses or reductions are frequently attributed to relaxed selection. However, anuran species have lost tympanic middle ears many times, despite anurans' use of acoustic communication and the benefit of middle ears for hearing airborne sound. Here we determine whether pre-existing alternative sensory pathways enable anurans lacking tympanic middle ears (termed earless anurans) to hear airborne sound as well as eared species or to better sense vibrations in the environment. We used auditory brainstem recordings to compare hearing and vibrational sensitivity among 10 species (six eared, four earless) within the Neotropical true toad family (Bufonidae). We found that species lacking middle ears are less sensitive to high-frequency sounds, however, low-frequency hearing and vibrational sensitivity are equivalent between eared and earless species. Furthermore, extratympanic hearing sensitivity varies among earless species, highlighting potential species differences in extratympanic hearing mechanisms. We argue that ancestral bufonids may have sufficient extratympanic hearing and vibrational sensitivity such that earless lineages tolerated the loss of high frequency hearing sensitivity by adopting species-specific behavioural strategies to detect conspecifics, predators and prey.

A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 854-859 ◽  
Author(s):  
Xiao Ming Tang
Keyword(s):  
Elastic Wave ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Finite Size ◽  
Low Frequency ◽  
Frequency Range ◽  
Multiple Reflections ◽  
Low Frequencies ◽  
The Time Domain ◽  
Attenuation Values

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

Methods to isolate retrograde and prograde Rayleigh-wave signals

2019 ◽  
Vol 219 (2) ◽  
pp. 975-994 ◽  
Author(s):  
Gabriel Gribler ◽  
T Dylan Mikesell
Keyword(s):  
Rayleigh Wave ◽  
Time Domain ◽  
Fundamental Mode ◽  
Poisson Ratio ◽  
Low Frequency ◽  
Wave Dispersion ◽  
Low Frequencies ◽  
Retrograde Motion ◽  
Mode Identification ◽  
Time Frequency

SUMMARY Estimating shear wave velocity with depth from Rayleigh-wave dispersion data is limited by the accuracy of fundamental and higher mode identification and characterization. In many cases, the fundamental mode signal propagates exclusively in retrograde motion, while higher modes propagate in prograde motion. It has previously been shown that differences in particle motion can be identified with multicomponent recordings and used to separate prograde from retrograde signals. Here we explore the domain of existence of prograde motion of the fundamental mode, arising from a combination of two conditions: (1) a shallow, high-impedance contrast and (2) a high Poisson ratio material. We present solutions to isolate fundamental and higher mode signals using multicomponent recordings. Previously, a time-domain polarity mute was used with limited success due to the overlap in the time domain of fundamental and higher mode signals at low frequencies. We present several new approaches to overcome this low-frequency obstacle, all of which utilize the different particle motions of retrograde and prograde signals. First, the Hilbert transform is used to phase shift one component by 90° prior to summation or subtraction of the other component. This enhances either retrograde or prograde motion and can increase the mode amplitude. Secondly, we present a new time–frequency domain polarity mute to separate retrograde and prograde signals. We demonstrate these methods with synthetic and field data to highlight the improvements to dispersion images and the resulting dispersion curve extraction.

Optimally Sensitive and Efficient Compact Loudspeakers for Low Audio Frequencies

2007 ◽  
Vol 38 (7) ◽  
pp. 11-17
Author(s):  
Ronald M. Aarts
Keyword(s):  
Optimality Criterion ◽  
Low Frequency ◽  
Audio Signal ◽  
Design Procedure ◽  
Frequency Range ◽  
Force Factor ◽  
Low Frequencies ◽  
Limited Frequency ◽  
The Cost ◽  
Higher Sensitivity

Conventionally, the ultimate goal in loudspeaker design has been to obtain a flat frequency response over a specified frequency range. This can be achieved by carefully selecting the main loudspeaker parameters such as the enclosure volume, the cone diameter, the moving mass and the very crucial “force factor”. For loudspeakers in small cabinets the results of this design procedure appear to be quite inefficient, especially at low frequencies. This paper describes a new solution to this problem. It consists of the combination of a highly non-linear preprocessing of the audio signal and the use of a so called low-force-factor loudspeaker. This combination yields a strongly increased efficiency, at least over a limited frequency range, at the cost of a somewhat altered sound quality. An analytically tractable optimality criterion has been defined and has been verified by the design of an experimental loudspeaker. This has a much higher efficiency and a higher sensitivity than current low-frequency loudspeakers, while its cabinet can be much smaller.

An Analytical Model for the Interaction of Mass Inclusions in Heterogeneous (HG) Blankets

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
A. Wagner ◽  
M. E. Johnson ◽  
K. Idrisi ◽  
D. P. Bartylla
Keyword(s):  
Elastic Layer ◽  
Analytical Approach ◽  
Low Frequency ◽  
Control Device ◽  
Effective Stiffness ◽  
Special Focus ◽  
Dynamic Vibration Absorber ◽  
Low Frequencies ◽  
Dynamic Vibration ◽  
The Masses

The heterogeneous (HG) blanket is a passive treatment used to reduce the low frequency transmission of sound through partitions. HG blankets, glued onto a structure, consist of an elastic medium with embedded mass inhomogeneities that mechanically replicate a mass-spring-damper system to reduce efficient radiating structural modes at low frequencies. The elastic layer typically used has sound absorption properties to create a noise control device with a wide bandwidth of performance. The natural frequency of an embedded dynamic vibration absorber is determined by the mass of the inhomogeneity as well as by its effective stiffness due to the interaction of the mass inclusion with the elastic layer. A novel analytical approach has been developed to describe in detail the interaction of the mass inclusions with the elastic layer and the interaction between the masses by evaluating special elastomechanical concepts. The effective stiffness is predicted by the analytical approach based on the shape of the mass inclusions as well as on the thickness and material properties of the layer. The experimental validation is included and a simplified direct equation to calculate the effective stiffness of a HG blanket is proposed. Furthermore, the stress field inside the elastic material will be evaluated with focus on the stresses at the base to assess the modeling of one or more masses placed on top of the elastic layer as dynamic vibration absorbers. Finally, the interaction between two (or more) masses placed onto the same layer is studied with special focus on the coupling of the masses at low distances between them.

Sign in / Sign up

Export Citation Format

Share Document