Analysis and Interpretation of Longitudinal Waves in Periodic Multiphase Rods Using the Method of Reverberation-Ray Matrix Combined With the Floquet-Bloch Theorem

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Y. Q. Guo ◽  
D. N. Fang
Keyword(s):  
Phase Velocity ◽  
Longitudinal Wave ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Wave Number ◽  
Wave Band ◽  
Frequency Wave ◽  
Longitudinal Waves ◽  
Bloch Theorem ◽  
Velocity Spectra

The method of reverberation-ray matrix (MRRM) combined with the Floquet–Bloch theorem, which serves as an alternative method, is presented for accurately analyzing longitudinal waves in general periodic multiphase rods. Closed-form dispersion relation of periodic quaternary rods is derived. Based on this relation, the functions of constituent-rod parameters in the formation of longitudinal-wave band structures are analytically revealed. Numerical examples validate the proposed method and indicate the characteristics/applications of all kinds of dispersion curves that include the frequency-wave number spectra, the frequency-wavelength spectra, the frequency-phase velocity spectra, the wave number-phase velocity spectra and the wavelength-phase velocity spectra. The effect of unit-cell layout on the frequency band properties and the functions of constituent-rod parameters in the band structure formation are also illustrated numerically. The analysis and interpretation of longitudinal waves in periodic multiphase rods given in this paper will push forward the design of periodic structures for longitudinal wave filtering/guiding and vibration isolation/control applications.

scholarly journals Longitudinal Wave in a Thermally Conducting Elastic Medium

2019 ◽  
Vol 8 (4) ◽  
pp. 8769-8771
Keyword(s):  
Temperature Field ◽  
Phase Velocity ◽  
Elastic Medium ◽  
Longitudinal Wave ◽  
Frequency Equation ◽  
Damping Coefficient ◽  
Wave Number ◽  
Longitudinal Wave Propagation ◽  
Thermally Conducting ◽  
Equations Of Motions

The longitudinal wave propagation in a thermally conducting elastic medium has been investigated. Considering the equations of motions of longitudinal wave in displacement and temperature field, the frequency equation has been derived. The dispersion and damping equations have been derived for the propagation of longitudinal wave in four materials i.e Copper, Steel, Aluminum, and Lead. Effect of Phase velocity and damping coefficient are shown graphically. It is found that the increase in wave number results the decrease in Phase velocity and increase in damping coefficient.

ABOUT HEAD WAVES AND UNDER-SURFACE LONGITUDINAL WAVES, RADIATED BY THE NORMAL PROBE WHICH IS TAKING PLACE ON A FREE FLAT SURFACE OF THE ELASTIC ENVIRONMENT

2021 ◽  
pp. 4-19
Author(s):  
V. N. Danilov
Keyword(s):  
Longitudinal Wave ◽  
Flat Surface ◽  
Wave Number ◽  
Head Wave ◽  
Directivity Characteristic ◽  
Longitudinal Waves ◽  
Local Maxima ◽  
Normal Probe ◽  
Geometrical Acoustics ◽  
Head Waves

On the basis of integrated representations Fourier–Bessel a component of displacement of elastic waves, radiating by the normal converter which is taking place on a free flat surface of the elastic environment, receives analytical estimations of displacement a under-surface longitudinal and head (it is surface-longitudinal) waves. Components of displacement a under-surface longitudinal wave are the sum a component in approximation of geometrical acoustics (GA), the diffraction amendments to this approximation and the amendments which are taking into account influence of feature when the parameter of integrated representation is equal to wave number of a longitudinal wave. Components of displacement of a head wave are defined as the sum appropriate diffraction amendments for a component of displacement of a volumetric longitudinal wave in approximation GA and a component of displacement of a lateral wave. The maximum of amplitude of displacement a under-surface longitudinal wave in angular area of a direction of distribution near to a free surface of environment is caused by one of local maxima of the directivity characteristic of the normal probe. Thus dependence of change of amplitude of this wave of distance wave from the centre of the probe practically corresponds to similar dependence for displacement of a volumetric longitudinal wave in GA approximation. Quantitative estimations of maxima of amplitude of displacement under-surface longitudinal and head waves concerning the greatest amplitude, radiated by the normal probe of a volumetric longitudinal wave.

scholarly journals Evaluation Study of Boundary and Depth of the Soil Structure for Geotechnical Site Investigation using MASW

2017 ◽  
Vol 2 (1) ◽  
pp. 31
Author(s):  
A. Arisona ◽  
Mohd Nawawi ◽  
Amin E. Khalil ◽  
U K Nuraddeen ◽  
Mohd Hariri ◽  
...  
Keyword(s):  
Phase Velocity ◽  
Soil Structure ◽  
Subsurface Layer ◽  
Saturated Soil ◽  
Wave Number ◽  
Velocity Versus ◽  
Frequency Wave ◽  
Soil Zone ◽  
Clayey Silt ◽  
Best Fit

This study reviews the correlation between the experimental Rayleigh dispersion curve and the Vp & Vs ground model versus depth. Six samples of stations A , B , C , D ,  E  and  F  were used in the experiment.The geophone spacing used was set 1 m and total length of each line was 23 m. The result shows positive significance (best fit) of R2 that ranges from 0.80 to 0.90. The fk (frequency-wave number method) dispersion curves analysis confirmed that the soil structure investigated is divided into three zones: (1) Unsaturated soil zone (clay soil), in which the layer is dominated by soil with typically alluvial clayey silt and sand. The Vp ranges from 240 m/s to 255 m/s at a depth of 2 to 8 m. (2) The intermediate zone (stiff soil), in which the layer is dominated by sand, silt, clayey sand, sandy clay and clay of low plasticity. This structure is interpreted as partially saturated soil zone, the soil is typically very dense. It contains soft rock typically fill with cobble, sand, slight gravel and highly weathered at depth of 18 to 30 m with Vp of  255 to 300 m/s. (3) Saturated soil zone at a depth of  8 to 18 m with Vp of 300 to 390 m/s. There is a very good agreement between wave-number (k) and phase velocity (Vw)  produced. Both the two parameters shows similar pattern in the topsoil and subsurface layer, which constitute boundary field of soil structure. Moreover, relationship between phase velocity versus wave-length shows best fit of model from inversion with measured value (observed) in  implementation of the boundary and depth of each layer.

scholarly journals A Study of Longitudinal Waveguide with Band Gap Using Cylindrical and Conical Shape Periodic Structure

2021 ◽  
Vol 11 (16) ◽  
pp. 7257
Author(s):  
Dong Hyeon Oh ◽  
Gil Ho Yoon
Keyword(s):  
Wave Propagation ◽  
Longitudinal Wave ◽  
Wave Motion ◽  
Periodic Structures ◽  
Experimental Studies ◽  
Frequency Wave ◽  
Active Devices ◽  
Mechanical Filter ◽  
Specific Frequency ◽  
Mass Spring

This research presents the theoretical and experimental studies for cylindrical and conical periodic structures to control longitudinal wave motion. Many relevant researches exist to stop and pass a certain frequency wave without active devices with periodic structures called metamaterials. To modify or control longitudinal wave propagation, i.e., passing or blocking mechanical wave within specific frequency ranges, repeated mass-spring systems or metamaterials can be applied. By integrating a few identical structural components to form a whole structure, it is possible to make a mechanical filter for wave propagation. Most studies rely on straight bar with cylindrical structure. Thus, with a unit cell that have a cylindrical and conical structure, this research presents the extensions toward the studies of the wave motions for straight and curved bars with finite element simulations and experiment studies. The results show that the hybrid cylindrical and conical periodic structures can be effective in terms of wave motion control and stiffness.

Waves

2019 ◽  
pp. 1-19
Author(s):  
B. D. Guenther
Keyword(s):  
General Theory ◽  
Plane Wave ◽  
Phase Velocity ◽  
Harmonic Wave ◽  
Simple Wave ◽  
Wave Number ◽  
Plane Harmonic Wave ◽  
Frequency Wave

A description of the solution of the wace equation is described as a wave that propagates without change. The set of parameters needed to describe a wave are: period, frequency, wave number, wavelength, and phase velocity. We will use a plane harmonic wave In 3 dimensions in all of our discussions and use complex notation to make the math simplier. We show we are justified in using such a simple wave by the fact that Foourier Theory allows us to construct any wave as a series of hamonics of the plane wave. The theory also will be needed in our discussion of defraction and imaging. There are a few topics that are more difficult and are marked. Their discussion can be skipped without loss of understanding of the general theory of optics.

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

2006 ◽  
Vol 128 (4) ◽  
pp. 477-488 ◽  
Author(s):  
A. Chakraborty ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Shear Deformation ◽  
Mechanical Response ◽  
Laminated Composite ◽  
Wave Number ◽  
Single Element ◽  
Element Formulation ◽  
Frequency Wave ◽  
Spectral Finite Element

A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

Multifrequency full-waveform sonic logging in the screened interval of a large-diameter production well

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. B243-B257 ◽  
Author(s):  
Majed Almalki ◽  
Brett Harris ◽  
J. Christian Dupuis
Keyword(s):  
Phase Velocity ◽  
Velocity Dispersion ◽  
Large Diameter ◽  
Low Frequency ◽  
Production Well ◽  
Frequency Wave ◽  
Full Waveform ◽  
Phase Velocity Dispersion ◽  
Production Wells ◽  
Sonic Logging

A set of field experiments using multiple transmitter center frequencies was completed to test the application potential of low-frequency full-waveform sonic logging in large-diameter production wells. Wireline logs were acquired in a simple open drillhole and a high-yield large diameter production well completed with wire-wound sand screens at an aquifer storage and recovery site in Perth, Western Australia. Phase-shift transform methods were applied to obtain phase-velocity dispersion images for frequencies of up to 4 kHz. A 3D representation of phase-velocity dispersion was developed to assist in the analysis of possible connections between low-frequency wave propagation modes and the distribution of hydraulic properties. For sandstone intervals in the test well, the highest hydraulic conductivity intervals were typically correlated with the lowest phase velocities. The main characteristics of dispersion images obtained from the sand-screened well were highly comparable with those obtained at the same depth level in a nearby simple drillhole open to the formation. The sand-screened well and the open-hole displayed an expected and substantial difference between dispersion in sand- and clay-dominated intervals. It appears that for clay-dominated formations, the rate of change of phase velocity can be associated to clay content. We demonstrated that with appropriate acquisition and processing, multifrequency full-waveform sonic logging applied in existing large-diameter sand-screened wells can produce valuable results. There are few wireline logging technologies that can be applied in this setting. The techniques that we used would be highly suitable for time-lapse applications in high-volume production wells or for reassessing formation properties behind existing historical production wells.

scholarly journals Axially Symmetric Vibrations of Composite Poroelastic Spherical Shell

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Rajitha Gurijala ◽  
Malla Reddy Perati
Keyword(s):  
Wave Propagation ◽  
Phase Velocity ◽  
Spherical Shell ◽  
Wave Number ◽  
Biot’S Theory ◽  
Impervious Surfaces ◽  
Axially Symmetric ◽  
Spherical Shells ◽  
Biot's Theory

This paper deals with axially symmetric vibrations of composite poroelastic spherical shell consisting of two spherical shells (inner one and outer one), each of which retains its own distinctive properties. The frequency equations for pervious and impervious surfaces are obtained within the framework of Biot’s theory of wave propagation in poroelastic solids. Nondimensional frequency against the ratio of outer and inner radii is computed for two types of sandstone spherical shells and the results are presented graphically. From the graphs, nondimensional frequency values are periodic in nature, but in the case of ring modes, frequency values increase with the increase of the ratio. The nondimensional phase velocity as a function of wave number is also computed for two types of sandstone spherical shells and for the spherical bone implanted with titanium. In the case of sandstone shells, the trend is periodic and distinct from the case of bone. In the case of bone, when the wave number lies between 2 and 3, the phase velocity values are periodic, and when the wave number lies between 0.1 and 1, the phase velocity values decrease.

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