Strong nonlocalization induced by small scale parameter on terahertz flexural wave dispersion characteristics of a monolayer graphene

2010 ◽  
Vol 43 (1) ◽  
pp. 423-430 ◽  
Author(s):  
S. Narendar ◽  
S. Gopalakrishnan
Keyword(s):  
Scale Parameter ◽  
Wave Dispersion ◽  
Flexural Wave ◽  
Monolayer Graphene ◽  
Small Scale ◽  
Dispersion Characteristics

Model-based dispersive processing of borehole dipole wave data using an equivalent-tool theory

Geophysics ◽  
2016 ◽  
Vol 81 (1) ◽  
pp. D35-D43 ◽  
Author(s):  
Sheng-Qing Lee ◽  
Xiao-Ming Tang ◽  
Yuan-da Su ◽  
Chun-Xi Zhuang
Keyword(s):  
Data Processing ◽  
Dispersion Curve ◽  
Low Frequency ◽  
Wave Dispersion ◽  
Flexural Wave ◽  
Dispersion Characteristics ◽  
Acoustic Data ◽  
Model Based ◽  
Dispersion Data ◽  
Application Procedure

We have developed a model-based processing technique for borehole dipole S-wave logging data to estimate formation shear slowness from the data. During dipole acoustic logging, the presence of the logging tool can significantly affect the dispersion characteristics of flexural waves. Therefore, modeling the effects of the tool is essential for model-based processing. We have determined that an equivalent-tool theory using only two parameters, tool radius, and modulus, can adequately model the flexural-wave-dispersion characteristics. We used this theory, together with a calibration procedure, to determine the tool parameters to formulate an inversion method for the logging data processing. Our use of the equivalent tool theory played an important role in fitting the theoretical dispersion curve to the actual flexural-wave-dispersion data, enabling fast processing of the field acoustic data. An advantage of this model-based method is its prediction power, which, in the absence of low-frequency dispersion data, allows for predicting formation shear slowness from the low-frequency limit of the model-fitted dispersion curve. We have also developed an application procedure of the method for field-data processing and demonstrated its effectiveness in the dispersion correction using field acoustic data from fast and slow formations.

Mapping formation radial shear-wave velocity variation by a constrained inversion of borehole flexural-wave dispersion data

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. E183-E190 ◽  
Author(s):  
Xiao-Ming Tang ◽  
Douglas J. Patterson
Keyword(s):  
Shear Wave ◽  
Wave Velocity ◽  
Shear Wave Velocity ◽  
High Frequency ◽  
Wave Dispersion ◽  
Velocity Variation ◽  
Flexural Wave ◽  
Inversion Method ◽  
Dispersion Characteristics ◽  
Dispersion Data

We have developed a novel constrained inversion method for estimating a radial shear-wave velocity profile away from the wellbore using dipole acoustic logging data and have analyzed the effect of the radial velocity changes on dipole-flexural-wave dispersion characteristics. The inversion of the dispersion data to estimate the radial changes is inherently a nonunique problem because changing the degree of variation or the radial size of the variation zone can produce similar wave-dispersion characteristics. Nonuniqueness can be solved by developing a constrained inversion method. This is done by constraining the high-frequency portion of the model dispersion curve with another curve calculated using the near-borehole velocity. The constraint condition is based on the physical principle that a high-frequency dipole wave has a shallow penetration depth and is therefore sensitive to the near-borehole shear-wave velocity. We have validated the result of the constrained inversion with synthetic data testing. Combining the new inversion method with four-component crossed-dipole anisotropy processing obtains shear radial profiles in fast and slow shear polarization directions. In a sandstone formation, the fast and slow shear-wave profiles show substantial differences caused by the near-borehole stress field, demonstrating the ability of the technique to obtain radial and azimuthal geomechanical property changes near the wellbore.

scholarly journals Nonlinear magneto-thermo-elastic vibration of mass sensor armchair carbon nanotube resting on an elastic substrate

2020 ◽  
Vol 7 (1) ◽  
pp. 153-165
Author(s):  
Rajendran Selvamani ◽  
M. Mahaveer Sree Jayan ◽  
Rossana Dimitri ◽  
Francesco Tornabene ◽  
Farzad Ebrahimi
Keyword(s):  
Carbon Nanotube ◽  
Mechanical Response ◽  
Scale Effects ◽  
Nonlocal Elasticity Theory ◽  
Wave Dispersion ◽  
Elastic Vibration ◽  
Ultrasonic Waves ◽  
Small Scale ◽  
Dimensionless Frequency ◽  
Mass Sensors

AbstractThe present paper aims at studying the nonlinear ultrasonic waves in a magneto-thermo-elastic armchair single-walled (SW) carbon nanotube (CNT) with mass sensors resting on a polymer substrate. The analytical formulation accounts for small scale effects based on the Eringen’s nonlocal elasticity theory. The mathematical model and its differential equations are solved theoretically in terms of dimensionless frequencies while assuming a nonlinear Winkler-Pasternak-type foundation. The solution is obtained by means of ultrasonic wave dispersion relations. A parametric work is carried out to check for the effect of the nonlocal scaling parameter, together with the magneto-mechanical loadings, the foundation parameters, the attached mass, boundary conditions and geometries, on the dimensionless frequency of nanotubes. The sensitivity of the mechanical response of nanotubes investigated herein, could be of great interest for design purposes in nano-engineering systems and devices.

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