scholarly journals Modeling nonlinear compressional waves in marine sediments

2009 ◽  
Vol 16 (1) ◽  
pp. 151-157 ◽  
Author(s):  
B. E. McDonald
Keyword(s):  
Marine Sediments ◽  
Plane Waves ◽  
High Stress ◽  
Nonlinear Behavior ◽  
Analytic Solutions ◽  
Compressional Waves ◽  
Series Of Experiments ◽  
Model Equations ◽  
The Time Domain ◽  
Water Saturated

Abstract. A computational model is presented which will help guide and interpret an upcoming series of experiments on nonlinear compressional waves in marine sediments. The model includes propagation physics of nonlinear acoustics augmented with granular Hertzian stress of order 3/2 in the strain rate. The model is a variant of the time domain NPE (McDonald and Kuperman, 1987) supplemented with a causal algorithm for frequency-linear attenuation. When attenuation is absent, the model equations are used to construct analytic solutions for nonlinear plane waves. The results imply that Hertzian stress causes a unique nonlinear behavior near zero stress. A fluid, in contrast, exhibits nonlinear behavior under high stress. A numerical experiment with nominal values for attenuation coefficient implies that in a water saturated Hertzian chain, the nonlinearity near zero stress may be experimentally observable.

Nonlinear behavior for periodically excited brushless motor

2019 ◽  
Vol 38 (2) ◽  
pp. 522-535
Author(s):  
Jianzhe Huang ◽  
Xingzhong Xiong
Keyword(s):  
Working Condition ◽  
Analytic Solution ◽  
Nonlinear Behavior ◽  
Analytic Solutions ◽  
Strong Nonlinearity ◽  
Periodic Motions ◽  
Content Type ◽  
Strongly Nonlinear ◽  
Brushless Motor ◽  
Analytic Expressions

Purpose Due to the coupling between the direct-axis current, quadrature-axis current and rotor speed, the dynamic response could be strongly nonlinear. Besides, if the working condition is severe, the loading is no longer constant and multiple harmonics could be introduced. In this paper, the periodic motions for brushless motor will be solved, and accurate analytic solution will be obtained through the proposed method. The purpose of this study is to provide accurate analytic solution of periodic motions for brushless motor with fluctuated loading, which is a dynamic system with strong nonlinearity. Design/methodology/approach A newly developed semi-analytic algorithm called discrete implicit maps is used to give analytic solutions for both stable and unstable motions for such a motor. Findings The accurate analytic expressions for stable and unstable periodic motions have been obtained. For unstable motion, it can stay on the unstable orbit for many periods without any controller. Through bifurcation analysis, the parameter sensitivity has been obtained which can be a suggestion for design and operation. Originality/value This paper provides all possible analytical solutions for period-1 motion as well as the unstable motions in a range of system parameters. It offers a chance to control the unstable motion for such a motor.

Experimental measurements of seismic attenuation In microfractured sedimentary rock

Geophysics ◽  
1994 ◽  
Vol 59 (9) ◽  
pp. 1342-1351 ◽  
Author(s):  
Sheila Peacock ◽  
Clive McCann ◽  
Jeremy Sothcott ◽  
Timothy R. Astin
Keyword(s):  
Sedimentary Rock ◽  
Wave Attenuation ◽  
Crack Density ◽  
Seismic Attenuation ◽  
Experimental Measurements ◽  
Effective Pressure ◽  
Carrara Marble ◽  
Compressional Waves ◽  
Linear Relationships ◽  
Water Saturated

Ultrasonic compressional‐ and shear‐wave attenuation in water‐saturated Carrara Marble increase with increasing crack density and decreasing effective pressure. Between 0.4 and 1.0 MHz, empirical linear relationships between 1/Q and crack density CD were found to be: CD = 1.96 ± 0.63 × 1/Q, for compressional waves and CD = 6.7 ± 1.5 × 1/Q, for shear waves.

A theory of compressional wave attenuation in noncohesive sediments

Geophysics ◽  
1985 ◽  
Vol 50 (8) ◽  
pp. 1311-1317 ◽  
Author(s):  
C. McCann ◽  
D. M. McCann
Keyword(s):  
Wave Attenuation ◽  
Compressional Wave ◽  
Solid Particles ◽  
Biot’S Theory ◽  
Attenuation Coefficients ◽  
Low Frequencies ◽  
Biot's Theory ◽  
Compressional Waves ◽  
High Frequencies ◽  
Water Saturated

Published reviews indicate that attenuation coefficients of compressional waves in noncohesive, water‐saturated sediments vary linearly with frequency. Biot’s theory, which accounts for attenuation in terms of the viscous interaction between the solid particles and pore fluid, predicts in its presently published form variation proportional to [Formula: see text] at low frequencies and [Formula: see text] at high frequencies. A modification of Biot’s theory which incorporates a distribution of pore sizes is presented and shown to give excellent agreement with new and published attenuation data in the frequency range 10 kHz to 2.25 MHz. In particular, a linear variation of attenuation with frequency is predicted in that range.

NOISE ATTENUATION ON COMMON‐DEPTH‐POINT SEISMIC RECORDS BY A SEMIDETERMINISTIC APPROACH

Geophysics ◽  
1968 ◽  
Vol 33 (5) ◽  
pp. 723-733 ◽  
Author(s):  
John C. Robinson
Keyword(s):  
Frequency Domain ◽  
Random Noise ◽  
Analytic Solutions ◽  
Harmonic Spectrum ◽  
Algebraic Equations ◽  
Coherent Noise ◽  
Common Depth Point ◽  
Seismic Records ◽  
Point Data ◽  
The Time Domain

A simple seismic record synthesis for common‐depth‐point data was examined for analytic representation in terms of its harmonic spectrum. This frequency‐domain investigation revealed that the primary‐reflection signal can be completely recovered in the absence of random noise, or it can be better recovered in the presence of random noise than normal stacking affords, especially, if the coherent‐noise‐to‐random‐noise ratio is high. The success of this technique is founded upon the principle that difference equations in the time domain become algebraic equations in the frequency domain. The technique is partially “probabilistic” because analytic solutions for the primary‐reflection signal are stacked for further attenuation of noise. The constituents of the seismic records, after static and normal‐moveout corrections, are: identical, coincident, primary‐reflection signal; identical, time‐shifted coherent noise; and random noise. The coherent‐noise time shifts must be determined for application of the semideterministic technique; methods are discussed in the Data Processing section.

Compensation for the Residual Error of the Voltage Drive of the Charge Control of a Piezoelectric Actuator

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Shih-Tang Liu ◽  
Jia-Yush Yen ◽  
Fu-Cheng Wang
Keyword(s):  
Piezoelectric Actuator ◽  
Voltage Drop ◽  
Tracking Error ◽  
Nonlinear Behavior ◽  
Piezo Actuator ◽  
Charge Control ◽  
In Series ◽  
Series Of Experiments ◽  
The One ◽  
Positional Control

One very effective approach to suppress hysteresis from the piezoelectric actuator is to use the charge control across the associated capacitance. The charge driver often uses an additional capacitor connected to the piezo-actuator in series for the charge sense feedback control. When this charge sense is used with a voltage drive for the charge control, the applied voltage will include two parts. The one is the voltage drop across the useful electro-mechanical part and effectively converted to the driving force, whereas the other part indicates the equivalent voltage drop due to the hysteresis. In our research, we noticed that it is possible to use a simple estimator as the hysteresis voltage observer and use it to precompensate for the voltage drop. Comparing to the conventional hysteresis suppression achieved by the closed-loop positional control, we show significant improvement of the control performance. For dynamic applications, we also proposed a combination of the Preisach model with the hysteresis estimator to better suppress the nonlinear behavior. A series of experiments were conducted to demonstrate the performance improvement of the proposed compensator. A 10 nm and 25 nm maximum tracking error can be maintained while tracking a staircase reference and a 30 Hz sinusoidal signal, respectively.

Attenuation of seismic waves in dry and saturated rocks: I. Laboratory measurements

Geophysics ◽  
1979 ◽  
Vol 44 (4) ◽  
pp. 681-690 ◽  
Author(s):  
M. N. Toksöz ◽  
D. H. Johnston ◽  
A. Timur
Keyword(s):  
Seismic Waves ◽  
Reference Sample ◽  
Spectral Ratios ◽  
Attenuation Coefficients ◽  
Compressional Waves ◽  
S Waves ◽  
Pulse Transmission ◽  
Water Saturated ◽  
Quality Factor Q ◽  
Q Values

The attenuation of compressional (P) and shear (S) waves in dry, saturated, and frozen rocks is measured in the laboratory at ultrasonic frequencies. A pulse transmission technique and spectral ratios are used to determine attenuation coefficients and quality factor (Q) values relative to a reference sample with very low attenuation. In the frequency range of about 0.1–1.0 MHz, the attenuation coefficient is linearly proportional to frequency (constant Q) both for P‐ and S‐waves. In dry rocks, [Formula: see text] of compressional waves is slightly smaller than [Formula: see text] of shear waves. In brine and water‐saturated rocks, [Formula: see text] is larger than [Formula: see text]. Attenuation decreases substantially (Q values increase) with increasing differential pressure for both P‐ and S‐waves.

scholarly journals Localized Heating Near a Rigid Spherical Inclusion in a Viscoelastic Binder Material Under Compressional Plane Wave Excitation

2017 ◽  
Vol 84 (4) ◽  
Author(s):  
Jesus O. Mares ◽  
Daniel C. Woods ◽  
Caroline E. Baker ◽  
Steven F. Son ◽  
Jeffrey F. Rhoads ◽  
...  
Keyword(s):  
Energetic Materials ◽  
Scale Effects ◽  
Spherical Inclusion ◽  
Plane Waves ◽  
Thermal Response ◽  
Resonant Scattering ◽  
Compressional Waves ◽  
Dynamic Events ◽  
Bulk Heating ◽  
Viscoelastic Effects

High-frequency mechanical excitation has been shown to generate heat within composite energetic materials and even induce reactions in single energetic crystals embedded within an elastic binder. To further the understanding of how wave scattering effects attributable to the presence of an energetic crystal can result in concentrated heating near the inclusion, an analytical model is developed. The stress and displacement solutions associated with the scattering of compressional plane waves by a spherical obstacle (Pao and Mow, 1963, “Scattering of Plane Compressional Waves by a Spherical Obstacle,” J. Appl. Phys., 34(3), pp. 493–499) are modified to account for the viscoelastic effects of the lossy media surrounding the inclusion (Gaunaurd and Uberall, 1978, “Theory of Resonant Scattering From Spherical Cavities in Elastic and Viscoelastic Media,” J. Acoust. Soc. Am., 63(6), pp. 1699–1712). The results from this solution are then utilized to estimate the spatial heat generation due to the harmonic straining of the material, and the temperature field of the system is predicted for a given duration of time. It is shown that for certain excitation and sample configurations, the elicited thermal response near the inclusion may approach, or even exceed, the decomposition temperatures of various energetic materials. Although this prediction indicates that viscoelastic heating of the binder may initiate decomposition of the crystal even in the absence of defects such as initial voids or debonding between the crystal and binder, the thermal response resulting from this bulk heating phenomenon may be a precursor to dynamic events associated with such crystal-scale effects.

scholarly journals Plane Waves Scattered by a Spherical Inclusion in a Half Space of Poroelastic Material

2020 ◽  
Vol 03 (02) ◽  
pp. 1-1
Author(s):  
Doo-Sung Lee ◽  
Keyword(s):  
Half Space ◽  
Existence And Uniqueness ◽  
Spherical Inclusion ◽  
Plane Waves ◽  
Spherical Wave ◽  
Wave Functions ◽  
Successive Approximations ◽  
Compressional Waves ◽  
Poroelastic Material ◽  
The Given

This paper concerns a poroelastic half-space in which plane compressional waves are scattered by a spherical inclusion. Addition theorems for the spherical wave functions are utilized to meet the boundary conditions on the plane, and the satisfaction of the given conditions on the boundary of the sphere leads to three infinite series equations, whose solution can be acquired by successive approximations. Further, its existence and uniqueness are discussed.

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