scholarly journals A Simple Demonstration of the Frequency Dependences of Elastic Moduli and the Damping of Stress Waves at Seismic Frequencies

1982 ◽  
Vol 13 (2) ◽  
pp. 23-25
Author(s):  
Sharon L. Webb ◽  
Frank D. Stacey
Keyword(s):  
Elastic Moduli ◽  
Stress Waves ◽  
Seismic Frequencies ◽  
Simple Demonstration ◽  
Frequency Dependences

scholarly journals Biot‐consistent elastic moduli of porous rocks: Low‐frequency limit

Geophysics ◽  
1985 ◽  
Vol 50 (12) ◽  
pp. 2797-2807 ◽  
Author(s):  
Leon Thomsen
Keyword(s):  
Bulk Modulus ◽  
Model Theory ◽  
Elastic Moduli ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Porous Rocks ◽  
Seismic Frequencies ◽  
New Formulation ◽  
Special Case ◽  
Finite Concentrations

The semiphenomenological Biot‐Gassmann (B-G) formulation of the low‐frequency elastic moduli of porous rocks does contain two well‐known predictions: (1) the shear modulus of an unsaturated rock (which is permeated by a compressible fluid, e.g., gas) is identical to that of the same rock saturated with liquid, and (2) the unsaturated bulk modulus differs from the saturated bulk modulus by a defined amount. These predictions are tested by ultrasonic data on a large number of sedimentary rocks and are approximately verified, despite the evident frequency discrepancy. The B-G theory makes only minimal assumptions about the microscopic geometry of the rock; therefore, any model theory which does make such assumptions (e.g., spherical pores) should be a special case of B-G theory. In particular, such model theories should also predict the two relations described above. Standard models for dilute concentrations of spherical pores and/or ellipsoidal cracks do predict these relationships. However, in general, the “Self‐Consistent” (S-C) model (developed to deal with finite concentrations of heterogeneities) violates these predictions and hence is not consistent with the underlying Biot‐Gassmann theory. [The special case of S-C theory, corresponding to pores only (no cracks), is consistent with the B-G model.] A new formulation of the model theory, for finite concentrations of heterogeneities of ideal shape, is developed so as to be explicitly consistent with B-G. This “Biot‐consistent” (B-C) formalism is the first theory truly suitable for modeling most sedimentary rocks at seismic frequencies, in terms of porosity and pore shape.

An Experimental Study of Dispersion of Stress Waves in a Fiber-Reinforced Composite

1972 ◽  
Vol 39 (1) ◽  
pp. 98-102 ◽  
Author(s):  
T. R. Tauchert ◽  
A. N. Guzelsu
Keyword(s):  
Elastic Moduli ◽  
Epoxy Composite ◽  
Ultrasonic Pulse ◽  
Stress Waves ◽  
Transverse Waves ◽  
Pulse Technique ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite ◽  
First Approximation ◽  
Static Elastic Moduli

An ultrasonic pulse technique was used to investigate the dispersive behavior of plane harmonic waves in a boron-epoxy composite. The dependence of group velocity upon frequency is determined for longitudinal and transverse waves propagating either parallel or perpendicular to the fibers. The static elastic moduli for the composite are also obtained, and to a first approximation the material is found to be tetragonal.

A simple demonstration of Newton's laws

1978 ◽  
Vol 124 (4) ◽  
pp. 717-719
Author(s):  
Lev A. Gribov ◽  
A.N. Gornostaev
Keyword(s):  
Simple Demonstration ◽  
Newton’S Laws

Epitaxial Growth in Dislocation-Free Strained Alloy Films

2002 ◽  
Vol 715 ◽  
Author(s):  
Zhi-Feng Huang ◽  
Rashmi C. Desai
Keyword(s):  
Deposition Rate ◽  
Elastic Moduli ◽  
Composition Dependence ◽  
Critical Thickness ◽  
Lattice Misfit ◽  
Misfit Strain ◽  
Joint Stability ◽  
Alloy Films ◽  
The Stability ◽  
Stability Results

AbstractThe morphological and compositional instabilities in the heteroepitaxial strained alloy films have attracted intense interest from both experimentalists and theorists. To understand the mechanisms and properties for the generation of instabilities, we have developed a nonequilibrium, continuum model for the dislocation-free and coherent film systems. The early evolution processes of surface pro.les for both growing and postdeposition (non-growing) thin alloy films are studied through a linear stability analysis. We consider the coupling between top surface of the film and the underlying bulk, as well as the combination and interplay of different elastic effects. These e.ects are caused by filmsubstrate lattice misfit, composition dependence of film lattice constant (compositional stress), and composition dependence of both Young's and shear elastic moduli. The interplay of these factors as well as the growth temperature and deposition rate leads to rich and complicated stability results. For both the growing.lm and non-growing alloy free surface, we determine the stability conditions and diagrams for the system. These show the joint stability or instability for film morphology and compositional pro.les, as well as the asymmetry between tensile and compressive layers. The kinetic critical thickness for the onset of instability during.lm growth is also calculated, and its scaling behavior with respect to misfit strain and deposition rate determined. Our results have implications for real alloy growth systems such as SiGe and InGaAs, which agree with qualitative trends seen in recent experimental observations.

Buckling Behavior of Tire Breaker Structure

1983 ◽  
Vol 11 (1) ◽  
pp. 3-19
Author(s):  
T. Akasaka ◽  
S. Yamazaki ◽  
K. Asano
Keyword(s):  
Elastic Foundation ◽  
Elastic Moduli ◽  
Wave Length ◽  
Bending Moment ◽  
Experimental Results ◽  
Automobile Tire ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Steel Cord ◽  
Interlaminar Shear

Abstract The buckled wave length and the critical in-plane bending moment of laminated long composite strips of cord-reinforced rubber sheets on an elastic foundation is analyzed by Galerkin's method, with consideration of interlaminar shear deformation. An approximate formula for the wave length is given in terms of cord angle, elastic moduli of the constituent rubber and steel cord, and several structural dimensions. The calculated wave length for a 165SR13 automobile tire with steel breakers (belts) was very close to experimental results. An additional study was then conducted on the post-buckling behavior of a laminated biased composite beam on an elastic foundation. This beam is subjected to axial compression. The calculated relationship between the buckled wave rise and the compressive membrane force also agreed well with experimental results.

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