scholarly journals Linear models of dissipation whose Q is almost frequency independent

2011 ◽  
Vol 19 (4) ◽  
Author(s):  
M. CAPUTO
Keyword(s):  
Fractional Derivatives ◽  
Linear Models ◽  
Solid Sphere ◽  
Inorganic Solids ◽  
The Earth ◽  
Single Substance ◽  
Stress Strain Relation ◽  
Frequency Independent ◽  
Experimental Values ◽  
Large Frequency

Laboratory experiments and field observations indicate<br />that tlie Q of many non ferromagnetic inorganic solids is almost frequency<br />independent in the range 10' to 10~2 cps; although no single substance has<br />been investigated over the entire frequency spectrum. One of the purposes<br />of this investigation is to find the analytic expression of a linear dissipative<br />mechanism whose Q is almost frequency independent over large frequency<br />ranges. This will be obtained by introducing fractional derivatives in the<br />stress strain relation.<br />Since the aim of this research is to also contribute to elucidating the<br />dissipating mechanism in the earth free modes, we shall treat the cases of<br />dissipation in the free purely torsional modes of a shell and the purely<br />radial vibration of a solid sphere.<br />The theory is checked with the new values determined for the Q of<br />the spheroidal free modes of the earth in the range between 10 and 5 minutes<br />integrated with the Q of the Railegh waves in the range between 5 and 0.6<br />minutes.<br />Another check of the theory is made with the experimental values<br />of the Q of the longitudinal waves in an alluminimi rod, in the range between<br />10-5 and 10-3 seconds.<br />In both clicks the theory represents the observed phenomena very<br />satisfactory.

Stress-Strain Relations and Vibrations of a Granular Medium

1957 ◽  
Vol 24 (4) ◽  
pp. 585-593
Author(s):  
J. Duffy ◽  
R. D. Mindlin
Keyword(s):  
Energy Dissipation ◽  
Contact Forces ◽  
Face Centered Cubic ◽  
Stress Strain ◽  
Differential Stress ◽  
Elastic Bodies ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Face Centered ◽  
Experimental Values

Abstract A differential stress-strain relation is derived for a medium composed of a face-centered cubic array of elastic spheres in contact. The stress-strain relation is based on the theory of elastic bodies in contact, and includes the effects of both normal and tangential components of contact forces. A description is given of an experiment performed as a test of the contact theories and the differential stress-strain relation derived from them. The experiment consists of a determination of wave velocities and the accompanying rates of energy dissipation in granular bars composed of face-centered cubic arrays of spheres. Experimental results indicate a close agreement between the theoretical and experimental values of wave velocity. However, as in previous experiments with single contacts, the rate of energy dissipation is found to be proportional to the square of the maximum tangential contact force rather than to the cube, as predicted by the theory for small amplitudes.

Investigating the in-plane mechanical behavior of single-ply quasi-unidirectional glass fiber/polypropylene composites

2017 ◽  
Vol 37 (4) ◽  
pp. 401-409 ◽  
Author(s):  
Zhanyu Zhai ◽  
Christian Gröschel ◽  
Dietmar Drummer
Keyword(s):  
Tensile Stress ◽  
Glass Fiber ◽  
Tensile Tests ◽  
Stress Strain ◽  
Polypropylene Composites ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Pp Composites ◽  
Experimental Values ◽  
First Time

Abstract The objective of this study was to determine the engineering constants and off-axis tensile stress-strain relation of single-ply quasi-unidirectional (UD) glass fiber (GF)/polypropylene (PP) composites using the new approach. A series of off-axis tensile tests of quasi-UD composites were carried out. In this study, Puck’s interfiber fracture criterion was expanded for the first time to estimate the off-axis tensile stresses of UD composites. With the experimental values, the shear properties were obtained through the curve-fitting methods. Damage mechanisms were demonstrated to evolve with the loading angle. By comparison to experimental data, the Hahn-Tsai equation, together with the transformation equation, was found to be adequate to describe the off-axis tensile stress-strain relation of single-ply quasi-UD GF/PP composites.

scholarly journals Amplitude of Sunspot-Dependent Radiocarbon Variations: Data from Corals and Wine

Radiocarbon ◽  
1985 ◽  
Vol 27 (1) ◽  
pp. 111-115
Author(s):  
Mordeckai Magaritz ◽  
Israel Carmi ◽  
Ziv Sirkes
Keyword(s):  
Theoretical Analysis ◽  
Theoretical Calculation ◽  
Production Rate ◽  
Sunspot Cycle ◽  
Published Data ◽  
Earth Surface ◽  
The Earth ◽  
Surface System ◽  
Experimental Values

It has been suggested that the sunspot cycle modulates the production rate of radionuclides in the atmosphere and that these modulations can be traced in various parts of the earth surface system. On the basis of a theoretical analysis, Damon, Sternberg, and Radnell (1983) have concluded that the effects of the 11-yr cycle of sunspots should be observable in 14C data provided the measurements are done at a 2 permil (sd) level. This conclusion is based on calculations using models discussed by Lingenfelter and Ramaty (1970) and by O'Brien (1979) and on the 14C inventory modified from Damon, Lerman, and Long (1978). In this note we compare the amplitude estimate of Damon, Sternberg, and Radnell (1983), who calculated a representative peak-to-peak variation of 1.7‰ in 14C for the sunspot cycle between 1848 and 1856, with experimental values derived from recently published data. We find the experimental value to be larger by a significant factor from the theoretical calculation.

Frequency dependence of CO2 elimination and respiratory resistance in monkeys

1985 ◽  
Vol 58 (2) ◽  
pp. 653-657 ◽  
Author(s):  
J. W. Watson ◽  
A. C. Jackson
Keyword(s):  
Frequency Dependence ◽  
Nonlinear Frequency ◽  
Frequency Dependent ◽  
Dependent Behavior ◽  
Frequency Independent ◽  
Respiratory System Resistance ◽  
The Relationship ◽  
High Frequency Oscillatory ◽  
Large Frequency ◽  
Co2 Elimination

In dogs, respiratory system resistance (Rrs) is frequency independent, and during high-frequency oscillatory ventilation (HFO) the relationship between CO2 elimination (VCO2) and frequency is linear. In contrast, we found in rabbits a large frequency-dependent decrease in Rrs with increasing frequency along with a nonlinear relationship between frequency and VCO2 (J. Appl. Physiol. 57: 354–359, 1984). We proposed that frequency dependent mechanical properties of the lung account for inter-species differences in the frequency dependence of gas exchange during HFO. In the current study we tested this hypothesis further by measuring VCO2 and Rrs as a function of frequency in a species of monkey (Macaca radiata). In these monkeys, Rrs decreased minimally between 4 and 8 Hz and in general increased at higher frequencies, whereas VCO2 was linearly related to frequency. This is further evidence supporting the hypothesis that nonlinear frequency-VCO2 behavior during HFO is related to frequency-dependent behavior in Rrs.

scholarly journals Some Numerical Examples on the Stability of Fractional Linear Dynamical Systems

2018 ◽  
Vol 17 (3) ◽  
pp. 51-66
Author(s):  
S Priyadharsini
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Linear Models ◽  
Sufficient Conditions ◽  
Characteristic Polynomials ◽  
Caputo Fractional Derivatives ◽  
Linear Dynamical Systems ◽  
Numerical Examples ◽  
Eigen Values ◽  
The Stability

The concept of stability of a class of fractional-order linear system is considered in this paper. Existing sufficient conditions are assumed to guarantee the stability of linear models with the Caputo fractional derivatives. The results have been developed by using the concept of Laplace transform, and approximations of Mittag-Leffler.  Furthermore, results concerning asymptotical stability of linear fractional-order models are also achieved. The proposed method is based upon Eigen values and the characteristic polynomials. Numerical illustrations are specified to exhibit effectiveness of the proposed method.

scholarly journals GEODYNAMICS

GEODYNAMICS ◽  
2007 ◽  
Vol 1(6)2007 (1(6)) ◽  
pp. 5-10
Author(s):  
T.V. Guseva ◽  
◽  
L. Latynina ◽  
Keyword(s):  
Earthquake Precursors ◽  
Gps Measurements ◽  
Strong Earthquakes ◽  
The Earth ◽  
Gps Measurement ◽  
Large Frequency ◽  
Crust Surface ◽  
Horizontal Displacements

The important problems of the GPS measurements are the searches of the earthquake precursors and study of irreversible and varying displacement of the Earth crust, due to the strongest earthquakes. With development of GPS systems and improvement of satellite technologies of measurements and methods of processing there was possible to in detail register the processes occurring during activization of seismicity. GPS measurement with the large frequency of registration of satellite signals are the powerful tool of study longperiodical waves at the strongest earthquakes. There are considered the examples of registration of the irreversible and coseismical horizontal displacements and deformations of the Earth crust surface arising during the tectonical processes, accompanied the strong earthquakes (Izmit by 1999, Alaska 2002, Sumatra 2004 etc.).

scholarly journals Recommended and experimental values of the earth surface shift troughs parameters when conducting the stope works

2018 ◽  
Vol 60 ◽  
pp. 00040
Author(s):  
Mykhailo Filatiev ◽  
Elvira Filatieva
Keyword(s):  
Reference Points ◽  
Crustal Movement ◽  
Face Advance ◽  
Earth Surface ◽  
Normative Documents ◽  
The Earth ◽  
The Face ◽  
Characteristic Points ◽  
Maximum Subsidence ◽  
Experimental Values

The correspondence of angular and linear parameters of the undermined rocks displacement and the crustal movement to their values determined according to the normative document has been established. Based on the surveying observations over the reference points movement on the earth surface and the stope face advance, the empirical curve of the trajectory of the earth surface maximum subsidence is determined from the points of maximum subsidence. The curve of the maximum subsidence of the earth surface points when removing the stope face from the face entry has been experimentally established, which allowed to determine the location of the point of the beginning of the crustal movement and the dimension of the stope mine working corresponding to this situation. The coordinates of the characteristic points of the earth surface subsidence above the stope face have been determined. A unified method has been developed for determining the angular and linear parameters of the undermined rocks displacement for the two stages of shift troughs formation on the earth surface. The nonconformities have been established between the recommended parameters and the experimental data normative documents during the anthracite seams mining.

Investigation of EFG Parameters at the Halogen Site in XO3 and XO32⊝ Radicals (X = Cl, Br) in Certain Inorganic Solids

1986 ◽  
Vol 41 (1-2) ◽  
pp. 169-170
Author(s):  
Y. Umasasidhar ◽  
S. Ramaprabhu ◽  
K. V. S. Rama Rao
Keyword(s):  
Electric Field ◽  
Single Crystals ◽  
Bond Distance ◽  
Mo Calculations ◽  
Electric Field Gradients ◽  
Γ Irradiation ◽  
Inorganic Solids ◽  
Field Gradients ◽  
Experimental Values ◽  
Good Agreement

Electric field gradients at the halogen site in XO3and XO32⊝radicals (X = Cl, Br), formed bythe γ-irradiation of single crystals of NaClO3 , KClO3 , KBrO3and Sr(BrO3)2 · H20 have beenevaluated by MO calculations using the CNDO/2 method. The symmetry of the XO3radicals isassumed to be that of XO3⊝ ions which have C3v symmetry, whereas XO32⊝radicals are assumedto have CS symmetry with one X -O bond distance being stretched due to the excess electron.The results are in good agreement with the experimental values deduced from published ESRstudies on these single crystals.

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