Identification of the Model of Nonlinear Elasticity in Dynamic Experiments

Author(s):  
Marina Sokolova ◽  
Yuri Astapov ◽  
Dmitrii Khristich

Dynamic methods for identifying a model of a nonlinearly elastic deformable body are considered. By the effective phase velocities of longitudinal and transverse waves propagating along and across the axis of the compressed bar, it is possible to determine five elastic constants of the second and third orders included in the model relations. Calculation formulae are obtained and an example of determining the dependence of phase velocities on the preliminary deformation for polyamide 6 is given. The influence of preliminary deformations on polar diagrams of wave velocities is investigated.

Author(s):  
Марина Юрьевна Соколова ◽  
Юрий Владимирович Астапов

Рассмотрены динамические методы идентификации модели нелинейно упругого деформируемого тела. По эффективным фазовым скоростям продольных и поперечных волн, распространяющихся вдоль и поперек оси сжимаемого стержня, возможно определить пять констант упругости второго и третьего порядков, входящих в соотношения модели. В статье получены расчетные формулы и приведен пример определения зависимости фазовых скоростей для полиамида 6. The dynamic methods for selecting models of a nonlinear elastic deformable body are considered. Depending on the model, five elastic constants of the second and third orders, which are available in the relations of the models, can be determined. The calculation formulas and the given example of determining the dependence of phase velocities for polyamide 6 are obtained in the article.


2021 ◽  
Author(s):  
Giovanni Diaferia ◽  
Fabrizio Magrini ◽  
Matthew Agius ◽  
Fabio Cammarano

<p><span>The dynamics of crustal extension and the crust-mantle interaction i</span>n the Central-Western Mediterranean and Italian peninsula (i.e. Liguro-Provençal and Tyrrhenian Basin), and plate convergence (i.e. Alpine and Apennines chains) are key for the understating of the current geodynamics setting and its evolution<span> in the region</span>. However, open questions <span>such as the style, depth and extent of the deformation </span>still exist despite the wealth of seismological and non-seismological data acquired in the past decades. In this context, it is necessary to provide improved subsurface models in terms of seismic velocities, from which better constraints on the geodynamic models can be derived.</p><p>We use seismic ambient noise for retrieving phase velocities of Rayleigh and Love waves in the 4-35 s period range, using private (LiSard network<span> in Sardinia island</span>) and publicly available continuous recordings from more than 500 seismic stations. Considering the excellent coverage and the short period of recovered phase velocities, our study aims to provide an unprecedented, high-resolution image of the shallow crust and uppermost mantle.</p><p>We employ a Bayesian trans-<span>dimensional</span>, Monte Carlo Markov chain inversion approach that requires no a-priori model nor a fixed parametrization. In addition to the (isotropic) shear wave velocity structure, we also recover the values of radial anisotropy (ξ=(V<sub>SH</sub>/V<sub>SV</sub>)<sup>2</sup>) as a function of depth, thanks to the joint inversion of both Rayleigh and Love phase velocities.</p><p>Focusing on radial anisotropy, this appears clearly uncoupled with respect to the shear wave velocity structure. The largest negative anisotropy anomalies (V<sub>SH</sub><V<sub>SV</sub>, ξ<0.9) are found in the Liguro-Provençal and western Tyrrhenian basins in the top 10-15 km, suggesting a common structural imprint inherited during the extensional phases of such basins. Conversely, the eastern Tyrrhenian basin shows positive radial anisotropy (V<sub>SH</sub>>V<sub>SV</sub>, ξ>1.1) within the same depth range. This evidence, combined with the observed shear wave velocities typical of the uppermost mantle, corroborates the presence of a sub-horizontal asthenospheric flow driving the current extension and <span>oceanization </span>of the eastern Tyrrhenian basins.</p><p>Moving towards the Italian mainland, a strong anomaly of negative anisotropy appears in the eastern portion of the Apennines chain. We relate such an anisotropic signal with the ongoing compressive regime affecting the area. Here, the high-angle thrust faults and folds, that accommodates the horizontal shortening, obliterate the horizontal layering of the sedimentary deposits, currently constituting the flanks of the fold system.</p><p>Our results suggest that the combination of radial anisotropy and shear wave velocities can unravel key characteristics of the crust and uppermost mantle, such as inherited or currently active structures resulting from past or ongoing geodynamic processes.</p>


1951 ◽  
Vol 41 (2) ◽  
pp. 143-163 ◽  
Author(s):  
B. Gutenberg

Abstract Discrepancies of up to 20 per cent between wave velocities calculated from blast records in southern California and those found from earthquakes necessitate a reinterpretation of seismograms of all near-by shocks and a revision of travel-time curves. A combination of findings for S — P intervals as a function of distance in southern California earthquake records with the ratio of mean interval velocities for P and S waves shows (without assumption of origin times) that the mean velocities of the two waves between the source and the surface are about 6.35 and 3.67 km/sec., respectively. This agrees with the results found from blast records. Most revised origin times are between ¾ sec. and 1 1/2 sec. later than those found previously from P¯. The method applied here removes the difference in origin time for longitudinal and transverse waves which was found formerly for earthquakes. Travel-time curves of various phases are revised and reinterpreted. The change in amplitudes with distance of several wave types is discussed.


1965 ◽  
Vol 55 (5) ◽  
pp. 919-923
Author(s):  
H. Deresiewicz

abstract The dispersion equation in the second approximation for small porosity is deduced for the problem of transverse waves in a porous layer separating two impermeable elastic half-spaces, and the expression for the dissipation per cycle displayed. It is shown that Love waves can be propagated in a porous layer only with phase velocities smaller than that of body shear waves in either of the half-spaces, whereas in an impermeable layer Love waves may exist having phase velocity equal to that of body shear waves in one of the half-spaces.


2006 ◽  
Vol 321-323 ◽  
pp. 574-577
Author(s):  
Noh Yu Kim ◽  
Cheol Kyou Lee

Scanning acoustic microscopy (SAM) has been applied successfully to measure leaky surface wave(LSAW) velocity from V(z) curve for material characterization. Besides LSAW, SAM produces a variety of wave modes in the material propagating with different phase speeds and features, one of which is the mode-converted ultrasound. In this paper, a novel method for simultaneous measurement of longitudinal and transverse acoustic wave velocities using the mode-converted ultrasound is developed and studied at SAM. Each ultrasound arriving at the acoustic lens with different speed and phase (or time-of-flight (TOF)) is measured by the defocused transducer to calculate longitudinal and transverse wave velocities. Simple mathematical ray analysis for the mode conversion is conducted to determine the relationship of acoustic velocities with TOF of the waves in plate. Experimental results for metals and glass show that the longitudinal and transverse wave velocities measured by the proposed method are as accurate as maximum 3% in error.


Author(s):  
Yanbao Ma

In this paper, heat pulse propagation in pure NaF at low temperature is studied by using hydrodynamic equations of a weakly interacting phonon gas. The observed longitudinal waves, transverse waves, second sound waves, and diffusive waveforms from the experiments conducted in early 1970s are numerically reconstructed. In the numerical simulations, the phase velocities of the longitudinal waves and the transverse waves are based on the experimental results, while two relaxation times for normal scattering process (τN) and resistive scattering process (τR) respectively are adjusted to fit the arrival time of second sound or to fit the observed waveforms observed in the experiments. The waveforms based on numerical results can fit the observed waveforms quite well. It is elucidated how heat pulse is transmitted by different waves in the dielectric crystal from ballistic to diffusive regions.


Geophysics ◽  
2013 ◽  
Vol 78 (1) ◽  
pp. F1-F5 ◽  
Author(s):  
Vladimir Grechka

Two-point ray tracing in anisotropic media requires the group and phase velocities to be calculated along ray directions available at each step of a ray bending algorithm. This computation, usually done iteratively or through velocity tables, becomes exceedingly involved for shear-waves that have multivalued group-velocity surfaces, such as in the presence of triplications on the SV wavefronts in vertically transversely isotropic (VTI) media. The difficulties encountered in computing the SV-wave velocities for a given ray direction can be circumvented by solving a polynomial equation whose real-valued roots provide the phase directions of the P- and either one or three SV-waves propagating along a selected ray; those phase directions then allow the group and phase velocities to be computed in a standard fashion. I construct the polynomial and supply computer codes implementing its solution, the codes that can be used in two-point ray-tracing software to improve its performance.


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