Shock Theory Research Articles

Numerical study of solitary waves and reversible shock structures in tubes with controlled pressure

Methods for computing and analyzing solutions for a model of a tube with elastic walls in the case of controlled internal pressure is developed. A membrane model or a plate model is used for the tube walls. Numerical methods are applied. The Boussinesq equations are used to describe waves near the transition to the instability zone of homogeneous states and to verify the numerical methods. Solitary waves and soliton shock structures for these equations are studied. The Boussinesq equations are analyzed and generalized. Next, the same methods are applied to the complete equations. Solitary waves and reversible shock structures (generalized kinks) are studied. The stability of the solitary waves is analyzed by finding an eigenfunction. The kinks are studied using general methods of the theory of reversible shocks.

High velocity impact mitigation with gradient cellular solids

The dynamic behavior of gradient cellular solids subjected to high velocity impact is investigated, with shock theory and rigid-perfectly-plastic-locking idealization. The impact is induced by the fragments of a cased charge explosion in near field, sufficiently high to progressively crush the cellular solids from the loading part, regardless of the density variation of the cellular solids. The dynamic response and energy absorption are examined for different gradient cellular solid layers with the same mass and thickness, but different density variation. The cellular solids with larger density gradient lead to smaller crushed distance and higher energy absorption compared to those with smaller density gradients, when subjected to the same impact, provided that the cellular solid is not fully densified. However, when the cellular layer is fully crushed, the effect of density variation on energy absorption vanishes.

Curved shock theory

Curved shock theory (CST) is introduced, developed and applied to relate pressure gradients, streamline curvatures, vorticity and shock curvatures in flows with planar or axial symmetry. Explicit expressions are given, in an influence coefficient format, that relate post-shock pressure gradient, streamline curvature and vorticity to pre-shock gradients and shock curvature in steady flow. The effect of pre-shock flow divergence/convergence, on vorticity generation, is related to the transverse shock curvature. A novel derivation for the post-shock vorticity is presented that includes the effects of pre-shock flow non-uniformities. CST applicability to unsteady flows is discussed.

Energy absorption of graded foam subjected to blast: A theoretical approach

Abstract Energy absorption of graded foam subjected to blast is investigated, in which the high velocity crushing of foam is modeled with shock theory and rigid-perfectly-plastic-locking idealization. The characteristics of a typical blast are taken into account when determining the foam density profile. Different from the homogeneous foam, the graded foam density variation is designed largest at the loading end and smallest at the supporting end, with an exponential decay in between. It is found that, subjected to the same blast load, the total input energy, in fact the energy to be dissipated by the cladding, decreases with increasing density gradient. The final foam deformation with larger density gradient is smaller.

U.S. college students’ lay theories of culture shock

As researchers strive to identify the components of effective preparation for study abroad, it is also critical to investigate the beliefs and expectations about intercultural adjustment that students bring to these interventions. A questionnaire assessed the structure and correlates of 149 U.S. undergraduate students’ lay theories of culture shock. Findings indicated that students tended to attribute culture shock to differences in the external environment, such as language, communication, and surroundings, rather than to internal affective or cognitive factors, such as poor stress management, identity confusion, or prejudice. The tendency to attribute culture shock to internal causes was greater for those with higher levels of cultural competence, whereas low travel experience and interest in foreign language learning predicted the tendency to attribute culture shock to external causes. These results are discussed in terms of implications for sojourner adjustment and intercultural training.

Strain rate effect on the out-of-plane dynamic compressive behavior of metallic honeycombs: Experiment and theory

Many studies reveal that the dynamic compressive strength of metallic honeycombs is higher than the quasi-static one, but the reasons for that are still debatable. This paper aims to study the strain rate effect of parent materials on the out-of-plane dynamic compressive behavior of metallic honeycombs. Quasi-static and dynamic tests on aluminum honeycombs were performed with universal testing machine and Split Hopkinson Pressure Bar, respectively. The velocity values of dynamic tests were from about 6 to 19m/s. The present and existing measures of plateau stress are evaluated by both the rate-independent (R-I) and rate-dependent (R-D) shock theories. It is shown that the R-D shock theory proposed in our previous study provides more accurate predictions at low, medium and high impact velocities. Based on the R-D shock theory, the influences of strain rate effect are analyzed quantitatively and the change tendencies of measured plateau stresses with impact velocities are explained reasonably. The analysis indicates that the strain rate effect has a large contribution to the dynamic enhancement of metallic honeycombs in a wide velocity range.

Optical observations of meteors generating infrasound: Weak shock theory and validation

AbstractWe have recorded a data set of 24 cm sized meteoroids detected simultaneously by video and infrasound to critically examine the ReVelle (1974) weak shock meteor infrasound model. We find that the effect of gravity wave perturbations to the wind field and updated absorption coefficients in the linear regime on the initial value of the blast radius (R0), which is the strongly nonlinear zone of shock propagation near the body and corresponds to energy deposition per path length, is relatively small (<10%). Using optical photometry for ground truth for energy deposition, we find that the ReVelle model accurately predicts blast radii from infrasound periods (τ) but systematically underpredicts R0 using pressure amplitude. If the weak shock to linear propagation distortion distance is adjusted as part of the modeling process, we are able to self‐consistently fit a single blast radius value for amplitude and period. In this case, the distortion distance is always much less (usually just a few percent) than the value of 10% assumed in the ReVelle model. Our study shows that fragmentation is an important process even for centimeter‐sized meteoroids, implying that R0, while a good measure of energy deposition by the meteoroid, is not a reliable means of obtaining the meteoroid mass. We derived an empirical period‐blast radius relation of the form R0 = 15.4τ − 0.5 (τ ≤ 0.7 s) and R0 = 29.1τ − 11.6 (τ > 0.7 s) appropriate to centimeter‐sized meteoroids. Our observations suggest that meteors having blast radii as small as 1 m are detectable infrasonically at the ground, an order of magnitude smaller than previously considered.

Financial Crises, Debt Financing, and Default Risks

We examine the mechanism through which a financial crisis affects the default risk of real economy firms. We find that firms with strong dependence on bank financing suffer from higher increases in default risk than firms with no such dependence. Conversely, firms that rely solely on financing from public debt markets do not experience significant increases in default risk. We also find that the increase in default probabilities, caused by a decrease in bank lending, is only significant for firms with low credit quality. These findings suggest that the bank supply shock theory helps explain the transmission channel of shocks from the financial sector to the real economy. Finally, firms dependent on bank financing cannot completely offset adverse impacts stemming from supply shocks in bank lending by substituting bank loans with publicly traded debt.

Strain Rate Effect on Mechanical Behavior of Metallic Honeycombs Under Out-of-Plane Dynamic Compression

Although many researches on the dynamic behavior of honeycombs have been reported, the strain rate effect of parent materials was frequently neglected, giving rise to the underestimated plateau stress and energy absorption (EA). In this paper, the strain rate effect of parent materials on the out-of-plane dynamic compression and EA of metallic honeycombs is evaluated by both numerical simulation and theoretical analysis. The numerical results show that the plateau stress and the EA increase significantly if the strain rate effect is considered. To account for the strain rate effect, a new theoretical model to evaluate the dynamic compressive plateau stress of metallic honeycombs is proposed by introducing the Cowper–Symonds relation into the shock theory. Predictions of the present model agree fairly well with the numerical results and existing experimental data. Based on the present model, the plateau stress is divided into three terms, namely static term, strain rate term, and inertia term, and thus the influences of each term can be analyzed quantitatively. According to the analysis, strain rate effect is much more important than inertia effect over a very wide range of impact velocity.

ACHANDRAOBSERVATION OF THE ECLIPSING WOLF-RAYET BINARY CQ Cep

The short-period (1.64 d) near-contact eclipsing WN6+O9 binary system CQ Cep provides an ideal laboratory for testing the predictions of X-ray colliding wind shock theory at close separation where the winds may not have reached terminal speeds before colliding. We present results of a Chandra X-ray observation of CQ Cep spanning ~1 day during which a simultaneous Chandra optical light curve was acquired. Our primary objective was to compare the observed X-ray properties with colliding wind shock theory, which predicts that the hottest shock plasma (T > 20 MK) will form on or near the line-of-centers between the stars. The X-ray spectrum is strikingly similar to apparently single WN6 stars such as WR 134 and spectral lines reveal plasma over a broad range of temperatures T ~ 4 - 40 MK. A deep optical eclipse was seen as the O star passed in front of the Wolf-Rayet star and we determine an orbital period P = 1.6412400 d. Somewhat surprisingly, no significant X-ray variability was detected. This implies that the hottest X-ray plasma is not confined to the region between the stars, at odds with the colliding wind picture and suggesting that other X-ray production mechanisms may be at work. Hydrodynamic simulations that account for such effects as radiative cooling and orbital motion will be needed to determine if the new Chandra results can be reconciled with the colliding wind picture.

Convex Entropy, Hopf Bifurcation, and Viscous and Inviscid Shock Stability

We consider by a combination of analytical and numerical techniques, some basic questions regarding the relations between inviscid and viscous stability and the existence of a convex entropy. Specifically, for a system possessing a convex entropy, in particular for the equations of gas dynamics with a convex equation of state, we ask: (1) can inviscid instability occur? (2) can viscous instability not detected by inviscid theory occur? (3) can there occur the—necessarily viscous—effect of Hopf bifurcation, or “galloping instability”? and, perhaps most important from a practical point of view, (4) as shock amplitude is increased from the (stable) weak-amplitude limit, can there occur a first transition from viscous stability to instability that is not detected by inviscid theory? We show that (1) does occur for strictly hyperbolic, genuinely nonlinear gas dynamics with certain convex equations of state, while (2) and (3) do occur for an artifically constructed system with convex viscosity-compatible entropy. We do not know of an example for which (4) occurs, leaving this as a key open question in viscous shock theory, related to the principal eigenvalue property of Sturm Liouville and related operators. In analogy with, and partly proceeding close to, the analysis of Smith on (non-)uniqueness of the Riemann problem, we obtain convenient criteria for shock (in)stability in the form of necessary and sufficient conditions on the equation of state.

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Theoretical Analysis on Thermal Shock Resistance of Refractories

So far, thermal shock theories have not been well verified in refractories. This paper compared hypothesis and failure mechanism of two typical thermal shock theories, analyzed the applications of two typical theories in refractories from working environment, failure process and microstructure differences. And thinks that the critical stress fracture theory is suitable for nearly ideal brittle refractory with ceramic bond and used in thermal shock extremely harsh environment; thermal shock damage theory suites to evaluate multiple loops thermal shock. Analyzed the factors influencing the thermal shock parameters, and discussed Ways to improve the thermal shock resistance of refractories from destructive force and resistive force of refractories. Conclusions are that choosing small swelling expansion rate and high thermal conductivity material, reducing the micro stress concentration and adding flexible phase, these three methods can be used to make refractories with good resistance to thermal shock.

Multidimensional ion-acoustic solitary waves and shocks in quantum plasmas

The nonlinear theory of two-dimensional ion-acoustic (IA) solitary waves and shocks (SWS) is revisited in a dissipative quantum plasma. The effects of dispersion, caused by the charge separation of electrons and ions and the quantum force associated with the Bohm potential for degenerate electrons, as well as, the dissipation due to the ion kinematic viscosity are considered. Using the reductive perturbation technique, a Kadomtsev–Petviashvili–Burgers (KPB)-type equation, which governs the evolution of small-amplitude SWS in quantum plasmas, is derived, and its different solutions are obtained and analyzed. It is shown that the KPB equation can admit either compressive or rarefactive SWS according to when H≶2/3, or the particle number density satisfies n0≷1.3×1031cm−3, where H is the ratio of the electron plasmon energy to the Fermi energy densities. Furthermore, the properties of large-amplitude stationary shocks are studied numerically in the case when the wave dispersion due to charge separation is negligible. It is also shown that a transition from monotonic to oscillatory shocks occurs by the effects of the quantum parameter H.

Novice Agriculture Teachers’ General Self Efficacy and Sense of Community Connectedness

The attrition rate for novice teachers can range between 20%-50% in the first five years. This problem has concerned researchers in school-based agricultural education because of the shortage of agriculture teachers and high demands of the job. Researchers narrowed down the reasons why teachers leave the profession including the role of self-efficacy. While self-efficacy of novice teachers in the classroom has been researched, general self-efficacy of novice teachers has not been examined. We investigated the influence of moving into a new community and adjusting to the new culture and social connections of the new community on the teacher’s self-efficacy. The purpose was to determine if culture shock and social connectedness explained general self-efficacy of novice agriculture teachers. It was concluded that the construct of core beliefs and how people react internally to their community within the culture shock theory significantly explained a proportion of the variance in general self-efficacy. The findings implied that the culture distance experienced by a novice teacher in a new community could affect their general well-being and ability to accomplish their goals.

Bank Supply Shocks and Default Risk

We examine the mechanism through which a financial crisis affects the default risk of real economy firms. Specifically, firms with strong dependence on bank financing suffer higher increases in default risk than firms with no such dependence. Conversely, firms relying solely on financing from public-debt markets do not experience significant increases in default risk. These findings suggest that the bank supply shock theory helps to understand the transmission channel of shocks from the financial sector to the real economy. Finally, bank-dependent firms cannot completely offset adverse impacts stemming from bank-lending supply shocks by substituting bank loans with publicly traded debts.

Mach reflection of cellular detonations

The present paper reports the results of an experimental study of the Mach reflection of cellular detonations. Mixtures representing regular smoked foil pattern (C2H2+2.5O2+70%Ar) and irregular pattern (C2H2+2.5O2, C3H8+5O2) are used in the experiments. The range of the initial pressures used is 3kPa<Po<20kPa which provide a range of cell sizes of the detonation front. Schlieren photographs as well as smoked foils are used to observe the phenomenon. Wedges of angles ranging from 10°<θ<40° are used. Measurement of the Mach stem height with distance traveled from schlieren photographs and smoked foils indicate that the triple point lies on a curved trajectory instead of a straight line from the wedge apex as obtained from self-similar three shock theory. This is due to the finite thickness of the detonation front presenting a characteristic length scale that renders the self-similar three shock theory invalid. Following the work of Hornung and Shepherd et al., the present results are analyzed according to the so called frozen and equilibrium limits. The results do seem to agree with the frozen limit for the initial propagation of the Mach stem near the apex of the wedge when the distance traveled by the Mach stem is small compared to the characteristic length of the detonation front (e.g. cell size “λ”, hydrodynamic thickness, etc.). In the asymptotic far field region when the distance traveled is large compared to the effective detonation thickness, the present results appear to approach the prediction using three shock theory based on a discontinuous detonation front. Thus in spite of the transient three dimensional structure of a cellular detonation front, the frozen and equilibrium limit concept based on a global quasi-steady reaction zone thickness of the detonation front appears to provide a useful scheme to interpret the results. Examination of the smoked foils indicate that the interaction of the transverse waves of cellular instability with the reflected shock and shear layer of the Mach reflection play an important role in the description of the triple point region.

Dynamic response of a cellular block with varying cross-section

In this paper, the plastic crushing response is studied for an aluminum foam block of varying cross-section under impact. The influence of the gradient on the cross-section is investigated. Based on the one-dimensional shock theory, an analytical model is proposed to investigate an impact scenario, in which a foam block with a gradient in its cross-section together with a rigid mass impinges onto a rigid target. Because of the change in the cross-sectional area along the length, two possible deformation modes may appear, namely the double shock mode and the single shock mode. When the largest cross-section is impinged, two compaction zones in the foam block are found, while only one compaction zone appears from the impinged end when the smallest cross-section is impinged. Of particular interests are the absorbed energy and the force transmitted to the target. The analysis reveals that the energy absorption capacity is weakened with a negative gradient while positive gradient has no influence on the energy absorption capacity of the graded foam.An experiment was then designed to investigate the behavior of the graded foam block under impact. The rigid mass together with the foam block was fired from a gas gun barrel, and its speed was measured before it collided onto the rigid target. The deformation history of the specimen was recorded by a high-speed video camera. Image analysis was employed to obtain the velocity of the impinging mass during the process. Observation of the deformation profile demonstrates the two basic deformation modes described in the analytical modeling.

Dynamics of multi layered fragment separation by explosion

Spatial dispersion of a Fragment Generator Warhead (FGW), in terms of projection angle and velocity, is essential to focus the maximum number of fragments on the target missile for effective neutralization. The authors carried out experiments to study the fragment dispersion in single, double and triple layered FGW configurations with tungsten alloy fragments. The projection angle and velocity are estimated by capturing the fragments in straw boards panel and correlating their position on the FGW. The paper presents the explanation of the phenomenon of fragment dispersion and deformation using one dimensional shock theory.

Investigation into the behavior of a graded cellular rod under impact

Over the past few decades, functionally graded materials (FGMs) have attracted many research interests. For the cellular material, the variation of the mechanical property may significantly influence the global performance of the structure. Previously the authors have presented the basic deformation patterns in a simple case, in which only the quasi-static plateaus stress gradually decreases or increases along the rod and the density is uniform. In the current study, further investigations are carried out into the effect of the gradient in the initial density, which inherently leads to variation in the quasi-static plateau stress. A simple impact scenario is considered, in which a rigid mass strikes a stationary cellular rod with variation in the initial density of the material. Similar to the previous studies, the rigid-perfectly plastic-locking (R-PP-L) material model and the simple shock theory are employed to carry out the analysis. Current study confirms that the basic deformation modes (i.e. double shock (DS) and single shock (SS) modes) still exist in the cellular rod with density gradient. The analytical results indicate that the negative gradient weakens the capacity of energy absorption while positive gradient has little influence. Then, the effect of the initial density gradient is further investigated by considering two artificial cases with only one gradient either in the quasi-static stress or in the initial density. Finally, finite element (FE) simulations are carried out with practical metal foam in order to verify the analytical modeling.