Dynamic stability of bombs and projectiles

The four chapters comprising pages 1 to 123, inclusive, report were previously released in limited distribution with desigtions and dates as follows: Chapter I, CIT/JPC 4, January 2, 1943 Chapter II, CIT/JPC 5, January 2, 1943 Chapter III, CIT/JPC 6, January 2, 1943 Chapter IV, CIT/JPC 11, May 26, 1943 Chapters I and II were prepared as of July 1, 1942, Chapter III as of, September 1, 1942, and Chapter IV as of the publication date. The text is herewith reproduced from the original vellum copy by the photo-offset process, with mathematical notation in the author's hand. The references listed at the end of Chapter IV were originally contained in CIT/JPC 11 and since this list includes all references cited in JPC 4, 5, and 6, the lists originally contained in these reports are here omitted. The study as planned was intended to cover all aspects of the dynamic stability problems involved in solids moving through fluids. The chapters contained herein only partially cover the general subject. The results presented are immediately applicable to the ballistics of aerial bombs or the air trajectory of torpedoes. They also apply to the underwater ballistics of depth bombs and the underwater behavior of torpedoes in that phase of the trajectory where cavitation is absent

Nanoscale buckling deformation in layered copolymer materials

In layered materials, a common mode of deformation involves buckling of the layers under tensile deformation in the direction perpendicular to the layers. The instability mechanism, which operates in elastic materials from geological to nanometer scales, involves the elastic contrast between different layers. In a regular stacking of "hard" and "soft" layers, the tensile stress is first accommodated by a large deformation of the soft layers. The inhibited Poisson contraction results in a compressive stress in the direction transverse to the tensile deformation axis. The hard layers sustain this transverse compression until buckling takes place and results in an undulated structure. Using molecular simulations, we demonstrate this scenario for a material made of triblock copolymers. The buckling deformation is observed to take place at the nanoscale, at a wavelength that depends on strain rate. In contrast to what is commonly assumed, the wavelength of the undulation is not determined by defects in the microstructure. Rather, it results from kinetic effects, with a competition between the rate of strain and the growth rate of the instability. http://www.pnas.org/content/early/2011/12/23/1111367109.abstrac

Unfolding the Sulcus

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, sub-critical {\em nonlinear} instability. In contrast with classical nucleation, sulcification is {\em continuous}, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasi-statically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with {\em no} energy barrier. Simple experiments confirm the existence of these two critical strains.Comment: Main text with supporting appendix. Revised to agree with published version. New result in the Supplementary Informatio

Enhacement in the dymanic response of a viscoelastic fluid flowing through a longitudinally vibrating tube

We analyzed effects of elasticity on the dynamics of fluids in porous media by studying a flow of a Maxwell fluid in a tube, which oscillates longitudinally and is subject to oscillatory pressure gradient. The present study investigates novelties brought about into the classic Biot's theory of propagation of elastic waves in a fluid-saturated porous solid by inclusion of non-Newtonian effects that are important, for example, for hydrocarbons. Using the time Fourier transform and transforming the problem into the frequency domain, we calculated: (A) the dynamic permeability and (B) the function $F(\kappa)$ that measures the deviation from Poiseuille flow friction as a function of frequency parameter $\kappa$. This provides a more complete theory of flow of Maxwell fluid through the longitudinally oscillating cylindrical tube with the oscillating pressure gradient, which has important practical applications. This study has clearly shown transition from dissipative to elastic regime in which sharp enhancements (resonances) of the flow are found

Aerodynamic Theory of the Oscillating Wing of Finite Span

The theory of the oscillating airfoil of infinite span with two-dimensional flow has been developed to a high degree of completeness (ref. 4, 7) In the present theory the oscillating airfoil of finite span is considered with the purpose of introducing the effect, of the trailing vortices and the three dimensional characters of the velocity field, on the aerodynamics forces. General formulae are established for the lift and moment on an elliptic airfoil oscillating in both translation and rotation and the numerical results are presented in tabular and graphical form

Mechanism of Deep-focus Earthquakes Anomalous Statistics

Analyzing the NEIC-data we have shown that the spatial deep-focus earthquake distribution in the Earth interior over the 1993-2006 is characterized by the clearly defined periodical fine discrete structure with period L=50 km, which is solely generated by earthquakes with magnitude M 3.9 to 5.3 and only on the convergent boundary of plates. To describe the formation of this structure we used the model of complex systems by A. Volynskii and S. Bazhenov. The key property of this model consists in the presence of a rigid coating on a soft substratum. It is shown that in subduction processes the role of a rigid coating plays the slab substance (lithosphere) and the upper mantle acts as a soft substratum. Within the framework of this model we have obtained the estimation of average values of stress in the upper mantle and Young's modulus for the oceanic slab (lithosphere) and upper mantle.Comment: 9 pages, 7 figure