Hopf-flip bifurcations of vibratory systems with impacts

Two vibro-impact systems are considered. The period n single-impact motions and Poincaré maps of the vibro-impact systems are derived analytically. Stability and local bifurcations of single-impact periodic motions are analyzed by using the Poincaré maps. A center manifold theorem technique is applied to reduce the Poincaré map to a three-dimensional one, and the normal form map associated with Hopf-flip bifurcation is obtained. It is found that near the point of codim 2 bifurcation there exists not only Hopf bifurcation of period one single-impact motion, but also Hopf bifurcation of period two double-impact motion. Period doubling bifurcation of period one single-impact motion is commonly existent near the point of codim 2 bifurcation. However, no period doubling cascade emerges due to change of the type of period two fixed points and occurrence of Hopf bifurcation associated with period two fixed points. The results from simulation shows that there exists an interest torus doubling bifurcation occurring near the value of Hopf-flip bifurcation. The torus doubling bifurcation makes the quasi-periodic attractor associated with period one single-impact motion transit to the other quasi-periodic attractor represented by two attracting closed circles. The torus bifurcation is qualitatively different from the typical torus doubling bifurcation occurring in the vibro-impact systems.     

Heavy ion induced cluster formation and fragmentation phenomena in amorphous graphite

A study has been conducted into the mechanisms of evolution of clusters and their subsequent fragmentation under energetic heavy ion bombardment of amorphous graphite. The evolving clusters and their subsequent fragmentation under continuing ion bombardment are revealed by detecting various clusters in the energy spectra of the Direct Recoils (DRs) emitted as a result of collisions between ions and surface constituents. The successive DR spectra reveal that the energetics of bond formation as well as any subsequent fragmentation can be related to the processes of energy dissipation in a cylindrical volume of a few ? surrounding the ion path. The dependence of formation or fragmentation is seen to be a function of the ionic stopping powers in this cylindrical volume. Received: 2 January 1998 / Accepted: 5 March 1998     

Particle impact on metal substrates with application to foreign object damage to aircraft engines

Foreign object damage (FOD) occurs when hard, millimeter-sized objects such as gravel or sand are ingested into aircraft jet engines. Particles impacting turbine blades at velocities up to about 300 m/s produce small indentation craters which can become sites for fatigue crack initiation, severely limiting the lifetime of the blade. A framework for analyzing FOD and its effect on fatigue cracking is established in this paper. Finite element analysis is used to determine the residual stresses and geometric stress concentration resulting from FOD. The roles of material rate sensitivity and inertia are delineated. The most important non-dimensional parameters governing impact indents are identified, significantly reducing the set of independent parameters. The second step in the analysis focuses on the potency of cracks emerging from critical locations at the indents. The results have been used to address the question: When and to what extent do the residual stresses and stress concentration caused by FOD reduce the critical crack size associated with threshold fatigue crack growth? For deep indents, it is found that elastic stress concentration is the dominant factor in reducing critical crack threshold when the applied cyclic load ratio, R, is large, otherwise the residual stresses are also important. Comparisons with a set of experiments conducted in parallel with the theory show that the numerical approach can account for various phenomena observed in practice.     

Modelling of Ground Moling Dynamics by an Impact Oscillator with a Frictional Slider

This paper describes current research into the mathematical modelling of a vibro-impact ground moling system. Due to the structural complexity of such systems, in the first instance the dynamic response of an idealised impact oscillator is investigated. The model is comprised of an harmonically excited mass simulating the penetrating part of the mole and a visco-elastic slider, which represents the soil resistance. The model has been mathematically formulated and the equations of motion have been developed. A typical nonlinear dynamic analysis reveals a complex behaviour ranging from periodic to chaotic motion. It was found out that the maximum progression coincides with the end of the periodic regime.     

Soil stress distribution related to neutralizing antipersonnel landmines from human locomotion and impact mechanisms

Soil stress distribution was investigated to understand and to develop means for detonating or neutralizing antipersonnel landmines. Specifically, the loading patterns within the soil attributable to the human gait, as well as those derived from a mechanism that delivers an impact load that is being developed for neutralizing antipersonnel landmines, were studied. Experiments were conducted in the soil bin facilities in the Department of Agricultural and Bioresource Engineering at the University of Saskatchewan. Both load cells and mechanically reproduced devices (MRDs), buried at depths of 50, 100, 150 and 200 mm, were used to measure the transmitted forces through the soil. The load cells provided measurements of the temporal load patterns as transferred through the soil, whereas the MRDs indicated the ability for the person or mechanism to successfully trigger a typical antipersonnel landmine. Both forces and impulses based on the load cell data were used as measures for comparison. The key results of the investigation showed human locomotion imparted a load of longer duration than did the impact from the mechanical device; the corresponding soil stresses increased with increasing human weight and impact loads; and forces in the soil increased with higher initial soil compaction level.     

Shock and shear initiation of explosive

Three reaction-rate models, Forest Fire, Arrhenius and a combined Forest Fire and Arrhenius, are incorporated in the hydrocode DEFEL. Simulations with this code for PBX-9404 explosive for bare and covered explosives by fragment impact are made. Results confirm the well-known shock-initiation theory for bare explosives. For explosives with a thick cover plate, code results show macroscopic shear initiation, as proposed by Howe (1985) and Frey (1981).This article was processed using Springer-Verlag TEX Shock Waves macro package 1990.     

Experimental study of an impact oscillator with viscoelastic and Hertzian contact

Modeling an impact event is often related to the desired outcome of an impact oscillator study. If the only intent is to study the dynamic behavior of the system, numerous researchers have shown that simpler impact models will often suffice. However, when the geometric contours and material properties of the two colliding surfaces are known, it is often of interest to model the contact event at a greater level of complexity. This paper investigates the application of a finite time impact model to the study of a parametrically excited planar pendulum subjected to a motion-dependent discontinuity. Experimental and numerical studies demonstrate the presence of multiple periodic attractors, subharmonics, quasi-periodic motions, and chaotic oscillations.     

Experiments on a beam-rigid body structure repetitively impacting a rod

This paper investigates the experimental dynamics of a beam structure that supports an attached rigid body and that can impact a comparatively compliant base structure. The problem area is motivated by impact phenomena that are observed in certain structures internal to nuclear reactors. The assembly is subjected to base excitation at specified frequency and acceleration, and the resulting displacement and velocity time histories are recorded and used to obtain spectra, phase diagrams, and Poincaré sections. The measurements validate simulation results obtained by using a constraint and modal mapping method based on the two sets of modes when the structure is in-contact, and when it is not-in-contact. Generalized coordinates are mapped across the impact discontinuities in the modal representation. The forced response simulation predicts the test specimen’s response over a range of excitation frequencies. The specimens are fabricated as single integral structures from acrylnitrile butadene styrene plastic through rapid prototyping technology in order to eliminate the undesirable dissipation and flexibility arising from joints and connections. The experimental system can exhibit complex response characteristics, and the influences on complexity of deadband clearance and of asymmetry in the point of impact are examined in the experiments.     

圆柱壳撞水时的弹塑性动力屈曲研究

本文研究圆柱壳在流固中冲击载荷下的弹塑性动力曲问题。建立了液体－气体－固体三相的数学模型。其中结构部分控制方程由弹塑性力学中关于加速度的最小原理获得，本构关系采用增量理论，液体假设为不可压缩，空气层认为最等熵压缩。分别讨论了不同冲击高度时压力变化规律，屈曲对载荷的影响。屈曲沿壳长的分布及发展规律等。