Post-impact State Research Articles

X-ray flux and spectral variability of the blazar OJ 287 with Suzaku

ABSTRACT We present analyses of Suzaku XIS light curves and spectra of the BL Lac object OJ 287 with observations positioned primarily around proposed recurrent optical outbursts. The first two observations were performed in 2007 April 10–13 (epoch 1) and 2007 November 7–9 (epoch 2) that, respectively, correspond to a low and a high optical state and which, within the binary supermassive black hole model for OJ 287, precede and follow the impact flare. The last three observations, made consecutively during 2015 May 3–9 (epoch 3), were during the post-impact state of the 2013 disc impact and are the longest continuous X-ray observation of OJ 287 taken before the optical outburst in 2015 December. Intraday variability is found in both the soft (0.5–2 keV) and hard (2–10 keV) bands. The discrete correction function analysis of the light curves in both bands peaks at zero lag during epochs 2 and 3, indicating that the emission in both bands was cospatial and emitted from the same population of leptons. Power spectral densities of all three light curves are red noise dominated, with a rather wide range of power spectrum slopes. These X-ray spectra are overall consistent with power laws but with significantly different spectral indices. In the 2015 observations the X-ray spectrum softens during the flare, showing an obvious soft X-ray excess that was not evident in the 2007 observations. We discuss the implications of these observations on the jet, the possible accretion disc, and the binary supermassive black hole model proposed for the nearly periodic optical flaring of OJ 287.

The Secular Dynamical Evolution of Binary Asteroid System (65803) Didymos Post-DART

The successful impact of NASA’s DART mission with Dimorphos, the secondary body of binary asteroid system (65803) Didymos, altered the attitude, shape, and orbit of Dimorphos. In addition to perturbing the immediate short-term dynamics of the system, these changes have major implications for the binary Yarkovsky–O’Keefe–Radzievskii–Paddack (BYORP) effect and resulting long-term secular evolution. In this study, we assess the range of possible reshaping-induced changes in BYORP. We produce high-fidelity numerical simulations of the orbit-attitude coupled tidal-BYORP dynamical evolution of the Didymos system to constrain how the secular evolution changed from its preimpact behavior. We find that the nature of the dynamics is highly dependent on a variety of initial conditions and assumptions, and it is difficult to fully predict how the system will secularly evolve following the impact. Rather, we provide a range of feasible possibilities within the bounds of observations and current best estimates of the Didymos system parameters. ESA’s Hera mission will help reduce uncertainties surrounding the postimpact state and shape of Dimorphos in 2027, allowing our predictions of the secular evolutionary effects and long-term fate of the Didymos system to be better refined.

A time-stepping method for multibody systems involving frictional impacts and phases with persistent contact

This work complements and continues efforts towards developing a complete numerical integration method for multibody dynamic systems with frictional impacts. Specifically, the new method is a time-stepping scheme, which is applicable to mechanical systems subject to a set of bilateral and a single unilateral motion constraint. During an impact free phase of the motion, a suitable augmented Lagrangian methodology is applied. When an impact is detected during a time step, the post-impact state is determined by employing a special process, which addresses properly the inherent numerical stiffness associated with the impact events. The basic contribution of the present study is the extension to cover cases where the contact between the interacting bodies is possible to exist for a finite period of time after an impact. This phenomenon occurs frequently in machines and mechanisms and is known as persistent contact. First, a complete strategy is developed for establishing a general numerical procedure for capturing and treating both activation of contact and loss of contact between two bodies. Then, the accuracy and efficiency of this procedure is tested and demonstrated by applying it to a selected set of mechanical examples.

A time-stepping method for multibody systems with frictional impacts based on a return map and boundary layer theory

This work presents a new numerical integration method for determining dynamics of a class of multibody systems involving impact and friction. Specifically, these systems are subject to a set of equality constraints and can exhibit single frictional impact events. Such events are associated to significant numerical stiffness, appearing in the equations of motion. The new method is a time-stepping scheme, involving proper incorporation of a novel return mapping into an augmented Lagrangian formulation, developed recently for systems with bilateral constraints only. Namely, when an impact is detected during a time step, this map is applied at the end of the step in order to bring the system position back to the configuration manifold with the allowable motions. The construction of this map is based on the concept of Jacobi fields on non-flat manifolds. Moreover, once an impact event is detected, the post-impact state is determined by employing a combination of analytical and numerical tools. First, a proper coordinate transformation is performed, bringing the system into a new set of coordinates, which are suitable for describing the impact dynamics. In these coordinates, the dominant dynamics is described by a system of three equations of motion only, which are valid during the short contact interval. In addition, these equations are geometrically discretized by using appropriate cubic splines on the configuration manifold. In this way, the inherent numerical stiffness of the class of systems examined is properly addressed, since it is restricted to a space with a much smaller dimension and a much shorter time scale. Finally, the accuracy and efficiency of the new method is demonstrated by applying it to a selected set of mechanical examples.

A novel return map in non-flat configuration spaces οf multibody systems with impact

This work presents a new return mapping, which can be an essential part in the numerical integration of the equations of motion of multibody systems involving impact events. For such systems, each unilateral constraint introduces a boundary hypersurface within the original configuration manifold, restricting the allowable motions on one side of this hypersurface only. When an impact is detected during a step of a time-stepping integration scheme, the position of the system may escape from the allowable range temporarily. Then, this return map is applied at the end of this step in order to bring the system position back to the constrained configuration manifold. The novelty of the new map is related to the fact that both the original and the constrained configuration manifolds of the class of systems examined are non-Euclidean. Its construction and application is based on geometric properties of Jacobi fields on a manifold, specialized for Lie groups. Specifically, once an impact is detected numerically, a sequence of appropriate projections is performed up until the converged position is located within the constrained manifold. Then, if the final position is sufficiently close to the boundary of this manifold and the generalized velocity has a direction pointing towards this boundary, the position and the velocity determined are considered to represent the pre-impact state of the system, which can be used to predict its post-impact state. Finally, the accuracy and efficiency of the new method is demonstrated by applying it to a selected set of mechanical examples.

Perforation of needle-punched carbon-carbon composites during high-temperature and high-velocity ballistic impacts

Thermal protection systems (TPS) used in spacecraft are likely to be subjected to hypervelocity impacts with debris at the reentry stage. The resultant ultra-high heat flow may damage the payload inside the impacted vehicle. Carbon fiber-reinforced carbon matrix composites are promising materials for TPS, however they have not been extensively evaluated in terms of crashworthiness at high velocities and temperatures. This work describes the impact resistance of 3D needle-punched carbon-carbon (NP-C/C) composites using both numerical and experimental methods. A multiscale-based model has been developed to predict the ballistic limit of NP-C/C composites. Impact experiments have been performed with a custom-made two-stage light gas gun system at 1200 °C and also higher temperatures. The test results have been used to validate the post-impact state of the targets obtained from the proposed model. The ballistic limits of the NP-C/C composites have also been identified as functions of the impact velocity, the impactor diameter and the target thickness. The predictions are in good agreement with the experimental data. Low-thickness NP-C/C laminates show similar absorbed energies per unit weight exhibited by same-dimension Inconel panels tested under comparable temperature and speed impacts, although the NP-C/C composites weight 4.4 times less than the analogous metallic panels.

Nonsmooth dynamic analysis of sticking impacts in rocking structures

This paper revisits from a nonsmooth dynamics perspective the contact process encountered in two archetypal rocking structures: the rigid rocking block and the flexible rocking oscillator. The analysis assumes impact is an instantaneous (unilateral) contact, and models the behavior along the normal direction with a set-valued Newton’s law. In the tangential direction it assumes that sliding is prevented. The study formulates both impact and uplifting phenomena as linear complementarity problems (LCPs). The proposed LCP formulation encapsulates all post-impact states and liberates from the need for additional ad-hoc assumptions. The results show that the proposed nonsmooth approach verifies the corresponding results of other studies with reference to the rigid rocking block. Focusing on the flexible rocking oscillator, the proposed model is compared with pertinent analytical, numerical and experimental results from literature. The present study offers original analytical solutions describing all physically feasible post-impact states and confirms, as a special case, existing solutions of rocking initiation. Importantly, the analysis unveils that a given rocking oscillator might choose a different post-impact state (e.g. bouncing, full contact, or immediate rocking) depending on its flexural deformation at the time of impact. Further, it shows that in the case of immediate rocking after impact, the post-impact flexural velocity of the rocking oscillator is not equal with its pre-impact value. The results also reveal the dominant role of the assumed value of the Newton’s coefficient of restitution on the response-history of the rocking oscillator.

A Multi-Level Decision Fusion Strategy for Condition Based Maintenance of Composite Structures.

In this work, a multi-level decision fusion strategy is proposed which weighs the Value of Information (VoI) against the intended functions of a Structural Health Monitoring (SHM) system. This paper presents a multi-level approach for three different maintenance strategies in which the performance of the SHM systems is evaluated against its intended functions. Level 1 diagnosis results in damage existence with minimum sensors covering a large area by finding the maximum energy difference for the guided waves propagating in pristine structure and the post-impact state; Level 2 diagnosis provides damage detection and approximate localization using an approach based on Electro-Mechanical Impedance (EMI) measures, while Level 3 characterizes damage (exact location and size) in addition to its detection by utilising a Weighted Energy Arrival Method (WEAM). The proposed multi-level strategy is verified and validated experimentally by detection of Barely Visible Impact Damage (BVID) on a curved composite fuselage panel.

Nonsmooth analysis of the impact between successive skew bridge-segments

Skew bridges with in-deck joints belong to the most common types of existing bridges worldwide. Empirical evidence from past earthquakes indicates that such, multi-segment, skew bridges often rotate in the horizontal plane, increasing the chances of deck unseating. The present paper studies the oblique in-deck impact between successive bridge segments, which triggers this peculiar rotation mechanism. The analysis employs a nonsmooth rigid body approach and utilizes set-valued force laws. A key feature of this approach is the linear complementarity problem (LCP) which encapsulates all physically feasible post-impact states. The LCP results in pertinent closed-form solutions which capture each of these states, and clarifies the conditions under which each post-impact state appears. In this context, a rational method to avoid the singularities arising from dependent constraints is coined. The results confirm theoretically the observed tendency of skew (bridge deck) segments to bind in their obtuse corners and rotate in such a way that the skew angle increases. Further, the study offers equations which describe the contact kinematics between two adjacent skew planar rigid bodies. The same equations can be used to treat successively as many pairs of skew bridge-segments as necessary.

Energy evolution in complex impacts with friction

In this paper, we base a theory established in an impulse-energy level to solve a problem of a disk-ball system, in which a moving ball collides perpendicularly against an disk staying on a horizontal surface. The impact process is an ensemble consisting of a point impact coupled with a line contact between bodies of the disk, the ball and the fixed horizontal surface. We experimentally and theoretically show that the post-impact states of the disk dramatically vary with the impacting position of the ball. Explanations are given by investigating the evolutions of the potential energies resided in the points involved in the complex frictional impacts. Good agreements between numerical and experimental results strongly suggest that the evolution of energy together with the dissipation must be reflected in mathematical models if a precise description for the post-impact state of systems is expected.

Energetic consistency conditions for standard impacts

The paper studies the conditions under which Newtonian impacts lead to an energetically consistent post-impact state, and identifies the mechanisms responsible for a potential violation. Unilateral and bilateral geometric and kinematic constraints, as well as various Coulomb type friction elements are equipped with a kinematic restitution coefficient and are taken into account in the impact problem as normal cone inclusions. Based on the condition number of the Delassus operator, bounds on the impact coefficients are derived that ensure energetic consistency. As counter-examples, a slide-push mechanism is presented, and Kane’s example of a frictional impact at a double pendulum is analyzed.

Dynamic analysis of impact in swing-through crutch gait using impulsive and continuous contact models

The dynamics associated with the impact of the crutch with the ground is an important topic of research, since this is known to be the main cause of mechanical energy loss during swing-through gait. In this work, a multibody system representing a subject walking with crutches is used to investigate the behavior of two different contact models, impulsive and continuous, used for impact analysis. In the impulsive (discrete) approach, the impact interval is considered to be negligible and, therefore, the system configuration is constant. The postimpact state is directly obtained from the preimpact one through algebraic equations. In the continuous approach, the stiffness and dissipation characteristics of the contact surfaces are modeled through nonlinear springs and dampers. The equations of motion are integrated during the impact time interval to obtain the postimpact state, which, in principle, can differ from that obtained by means of the impulsive approach. Although both approaches have been widely used in the field of biomechanics, we have not found any comparative study in the existing literature justifying the model chosen for impact analysis. In this work, we present detailed numerical results and discussions to investigate several dynamic and energetic features associated with crutch impact. Based on the results, we compare the implications of using one contact model or the other.

Dynamics of an oblique-impact vibrating system of two degrees of freedom

The dynamic analysis of oblique-impact vibration is presented in this paper through an illustrative system, where a spring–pendulum obliquely collides a mass–spring oscillator. The oblique-impact process and the relations between the pre-impact state and the post-impact state of system are analyzed first upon a hypothesis on instantaneous oblique impacts. On the basis of the oblique-impact relations, then, the dynamic equation of such an oblique-impact vibrating system is established. Consequently, the existence and the stability of the periodic motions are analyzed and a series of analytical solutions are derived in some simplified cases. Afterwards, the transitions of the steady state motions of the system with the variation of the excitation, the damping and the contact–friction are numerically studied in general cases. The study shows that the coefficient of restitution for an oblique-impact cannot be regarded as a constant, and that the relations between the pre-impact state and the post-impact state are directly associated with the impact angle and the coefficient of contact–friction between impacting bodies. For the system of concern, the system parameters and initial states have to be carefully selected if any stable periodic motion is expected. Furthermore, very rich dynamic behaviors, such as bifurcations and chaotic motions, are observed in the numerical results.

Experimental head injury and concussion: morphologic changes and pathophysiologic responses following translational acceleration in primates (author's transl)

Translational acceleration impact was applied to elicit cerebral concussion and contusion in subhuman primates (12 Japanese monkeys and 2 baboons) using a HYGE sled and a slider-impactor system. All animals were concussed more than 15 seconds by force ranging from 240 to 960 G (duration; 17.5-3.5 msec.) in average head accelerations. Five monkeys among 8 with frontal impact died within 27 minutes. This well correlated with thoracic trauma, including rib fracture and small mediastinal hemorrhage. Only one animal (baboon) among 6 with occipital impact died immediately and the cerebro-spinal junction was found traumatically severed. Bradycardia, apnea, systemic hypotension and depression of EEG activity occurred immediately after impact in every animal. No visible intracranial pathology, such as brain contusion, subdural hematoma, or intracerebral hematoma was noticed. Microscopic examination revealed central chromatolysis of nerve cells and degeneration of Purkinje cells. However, these findings did not correlate with the post-impact state of the animals nor with biomechanical data. Our experiment suggests that translational acceleration impact to the brain does not usually cause gross morphological changes. Secondly, the so-called brain concussion might be the result of the cumulative effect of, 1) transient medullary paralysis, 2) cardio-respiratory depression of cervical cord origin, as well as, 3) cardiocirculatory insufficiency due to thoracic impact (primary shock). If severe, these factors would generate a vicious cycle to lead to a state of circulatory catastrophe which ends in death only.