Off-center impact of an elastic column by a rigid mass

Based on the Timoshenko beam model the equations of motion are obtained for large deflection of off-center impact of a column by a rigid mass via Hamilton's principle. These are a set of coupled nonlinear partial differential equations. The Newmark time integration scheme and differential quadrature method are employed to convert the equations into a set of nonlinear algebraic equations for displacement components. The equations are solved numerically and the effects of weight and velocity of the rigid mass and also off-center distance on deformation of the column are studied.     

Damage resistance of carbon fibre reinforced epoxy laminates subjected to low velocity impact: Effects of laminate thickness and ply-stacking sequence

A major concern affecting the efficient use of composite laminates is the effect of low velocity impact damage on the structural integrity [1–3]. The aim of this study is to characterize and assess the effect of laminate thickness, ply-stacking sequence and scaling technique on the damage resistance of CFRP laminates subjected to low velocity impact. Drop-weight impact tests are carried out to determine impact response. Ultrasonic C-scanning and cross-sectional micrographs are examined to assess failure mechanisms of the different configurations.It is observed that damage resistance decreases as impact energy increases. In addition, thicker laminates show lower absorbed energy but, conversely, a more extensive delamination due to higher bending stiffness. Thinner laminates show higher failure depth. Furthermore, quasi-isotropic laminates show better performance in terms of damage resistance. Finally, the results obtained demonstrate that introducing ply clustering had a negative effect on the damage resistance and on the delamination area.     

Experimental characterization of dynamic behaviour of gelatin-based material using DIC

In this paper, the dynamic response of gelatin-based soft material under impact loading is investigated. The dynamic tests are principally performed by the classical SHPB (Split Hopkinson Pressure Bars) technique. However, due to the very low mechanical impedance of the specimen compared with the Hopkinson bars, the feeble impact forces are measured by highly sensitive piezoelectric polyvinylidene fluoride (PVDF) pressure sensors instead of SHPB measurement system. The PVDF pressure sensors are placed on the interfaces between the specimen and the bars. During the impact test, the non-equilibrium stress state and inhomogeneous strain fields are developed in the specimen; a digital image correlation (DIC) technique is proposed to identify the inhomogeneous displacement fields using high speed photography. A non-parametric approach based on the DIC technique is developed to deduce the transient stress fields in the longitudinal and transverse directions from the displacement fields measured by DIC. The validation of the calculated stress fields is performed by comparing them with the stress measurements from the PVDF pressure sensor at the bottom end of the specimen. Furthermore, stress-strain response is carried out using this approach throughout the specimen. It is clearly shown that the average highest strain rate varies with position in the specimen. This lead to multiple stress-strain relations determined at different strain rates by only one impact test. The significant strain rate sensitivity is observed at the tested rate range from 81/s to 269/s. Under compression loading, the axial stress state is developed as a simple compression only in the central part of the specimen due to the friction at the interfaces between the specimen and the bars. According to the calculated results based on movement of “long waves”, the region of the simple compression stress state in the central part of the specimen is localized. It is observed that the axial stress is much more important than the transverse stress in the central part and this confirms the assumption of uni-axial compression stress state in the specimen.     

An optimisation method for separating and rebuilding one-dimensional dispersive waves from multi-point measurements. Application to elastic or viscoelastic bars

When using a classical SHPB (split Hopkinson pressure bar) set-up, the useful measuring time is limited by the length of the bars, so that the maximum strain which can be measured in material testing applications is also limited. In this paper, a new method with no time limits is presented for measuring the force and displacement at any station on a bar from strain or velocity measurements performed at various places on the bar. The method takes the wave dispersion into account, as must inevitably be done when making long time measurements. It can be applied to one-dimensional and single-mode waves of all kinds propagating through a medium (flexural waves in beams, acoustic waves in wave guides, etc.). With bars of usual sizes, the measuring time can be up to 50 times longer than the time available with classical methods. An analysis of the sensitivity of the results to the accuracy of the experimental data and to the quality of the wave propagation modelling was also carried out. Experimental results are given which show the efficiency of the method.     

Modeling of terrain impact caused by tracked vehicles

Analytical models that can predict the terrain impact caused by tracked vehicles on a horizontal plane were developed and tested. The models included a disturbed width model and an impact severity model. Inputs of the terrain impact models included vehicle static properties, vehicle dynamic properties, and terrain properties. The tested vehicles included an M1A1 tank, an M577 Armored Personal Carrier (APC), and an M548 cargo carrier. The models were verified with field tests conducted in Yakima Training Center in Yakima, WA, Fort Riley, KS, and Camp Atterbury, Indiana. The average percentage errors of the disturbed width model for the M1A1, M577, and the M548 were 10.0%, 27.3%, and 8.5%, respectively. The average percentage errors of the impact severity model of the M1A1 and M577 were 25.0% and 21.4%, respectively.     

Effects of dry density and thickness of sandy soil on impact response due to rockfall

Sand cushions against impact force are widely used for rockfall prevention covers. The objective of this paper is to investigate the effects of the dry density and thickness of a sand cushion on an impact response due to a falling weight likened to a rockfall. A series of laboratory experiments for a decomposed granite soil was executed in the combination of the mass and drop height of the weight. As a result, the impact pressure applied to the soil surface increases with the dry density, but it does not depend on the thickness of the soil. The earth pressure at the bottom of the mold increases with the dry density, and it decreases with the thickness of the soil. Therefore, the transmissibility of the impact pressure decreases rapidly with the thickness of the soil.     

Friction oscillator excited by moving base and colliding with a rigid or deformable obstacle

The dynamics of non-smooth oscillators has not yet sufficiently been investigated, when damping is simultaneously due to friction and impact. Because of the theoretical and practical interest of this type of systems, an effort is made in this paper to lighten the behaviour of a single-degree-of-freedom oscillator colliding with an obstacle and excited by a moving base, which transfers energy to the system via friction. The different nature of discontinuities arising in the combined problem of friction and impact has been recognized and discussed. Closed-form solutions are presented for both transient and steady-state response, assuming Coulomb's friction law and a rigid stop-limiting motion. Furthermore, a deformable (hysteretic) obstacle has been considered, and its influence on the response has been investigated.     

Experimental analysis of the steady-state behaviour of beam systems with discontinuous support

This paper deals with the experimental analysis of the long-term behaviour of periodically excited linear beams supported by a one-sided spring or an elastic stop. Numerical analysis of the beams showed subharmonic, quasi-periodic and chaotic behaviour. Furthermore, in the beam system with the one-sided spring three different routes leading to chaos were found. Because of the relative simplicity of the beam systems and the variety of calculated nonlinear phenomena, experimental setups are made of the beam systems to verify the numerical results. The experimental results correspond very well with the numerical results as far as the subharmonic behaviour is concerned. Measured chaotic behaviour is proved to be chaotic by calculating Lyapunov exponents of experimental data.

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Sommario Il presente lavoro concerne l'analisi sperimentale del comportamento a regime di travi lineari, su supporti elastici nonlineari discontinui, eccitate periodicamente. L'analisi numerica dei sistemi in esame ha evidenziato risposte subarmoniche, quasi-periodiche e caotiche, nonchè l'esistenza, nel caso di trave con una molla laterale, di tre differenti percorsi verso il caos. La relativa semplicità dei sistemi di travi ha consentito di procedere ad una verifica sperimentale dei risultati numerici e della varietà dei fenomeni nonlineari da essi evidenziati. La corrispondenza fra risultati sperimentali e numerici è molto buona nel caso di risposta subarmonica. Il comportamento caotico sperimentale è stato convalidato attraverso il calcolo degli esponenti di Lyapunov a partire dai relativi dati.

     

Periodic sticking motion in a two-degree-of-freedom impact oscillator

Periodic sticking motions can occur in vibro-impact systems for certain parameter ranges. When the coefficient of restitution is low (or zero), the range of periodic sticking motions can become large. In this work the dynamics of periodic sticking orbits with both zero and non-zero coefficient of restitution are considered. The dynamics of the periodic orbit is simulated as the forcing frequency of the system is varied. In particular, the loci of Poincaré fixed points in the sticking plane are computed as the forcing frequency of the system is varied. For zero coefficient of restitution, the size of the sticking region for a particular choice of parameters appears to be maximized. We consider this idea by computing the sticking region for zero and non-zero coefficient of restitution values. It has been shown that periodic sticking orbits can bifurcate via the rising/multi-sliding bifurcation. In the final part of this paper, we describe three types of post-bifurcation behavior which occur for the zero coefficient of restitution case. This includes two types of rising bifurcation and a border orbit crossing event.