A general mathematical model for the collision between a free-fall hammer of a pile-driver and an elastic pile: Continuous dependence and low-frequency asymptotic expansion

Lê, Út V.

doi:10.1016/j.nonrwa.2010.07.012

Cited by 4 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Among these, we find nail hammering [1,2] or pile driving [3][4][5]. Another such process is down-the-hole percussive drilling, where penetration is achieved by repeated application of a large impulsive force to a rock drill bit [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A drifting impact oscillator with periodic impulsive loading: Application to percussive drilling

Depouhon

Denoël

Detournay

2013

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

Percussive drilling is extensively used to drill hard rocks in the earth resource industry, where it performs best compared to other drilling technologies. In this paper, we propose a novel model of the process that consists of a drifting oscillator under impulsive loading coupled with a bilinear force/penetration interface law, together with a kinetic energy threshold for continuous bit penetration. Following the formulation of the model, we analyze its steady-state response and show that there exists a parallel between theoretical and experimental predictions, as both exhibit a maximum of the average penetration rate with respect to the vertical load on bit. In addition, existence of complex long-term dynamics with the coexistence of periodic solutions in certain parameter ranges is demonstrated.

show abstract

Section: Introductionmentioning

confidence: 99%

A drifting impact oscillator with periodic impulsive loading: Application to percussive drilling

Depouhon

Denoël

Detournay

2013

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

show abstract

“…One of the two oscillators connected to an excitation system intermittently impacts with an obstacle fixed on the thick steel wall associated with different gap sizes. Along with the requirement of engineering application and the increasing thorough of basic research on nonsmooth dynamics, vibro-impact dynamics has been applied to a wide range of practical mechanical systems for finding the correlative relationship between dynamic performance and model parameters, such as wheel-rail impacts of railway coaches [56,57], vibrating hammer [58], pile driver [59,60], ground moling dynamics [61], fly-wheel model of the bouncing ball [62], link mechanism [63], ultrasonic percussive drilling [64,65], vibro-impact capsule system [66], pressure relief valve [48], Jeffcott rotors with bearing clearance [67][68][69], impact dampers [70,71], excited pendula with impacts [72], vibro-impact drilling [73], gears [36][37][38][74][75][76][77]. The dynamical models designed in Refs.…”

Section: Introductionmentioning

confidence: 99%

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

et al. 2014

View full text Add to dashboard Cite

A two-degree-of-freedom periodically forced system with a clearance is considered. The correlative relationship and matching law between dynamics and system parameters are analyzed by the co-simulation analysis of multi-parameter and multiperformance. Key parameters of the system, such as the exciting frequency, clearance value and constraint stiffness, are emphasized to analyze the influence of the main factors on its soft impact characteristics and reveal diversity, evolution and distribution regions of periodic-impact motions. The quantity of the fundamental group of p/1 impact motions, which have the excitation period and differ by the number p of impacts, is basically determined by the constraint stiffness. A series of grazing bifurcations occur with decreasing the exciting frequency so that the number p of impacts of the fundamental group of motions correspondingly increases one by one. As the constraint stiffness is very large, the impact number p of the fundamental group of motions becomes also big enough in low exciting frequency range. Consequently, the system possibly exhibits chattering-impact characteristics and the relative impact velocities successively attenuate in an excitation period. There exist a series of singular points between any two adjacent ones of the fundamental group of motions as the damping ratio or the damping constant of the viscous dashpot connecting two masses is very small, i.e., real-grazing and baregrazing bifurcation boundaries of one of them, saddlenode and period-doubling bifurcation boundaries of the other mutually cross themselves at the point of intersection and create two types of transition regions: hysteresis and tongue-shaped regions. A series of zones of regular and complex subharmonic impact motions are found to dominate in the tongue-shaped regions. The dimensionless parameters have been designed technically, under which large mass ratio or small supporting stiffness ratio leads to diversity and complexity of periodic-impact motions of the system. Based on the sampling ranges of parameters, the influence of system parameters on relative impact velocities, existence regions and correlative distribution of different types of periodic-impact motions of the system is emphatically studied.

show abstract

Vibro-impact dynamics of a two-degree-of freedom periodically-forced system with a clearance: Diversity and parameter matching of periodic-impact motions

Luo

Shi

2014

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

A two-degree-of-freedom system with a clearance and subjected to harmonic excitation is considered. The correlative relationship and matching law between dynamic performance and system parameters are studied by multi-parameter and multi-performance co-simulation analysis. Two key parameters of the system, the exciting frequency ω and clearance δ, are emphasized to reveal the influence of the main factors on dynamic performance of the system. Diversity and evolution of periodic impact motions are analyzed. The fundamental group of impact motions is defined, which have the period of exciting force and differ by the numbers p and q of impacts occurring at the left and right constraints of the clearance. The occurrence mechanism of chattering-impact vibration of the system is studied. As the clearance δ is small or small enough, the transition from 1-p-p to 1-(pþ1)-( pþ1) motion (the fundamental group of motions, pZ1) basically goes through the processes as follows: pitchfork bifurcation of symmetric 1-p-p motion, period-doubling bifurcation of asymmetric 1-p-p motion, non-periodic or chaotic motions caused by a succession of period-doubling bifurcations, symmetric 1-(pþ1)-(pþ1) motion generated by a degeneration of chaos. As for slightly large clearance, a series of grazing bifurcations of periodic symmetrical impact motions occur with decreasing the exciting frequency so that the number p of impacts of the fundamental group of motions increases two by two. As p becomes big enough, the incomplete chattering-impact motion will appear which exhibits a chattering sequence in an excitation period followed by a finite sequence of impacts with successively reduced velocity and reaches the non-sticking region. Finally, the complete chattering-impact motion with sticking will occur with decreasing the exciting frequency ω up to the sliding bifurcation boundary. A series of singular points on the boundaries between existence regions of any adjacent symmetrical impact motions with fundamental period are found, i.e., two different saddle-node bifurcation boundaries of one of them, real-grazing and bare-grazing bifurcation boundaries of the other alternately and mutually cross themselves at the points of intersection and create inevitably two types of transition regions: narrow hysteresis and small tongue-shaped regions. A series of zones of regular periodic and subharmonic impact motions are found to exist in the tongue-shaped regions. Based on the sampling ranges of parameters, the influence of dynamic parameters on impact velocities, existence regions and correlative distribution of different types of periodic-impact motions of the system is emphatically analyzed.

show abstract

A general mathematical model for the collision between a free-fall hammer of a pile-driver and an elastic pile: Continuous dependence and low-frequency asymptotic expansion

Cited by 4 publications

References 12 publications

A drifting impact oscillator with periodic impulsive loading: Application to percussive drilling

A drifting impact oscillator with periodic impulsive loading: Application to percussive drilling

Diversity evolution and parameter matching of periodic-impact motions of a periodically forced system with a clearance

Vibro-impact dynamics of a two-degree-of freedom periodically-forced system with a clearance: Diversity and parameter matching of periodic-impact motions

Contact Info

Product

Resources

About