•We proposed a critical contact depth, below which the Hertzian contact relationship applies (shallow impact), and above which Conway’s contact relationship applies (deep impact).•Two impact models ...were derived using homotopy analysis method.•The energy loss due to the flexural wave on coated plate is proportional to the impact velocity to the power of 1/3.
Impacting the coated plate induces flexural waves on the plate, and such dynamic effect can be considered in the Zener model, which couples the vibration of plate with Hertzian contact relationship. However, Zener model is not applicable for deep impact δm>δcr on a coated plate, because the Hertzian contact law requires an assumption that the contact depth cannot be larger than few percent of the film thickness. This assumption renders the Zener model invalid for the deep impact δm>δcr on plate coated with thin film, where high impact velocity may induce deep contact. In this study, we built up a control equation for the deep impact δm>δcr problem of sphere on the plate coated with soft film, where a nonlinear contact relationship different from Hertzian should be used. Then, we obtained an analytical solution by solving the control equation with homotopy analysis method (HAM). Using the analytical solution, we obtained an explicit expression for the contact history of sphere, as well as the vibration history of plate, which enables us to obtain the minimum distance between the impact location and the boundary applicable to the present model and Zener model. What is more, we proposed a model for a critical impact velocity, below which Zener’s model applies, and above which the present model does. By comparing with experiments with coated plate in the literature, we found that most experiments should use the present model rather than Zener model.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
The lateral impact between elastic cylinders is studied using two dynamic models. We propose an elementary example to justify the mechanical energy dissipation in a pure elastic contact and to define ...the parameters needed for its quantification. A finite element model is presented as the theoretical basis for the quantification of the mechanical energy dissipation produced by the propagation of elastic waves in continuous deformable impacting cylinders. The results are exploited to build an accurate and more numerically efficient dynamic lumped parameter model. The models are applied to the lateral impact of identical cylinders with various diameters and different impact speeds. The impact of the cylinders with a different mass and radius is also analyzed. The calculation of the coefficient of dissipation enables the global loss of mechanical energy to be quantified, and an equivalent damping ratio associated with the impact is calculated. The obtained damping values can be used as a reasonable underestimate of the dissipation produced in the engagement of spur gears, thus allowing a conservative prediction of the dynamic overloads of the system in resonant conditions.
•The lateral impact of elastic cylinders is studied using two dynamic models.•A novel lumped parameter dynamic model is proposed.•The impact of cylinders with identical and different diameter is considered.•The coefficient of dissipation is obtained to quantify the mechanical energy loss.•A good agreement between the results of the two models is obtained.•The calculated equivalent damping ratio is applied to model engaging spur gears.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
3.
Rotating rod and ball Kryzhevich, Sergey; Plakhov, Alexander
Journal of mathematical analysis and applications,
05/2024, Volume:
533, Issue:
1
Journal Article
Peer reviewed
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Discrete element simulations were carried out to investigate the elastic impact damage mechanism of PS@CeO2 core-shell abrasive (CSCAP). Aiming at understanding the deformation behavior and damage ...mechanism of CSCAP during the polishing process, effects of the impact velocity, impact angle on the rates of deformation and recovery deformation, stress distribution, the number of microcracks were systematically investigated. Tensile cracks formed owing to the CSCAP deformation was gradually increasing when impacting the workpiece downwards. After the CSCAP reached the maximum deformation, macroscopic cracks at the interface were extended gradually. Owing to the redistribution of the compressive force, the interface was observed to predominantly occur in shear cracks, while the shell layer was found to be distributed with tensile cracks. The number of microcracks increase with the increase in impact speed, the impact angle was within the range of 15° to 45°. This investigation enhances the comprehension of nanoscale deformation damage mechanism in CSCAP during ultra-precision machining processes.
Display omitted
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
Abstract
In this paper, the stochastic dynamics of a modified Rayleigh-Duffing oscillator with Coulomb frictional damping and elastic impact is investigated under combined harmonic and noise ...excitations. On the premise of retaining the non-smooth properties, a non-smooth steady-state probability density response numerical calculation method is introduced by taking advantage of Markov process. Utilizing this method, the stochastic P-bifurcation phenomena of oscillators without and with externally excitation are discussed in detail by inscribing changes in the topology of the steady-state probability density function. It is displayed that certain nonlinear damping coefficient and external excitation amplitude change the structure of the response, and that both the friction coefficient and the elastic coefficient of the contact surface induce stochastic P-bifurcation phenomena in systems without and with harmonic excitation, respectively. This study reveals the effect of non-smooth factors on the stability of the Rayleigh-Duffing oscillator.
•Explicit formulae are established to compute the maximum displacement of floor.•The effects of impactor mass, impact height, floor span, slab thickness, rebar diameter, and beam depth are ...studied.•Coefficient of restitution in impact is considered.•Practical recommendations for the maximum displacement of floor are proposed.
Analytical and numerical investigations on the maximum displacement of the steel-concrete composite floor system subjected to falling impact are presented in this paper. Explicit formulae are established to compute the floor maximum displacement under impacts with different kinetic energy transfer ratios. Parametric analyses are conducted to study the influence of impactor mass, impact height, floor longitudinal span, floor thickness, rebar diameter, beam depth, and coefficient of restitution on the maximum displacement of floor. Associated practical recommendations are also proposed for determining the maximum displacement of floor under falling impact. It is found that in fully elastic impact, the maximum displacement is highly sensitive to the impact height, whereas in fully plastic impact, the value is significantly affected by the impactor mass. The upper-bound estimation of the displacement can be achieved by using fully elastic impact model. However, fully plastic impact model should be adopted when the impactor mass increases to more than 30 % of the total mass of the floor.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
•Based on the Flores contact model, we establish the dynamic model of spherical rocks vertical impact on the metal plate with the considering the energy absorbed and consumed by the compression of ...the rock and energy absorbed by the bending deformation of the metal plate.•Based on the Drucker–Prager criterion, we obtain the function of maximum comprehensive stress ε0(α, μ1) and deduced the initial yield stress and initial yield impact velocity for the consideration of principal stress σ2.•We propose the approximate theoretical formula of the maximum contact compression of spherical rocks based on recursive solution. Influence law of impact velocity, material parameters and structure size on the dynamic response of the impact system is obtained.•The combining simulation based on ADAMS and Hypermesh was used to verify the correctness of the theoretical model.
In the process of top coal caving mining, the metal sheet of the tail beam of the hydraulic support will vibrate when coal and rock particles start to impact the tail beam. In the impact between the particles and the metal plate of finite dimension, there are many complicated problems such as short duration of impact, rapid enhancement of transient stress, local large deformation of particles and macroscopic deflection of the metal plate are involved. However, the analysis of the contact force between the spherical particles and other objects is still simplified to the ideal Hertz contact problem. In order to study the real contact states of coal and rock particles impact on the metal plate, we simplified the working conditions from the coal and rock particles impact the tail beam in top coal caving mining to the system that spherical particles have similar properties to coal or rocks impact vertically on the metal plate. Based on the Flores contact theory and the energy absorbed by the bending deformation of the metal plate, the contact model of spherical rock at the compression stage was established. At the same time, we researched the initial yield stress and initial yield impact velocity of spherical rock that obeys the Drucker–Prager (D–P) criterion and proposed the approximate theoretical calculation method of maximum contact compression of spherical rocks. In the range of elastic impact velocity, the influence of impact velocity, restitution coefficient, material parameters and structure sizes on the dynamic response of the system were also analyzed. Finally, the correctness of the theoretical model has been verified by the virtual prototype simulation combined by ADAMS and Hypermesh. The research will provide the basic theory reference for the recognition technology of a single particle of coal or rock that based on the impact vibration of the tail beam.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A fundamental question of earthquake science is what produces damaging high‐frequency ground motion, with the classic Brune‐Haskell model postulating that abrupt fault slip causes it. However, even ...when amended with heterogeneous rupture, the model fails to explain observations of different sized repeating earthquakes and has challenges explaining high‐frequency radiation patterns. We propose an additional cause for high‐frequency earthquake spectra from elastic collisions of structures within a rupturing fault zone. The collision spectrum is set by an impact contact time proportional to the size of colliding structures so that spectra depend on fundamentally different physical parameters compared with slip models. When added to standard models, collisions can reconcile the discrepant observations since the size, shape, and orientation of structures vary between different fault zones but remain constant within a fault segment. High‐frequency earthquake ground motions and damage may therefore be an outgrowth of fault‐zone structure rather than sudden initiation of slip.
Plain Language Summary
Why do earthquakes damage buildings? Many buildings are damaged most heavily by fast, jerky ground motion rather than the longer duration rolling motions that contain most of the earthquake energy. Despite the importance of these fast, jerky motions, most frictional models for earthquakes generally underpredict how strong they are, even when heterogeneous friction and realistic roughness are accounted for. We propose that collisions of structures as they attempt to slide past each other during an earthquake may also create jerky ground motion. We find that the ground motion from collisions depends mostly on the size of the structures and does not depend on stresses within the Earth and thus gives a very different interpretation of what causes the most damaging ground motions. When incorporated with standard frictional models, the collision model explains various observations that are otherwise difficult to explain, including why some earthquakes appear to be identical in time but with larger amplitudes, why faults that have had many earthquakes have less damaging ground motions, and why earthquake damage is observed to occur more uniformly than previously predicted.
Key Points
Collisions of structures within fault zones cause high‐frequency earthquake ground motion
The physics of elastic impact predicts that collisions depend on different physical parameters as compared with frictional fault slip
Accounting for elastic impact ground motion can explain stress drop and radiation pattern observations
Full text
Available for:
FZAB, GIS, IJS, KILJ, NLZOH, NUK, OILJ, SBCE, SBMB, UL, UM, UPUK
•An asymmetric 2 DOF oscillator with elastic and rigid impacts is investigated.•Negative feedback forces and nonlinear spring of cubic term are considered.•Switching conditions of motion at ...separation boundaries are explored.•Several typical motions are simulated numerically by MATLAB software.
In this paper, by using flow switching theory of discontinuous dynamical systems, the discontinuous dynamic behavior of a 2-DOF (two-degree-of-freedom) friction oscillator with elastic impact and rigid impact on different sides is investigated. For the 2-DOF friction oscillator, when the direction of object’s velocity changes, the negative feedback works and the inequality of maximum static friction force and kinetic friction force leads to the existence of flow barriers. In addition, the elastic impact and rigid impact can change motion states of object, resulting in the discontinuity of this 2-DOF system. Considering the multiple motion states of object and better analyzing the equation of object’s motion, the phase space of each object is divided into different motion domains and boundaries in relative and absolute coordinates by means of the discontinuities resulted from the friction and impact. Moreover, because the elastic impact exists in a time period, there will be a variety of motion behaviors coexisting, such as elastic and rigid impacts occur simultaneously. With that in mind, in absolute coordinate system, the phase space of the system is divided in six cases according to whether there are stick motion and stuck motion. Based on flow switching theory, the switching conditions at discontinuous boundaries for all possible motions are given by using G-functions, and it should be noted that the vanishing conditions of the sliding motion become more complicated due to the existence of flow barriers at speed boundaries. Through defining the switching sets on separation boundaries, the mapping structures are further introduced to demonstrate the global dynamic behavior and periodic motions. For a better understanding of the object’s motion and the switching criteria at separation boundaries, the numerical simulation method is used to demonstrate several typical motions such as passable motion, sliding motion, grazing motion, stick motion (elastic impact), rigid impact and periodic motions etc. The results obtained have reference value for the optimization design and noise control of mechanical systems with gap couplings and negative feedbacks.
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
10.
Elastic impact of sphere on large plate Peng, Qing; Liu, Xiaoming; Wei, Yueguang
Journal of the mechanics and physics of solids,
November 2021, 2021-11-00, 20211101, Volume:
156
Journal Article
Peer reviewed
Open access
•The Zener impact was solved by using homotopy analysis method.•Structural compliance breaks contact force symmetry.•Zener energy loss is proportional to the impact velocity to the power of 0.2.
...Different from the Hertz impact, a sphere impacting on a plate has an extra dissipation by the flexural wave propagating on the plate. This wave dissipation has been noticed by Zener (1941), who introduced this dissipation term into the governing equation. Because of this extra dissipation term by the flexural wave, the Zener equation cannot be treated as the same way as in the Hertz impact problem. As a result, in the past 80 years, except few numerical tries for Zener equation, no analytical solution has been provided for the evolution of compressive displacement or contact force during the Zener impact. In this paper, by using homotopy analysis method, we analytically solved the Zener impact problem. After constructing an auxiliary linear operator, we derived an analytical solution for the evolution of contact force up to the first order of the embedding homotopy parameter. Present model can take full account of the elongation of contact time by plate compliance, which is impossible by using Hertz impact model. Comparisons with finite element simulation show that the prediction of the contact force history is of high accuracy. With the solution of force history, we derived an explicit expression for the energy loss of Zener type, this Zener loss has a different dependence on the impact velocity as the Hunter loss does. Also, both the motions of the sphere and the plate are able to be predicted with high accuracy. In addition, with the zeroth-order solution, we derived explicit expressions for both the coefficient of restitution and the contact duration.
Display omitted
Full text
Available for:
GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
PDF
