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The primary goal of this article is to propose a new analysis tool that estimates the asymptotic trends in the time-varying oscillatory period of a non-linear mechanical system. The scope is limited to the step-response of a torsional oscillator containing a dry friction element and dual-staged spring. Prior work on the stochastic linearization techniques is extended and modified for application in time domain. Subsequently, an instantaneous expected value operator and the concept of instantaneous effective stiffness are proposed. The non-linear system is approximated at some instant during the step-response by a linear time-invariant mechanical system that utilizes the instantaneous effective stiffness concept. The oscillatory period of the non-linear step-response at that instant is then approximated by the natural period of the corresponding linear system. The proposed method is rigorously illustrated via two computational example cases (a near backlash and near pre-load non-linearities), and the necessary digital signal processing parameters for time domain analysis are investigated. Finally, the feasibility and applicability of the proposed method is demonstrated by estimating the softening and hardening trends in the time-varying oscillatory period of the measured response for two laboratory experiments that contain clearance elements and multi-staged torsional springs. [ABSTRACT FROM AUTHOR]

In the continuum structural mechanics framework, a unilateral contact condition between two flexible bodies does not generate impulsive contact forces. However, finite-dimensional systems, derived from a finite element semi-discretization in space for instance, and undergoing a unilateral contact condition, require an additional impact law: Unilateral contact occurrences then become impacts of zero duration unless (i) the impact law is purely inelastic, or (ii) the pre-impact velocity is zero. This contribution explores autonomous periodic solutions with one contact phase per period and zero pre-impact velocity [case (ii)], for any n-dof mechanical systems involving linear free-flight dynamics together with a linear unilateral contact constraint. A recent work has shown that such solutions seem to be limits of periodic trajectories with k impacts per period as k increases. Minimal analytic equations governing the existence of such solutions are proposed, and it is proven that, generically, they occur only for discrete values of the period. It is also shown that the graphs of such periodic solutions have two axes of symmetry in time. Results are illustrated on a spring-mass system and on a 4-dof two-dimensional system made of 1D finite elements. Animations of SPPs with up to 30 dofs are provided. [ABSTRACT FROM AUTHOR]

The study presents the dynamic structural response of steel member subjected to a localized impact from falling rock blocks in rockfall areas. A novel compliance contact model is derived for the interaction between the elastic-plastic member (the target) and an impacting rock block. Unlike other existing models, the proposed compliance contact model accurately evaluates the material properties of the rock block (considered as a deformable indenter) and of the steel target (considered as an elastic-plastic target of finite thickness). A simplified two degrees of freedom (2-DOF) lumped masses model accounting for nonlinear contact interaction and material nonlinearities is used to describe the dynamics of the phenomenon. The proposed contact law and the 2-DOF model are validated with detailed static and dynamic analyses conducted with finite element software ANSYS. The results are compared and commented in order to be implemented in future civil engineering applications. [ABSTRACT FROM AUTHOR]

In addition to an accurate mathematical representation of the material, a computational modelling method for assessing impact problems involving large plastic deformation, damage localization, fracture etc. requires a suitable discretization scheme which can simulate the relevant physical processes without introducing any numerical artifact or being unstable. In this paper, a computational framework based on Smoothed Particle Hydrodynamics (SPH) is presented for studying the deformation and failure of ductile material, steel plate, under impact loading. This provides a useful design tool to simulate penetration of the plate. Crack propagation is modelled through a pseudo spring analogy wherein the interacting particles are assumed to be connected through pseudo-springs and the interaction is continuously modified through an order-parameter based on the accumulated damage in the spring. At the onset of crack formation i.e., when the accumulated damage reaches the critical value, the spring breaks which results in termination of interaction between particles on either sides of the spring. A key feature of the computational model is that it can capture arbitrary propagating cracks without introducing any special treatment such as discontinuous enrichment, particle-splitting etc. This computational framework is used herein to study adiabatic shear plugging in metal plates when modelling penetration under impact loading by a flat-ended, cylindrical projectile. The effects of different damage criteria are discussed. Computed results are compared with the experimental observation given in the literature and the efficacy of the framework is demonstrated. [ABSTRACT FROM AUTHOR]

A new type of mineral car arrester, designed for transportation in the inclined shaft rail undermine, includes three degrees of freedom and seven links, to achieve the functions, like a one-way retarder, automatic resetting. The arrester achieves opening and closing functions by air cylinder driving and gravity resetting, and it arrests the car by the way of directly stopping the slipping car. Meanwhile, a buffering system installed under the track, including three buffering springs, as flexible energy absorption equipment absorbs the striking energy. This paper introduces the dynamics analysis of the impact behavior for the car arrester in detail, so that the impact dynamics for the ideal function of car arrester can be obtained by conclusion. The oscillatory differential equations freedom kinematics equations of the impact system are developed. The mineral car and arrester, under position-type nonlinear forces, are simplified to single mass bodies. The data such as the maximum spring force, maximum amplitude, the time and the numbers of impact are achieved by Mathcad, to solve the dynamic equations and analyze the motion law of the mine car after the impact. Then, the conclusion can be obtained that there are some reliability redundancies in the car arrester. Meanwhile, the three key components of the car arrester are analyzed in ANSYS finite-element analysis software. According to the analysis, it is confirmed that design of the structure and size parameters of the car arrester meets the security and functional requirements. [ABSTRACT FROM AUTHOR]

Modern railway tracks require electrification to power the trains and signaling systems to detect near real-time location of trains on railway networks. Such systems require the rail to carry and return the residual electricity back to substation, while enable signals to transfer within a track circuit. This track circuit requires rail joints to divide and insulate each loop of the circuit. Such the rail joints often generate impact transient dynamics to track systems. This paper presents the filed investigation into the vibration attenuation characteristic of under sleeper pads (USPs), which are the component installed under the concrete sleepers generally to improve railway track resilience. The field trial is aimed at mitigating rail joint impacts in a heavy haul track under mixed traffics. ‘Big Data’, obtained from both the track inspection vehicle and the sensors installed on tracks, demonstrate that track surface quality (top) of the section was improved after the track reconstruction. Fourier analysis results showed that the track surface (or vertical deviation) tends to deform at larger displacement amplitude and resonates at a lower wavelength of track roughness. Interestingly, the operational pass-by vibration measurements show that the USPs has resulted in an increased vibration of both rail and sleeper with USPs. Although the studies have found that the sleepers with USPs tend to have lesser flexures, the field data also confirms that a railway track with USPs could experience a large amplitude vibration, especially when excited by a high-frequency impact force. These dynamic behaviours imply that the use of soft to moderate USP could potentially induce dilation of ballast whilst the use of hard USP may reduce sleeper-ballast friction. In the end, these could then weaken lateral track stability over time. [ABSTRACT FROM AUTHOR]

Periodic solutions of autonomous and conservative second-order dynamical systems of finite dimension n undergoing one unilateral contact condition are investigated in continuous time. The unilateral constraint is complemented with a purely elastic impact law which preserves total energy. The dynamics is linear when there is no contact. The number k of impacts per period arises as a natural parameter of the proposed formulation. Interestingly, the existence of the targeted periodic solutions is essentially governed by a system of only k -1 nonlinear equations with k unknowns, regardless of the number of degrees of freedom. This serves to prove that the phase space is populated by one-dimensional continua of periodic solutions generating invariant manifolds which can be understood as nonsmooth modes of vibration in the context of vibration analysis. Additionally, these equations provide an effcient and systematic way of calculating nonsmooth modes of vibration. They also demonstrate the existence of interesting properties: symmetries of trajectories and emergence of unique features such as manifolds supporting constant-frequency orbits. All results are illustrated through a simple in-line spring-mass system whose last mass undergoes the unilateral impact law. Stability is briefly discussed and a few neutrally stable modes are depicted. [ABSTRACT FROM AUTHOR]

As a traditional protective material, steel has been developing towards higher strength and better ductility. The dynamic mechanical behavior, ballistic resistance, together with the deformation and fracture modes of steels vary with the characteristics of strength and ductility. In this study, three kinds of low-carbon alloy steel including Q235A, 10CrNiMo and 22SiMnTi, which have great differences in strength and ductility, were selected as research objectives. To compare the anti-penetration performance of these steel plates subjected to the ultra-high strength blunt-nosed cylindrical projectiles, the perforation tests were conducted with the impact velocity of 750±5 m/s in both. The analysis of pre and post-impact microstructure indicates that with the densest lath martensite structure, the highest strength steel 22SiMnTi forms adiabatic shearing fracture as the stress exceeds the shear strength; with better ductility, Q235A and 10CrNiMo are characterized by more compact post-impact microstructures and obvious plastic flow. Consistent with above analysis, the validation tests showed that 10CrNiMo exhibited the best resistance to blunt-nosed cylindrical projectiles, and followed by 22SiMnTi and Q235A. The excellent anti-penetration performance of low-carbon alloy steel is due to the integrated optimization of strength and ductility. [ABSTRACT FROM AUTHOR]

Although the superhydrophobic surfaces are preferable for passive anti-icing systems, as they provide water shedding before initiation of ice nucleation, their practical usage is still under debate. This is so, as the superhydrophobic materials are not necessarily icephobic and most of the synthesis techniques are characterized with low fabrication scalability. Here, we describe a rational strategy for the atmospheric icing prevention, based on chemically functionalized carbon soot, suitable for large-scale fabrication of superhydrophobic coatings that exhibit and retain icephobicity in harsh operational conditions. This is achieved through a secondary treatment with ethanol and aqueous fluorocarbon solution, which improves the coating’s mechanical strength without altering its water repellency. Subsequent experimental analyses on the impact dynamics of icy water droplets on soot coated aluminum and steel sheets show that these surfaces remain icephobic in condensate environments and substrate temperatures down to −35 °C. Furthermore, the soot’s icephobicity and non-wettability are retained in multiple icing/de-icing cycles and upon compressed air scavenging, spinning and water jetting with impact velocity of ∼25 m/s. Finally, on frosted soot surfaces, the droplets freeze in a spherical shape and are entirely detached by adding small amount of thermal energy, indicating lower ice adhesion compared to the uncoated metal substrates. [ABSTRACT FROM AUTHOR]

This paper presents impact dynamic analysis of a differential gears based underactuated robotic arm colliding with a moving target. The robotic arm employs a set of one-input-dual-output planetary gears to distribute driving torque of the underactuated joints, which takes advantage of the underactuation to cope with collision. Based on an analysis of the movement relation of three joints, the driving torque is resolved into generalized force corresponding to coordinates of two underactuated joints for establishing a dynamic model of the underactuated robotic arm. Along with the dynamic equation, impulse-momentum equations involving the restitution coefficient of the system (arm and target) are used to establish the impact dynamic model which can extrapolate the impact momentum on the drive component. With the impact dynamic model, the impact-absorbing capability of the underactuated robotic arm is illustrated that the impact momentum on the drive component is reduced by a factor of three compared with a 2-DOF fully actuated rigid robotic arm. Impact experiments were carried out to validate the inference results presented in this paper by using of a prototype of the proposed arm. [ABSTRACT FROM AUTHOR]

A model for the impact between a structurally deformable sphere and a rigid flat surface is presented. It includes a nonlinear contact element that accounts for energy loss due to local plastic deformation or flattening of the sphere, a viscous element that accounts for energy loss due to wave propagation and/or damping, and a linear stiffness element that accounts for recoil effects during and after impact. A linearized version of the model facilitates normalization of the equations with helpful insights into the impact problem. The results show that the impact event can be characterized by two non-dimensional parameters, namely the relative stiffness λ, which accounts for recoil effects, plastic deformation and/or flattening of the sphere, and the damping factor, ζ, which accounts for viscous and/or wave propagation effects. Model predictions compare well with experimental data for sports balls that are excellent examples of deformable spheres. The normalized impact force and the coefficient of restitution (COR) are dependent on both parameters. At low speeds and damping factors the normalized impact force and COR mainly depend on damping, whereas, at low speeds and large damping factors they depend on damping and flexibility. For a given damping factor, the normalized maximum impact force and COR decrease with higher flexibility. Depending on the deformation characteristics of the ball, at higher speeds the COR decreases further due to surface flattening effects. [ABSTRACT FROM AUTHOR]

A two-part experimental study was conducted in order to better understand how the delivered face angle and club path of a golf club influences the initial launch direction of a golf ball for various club types. A robust understanding of how these parameters influence the ball direction has implications for both coaches and club designers. The first study used a large sample of golfers hitting shots with different clubs. Initial ball direction was measured with a Foresight Sports camera system, while club delivery parameters were recorded with a Vicon motion capture system. The second study used a golf robot and Vision Research camera to measure club and ball parameters. Results from these experiments show that the launch direction fell closer to face angle than club path. The percent toward the face angle ranged from 61% to 83%, where 100% designates a launch angle entirely toward the face angle.

• The oblique impact experiment of fragments was carried out. • The empirical formulae of ricochet velocity and angle were proposed. • The effect of impact parameters on material deformation was analyzed. • The effect of target hardness on ricochet velocity and angle was studied. • A model of mass loss rate of fragments was proposed. When the casing charge exploded near or inside a steel installation such as a ship or plant, part of the fragments would impact the target plate and ricochet. Plastic deformation occurs on both the fragment and target plate during the oblique impact, in which the direction and velocity of fragments change. The ricochet of fragments would change the damage range, which cannot be predicted by previous theories. In our experiment, cylindrical fragments were used to impact target plates under different impact velocities and angles, and the target plates are made of marine steel 921A and commonly used Q345B, which are the two most commonly used steels for ships and steel installations. The empirical formulae of ricochet velocity and angle for two target plates were obtained, which were applicable to the positive ricochet. The ricochet velocity increased with the increase in impact velocity and angle, but the ricochet angle only increased with the increase in impact angle. In addition, the ricochet velocity increased with the increase in the hardness of target plate when the impact angle was less than 40° due to the deformation of the target plate, the ricochet angle increased with the increase in the hardness of target plate since the pile-up effect would increase the deflection, causing the ricochet angle decreased. The fragment mass loss model was obtained based on the experimental data, which is a strong function of impact velocity but a weak function of impact angle. With the increase in impact angle, the plastic deformation of fragments gradually decreased, the target plate changed from plastic compression deformation to shear deformation, the deformation energy of target plate changed from volumetric energy to more shear strain energy, and the impact crater became shallower. With the increase in impact velocity, the plastic deformation of fragments increased, the inertial resistance of target plate increased, the impact crater on the target surface became larger and deeper, and then only the depth of impact crater increased when the impact velocity reached a certain extent. The plastic deformation of target plate decreased with the increase in the hardness. The proposed formulae and model can provide guidance for the fragment damage range evaluation and equipment protection. [ABSTRACT FROM AUTHOR]

This study aimed to explore the single-legged landing kinematics that could lead to increase or decrease in the risk of anterior cruciate ligament (ACL) injury. Immediate pre-impact kinematics at the single-legged landing from 33 healthy young female handball players were evaluated. Thereafter, two-year follow-up for ACL injury incidence was conducted, in which six new ACL injuries in non-dominant leg were registered. The evaluation of pre-impact kinematics across participants was performed first by the principal component analysis to decompose them into the kinematic components (KCs), and then by the linear discrimination analysis (LDA) for a set of KC-scores to obtain important KCs for discriminating injured and non-injured legs. The result of LDA showed that the combination of second major KC (knee flexion/extension angle and angular velocity) and some minor KCs such as torso medial/lateral leaning accurately discriminated the injured and non-injured legs with the error rate of 12.5%. To examine the mechanisms of this discriminative ability, we generated hypothetical pre-impact kinematics in the subspaces spanned by eigenvectors of multiple KCs, and examined relationships between pre-impact kinematics and the corresponding knee valgus torque predicted by the motion-equation-based model. The result showed that the second major KC and the minor KCs representing torso medial/lateral leaning and/or hip adduction/abduction angle, which contributed in LDA to discriminating injured legs, also significantly affected the frontal-plane knee loading patterns. These findings suggested that KC-based postural characterization of the pre-impact landing kinematics and the motion-equation-based knee stress quantification possibly explain the future ACL injury risks of female athletes. • Drop-landing kinematics was analyzed from an ACL injury risk perspective. • Principal component analysis characterized athlete's pre-impact kinematics during single-legged landing. • Specific combination of principal components prospectively discriminated injured and non-injured leg. • Specific major and minor components were associated with the maximum knee valgus torque. [ABSTRACT FROM AUTHOR]

Four polydimethylsiloxane (PDMS) coatings with different surface free energies have been prepared and applied to smooth and roughened aluminum plates to form hydrophobic and superhydrophobic surfaces. Their surface wettability in terms of water contact angle (CA), sliding angle (SA) and water droplet impact dynamics was studied under an ambient (50% relative humidity, RH at 25 °C) and three different condensing environments (low, highly and extremely condensing, i.e. 30%, 60% and 90% RH at −10 °C). In addition, the surface ice adhesion was investigated under the extremely condensing condition. Different PDMS coatings on either smooth or roughened surfaces displayed a very similar impact to static and dynamic wettability under the ambient environment. However, the water impact behavior and ice adhesion under the extremely condensing condition between the hydrophobic and superhydrophobic surfaces are significantly different. One of the superhydrophobic surfaces (R2180) demonstrated an excellent water repelling capability to retard ice accumulation, and reduced ice adhesion strength even under the extremely condensing condition, and thus will be a good candidate for ice-phobic applications. This excellent ice-phobic property is attributed to the low surface free energy of the coating, which effectively prevents the water condensation inside the cavities of the hierarchical superhydrophobic structures and thus maintains “air cushion” on the solid/water interface, indicated by a very low solid-liquid contact area increase after surface is exposed to this condensing weather condition. This result demonstrates that the “air cushion” in a superhydrophobic surface could be maintained even under an extremely condensing condition by carefully selection of coating composition with a very low surface free energy. [ABSTRACT FROM AUTHOR]

Based on the similarity theory, this paper analyzed the influence parameters on plane shock wave pressure (PSWP), and proposed a scale test method to calculate the attenuation characteristics of PSWP of the original model. The scale model test and the original model test were simulated by using LS-DYNA code. Fitting the results of the scale model test, it obtained the dimensionless empirical model of attenuation characteristics of PSWP in oxygen-free copper within a certain scope of scale distance. Comparing the simulated values of PSWP of the original model with the values computed by the dimensionless empirical model at typical points, and the maximum relative errors of shock wave's peak pressure, pulse width and impulse are respectively less than 0.5%, 2% and 0.1%. The results are in good agreement with each other, which verifies the feasibility of this scale test method. This method provides a new idea to research on the attenuation characteristics of plane shock wave pressure in solid materials. [ABSTRACT FROM AUTHOR]

This paper presents a computational framework that analyzes the effect of fluid–structure interaction (FSI) on the impact dynamics and puncture failure of pressurized commodity tank cars carrying hazardous materials. Shell (side) impact tests have been conducted on full scale tank cars resulting in deformed or punctured tank cars. A finite element (FE) modeling method is applied that explicitly simulates the three distinct phases in a tank car loaded with a liquefied substance: pressurized gas, pressurized liquid and solid structure. Furthermore, an equivalent plastic strain based fracture initiation criterion expressed as a function of stress triaxiality is adopted to depict the fracture behavior of the tank car steel material. The fracture initiation is implemented for ductile, shear and mixed fracture modes and followed by further material deterioration governed by a strain softening law. The force, displacement and impact energy results obtained from the FE analysis show good agreement with the corresponding shell impact test data. The simulations demonstrate that FSI plays a critical role in predicting the correct dynamics of tank car impact. The puncture resistance of a tank car, characterized as limit impact conditions in terms of puncture energy or puncture velocity, is further analyzed in shell impact scenarios. The puncture energy is shown to increase as the initial fluid pressure decreases, the tank car thickness increases or the effective impactor size increases. Quantitative correlations between puncture energy/velocity and each of these factors are obtained using the FE analysis method developed in this paper. [ABSTRACT FROM AUTHOR]

A composite liquid metal marble made of metal droplet coated with water film was proposed and its impact dynamics phenomenon was disclosed. After encapsulating the liquid metal into water droplets, the fabricated liquid marble successfully avoided being oxygenized by the metal fluid and thus significantly improved its many physical capabilities such as surface tension modification and shape control. The striking behaviors of the composite liquid metal marbles on a substrate at room temperature were experimentally investigated in a high speed imaging way. It was disclosed that such marbles could disintegrate, merge, and even rebound when impacting the substrate, unlike the existing dynamic fluidic behaviors of liquid marble or metal droplet. The mechanisms lying behind these features were preliminarily interpreted. This fundamental finding raised profound multiphase fluid mechanics for understanding the complex liquid composite which was also critical for a variety of practical applications such as liquid metal jet cooling, inkjet printed electronics, 3D printing or metal particle fabrication etc. [ABSTRACT FROM AUTHOR]

We consider event-driven schemes for the simulation of nonseparable mechanical systems subject to holonomic unilateral constraints. Systems are modeled in discrete time using variational integrator (VI) theory, by which equations of motion follow from discrete variational principles. For smooth dynamics, VIs are known to exactly conserve a discrete symplectic form and a modified Hamiltonian function. The latter of these conservation laws can play a pivotal role in stabilizing the energy behavior of collision simulations. Previous efforts to leverage modified Hamiltonian conservation have been limited to integrators using the Störmer-Verlet method on separable, nonsmooth Hamiltonian mechanical systems. We generalize the existing approach to the family of all VIs applied to nonseparable, potentially nonconservative Lagrangian mechanical systems. We examine the properties of the resulting integrators relative to other structured collision simulation methods in terms of conserved quantities, trajectory errors as a function of initial condition, and required computation time. Interestingly, we find that the modified collision Verlet algorithm (MCVA) using the Störmer-Verlet integrator defined as a composition method leads to the best accuracy. Although relative to this method, the VI-based generalized MCVA method offers computational savings when collisions are particularly sparse. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The last two decades have seen a number of developments in creating robots to play billiards. The designed robotic systems have successfully incorporated the kinematics required and have had appropriate machine vision elements for a decent gameplay. Independently, computer scientists have also developed the artificial intelligence programs needed for the strategy to play billiards. Despite these developments, the accurate ball manipulation aspect of the game, needed for good performance, has not been addressed enough; two important parameters are the potting accuracy and advantageous cue ball positioning for next shot. In this regard, robotic ball manipulation by predicting the ball trajectories under the action of various dynamic phenomena, such as ball spin, impacts and friction, is the key consideration of this research. By establishing a connection to the methods used in nonprehensile robotic manipulation, a forward model is developed for the rolling, sliding, and two distinct types of frictional impacts of billiards balls are developed. High-speed camera-based tracking is performed to determine the physical parameters required for the developed dynamic models. To solve the inverse manipulation problem, i.e., the decision on shot parameters, for accurate ball positioning, an optimization based solution is proposed. A simplistic ball manipulator is designed and used to test the theoretical developments. Experimental results show that a 90% potting accuracy and a 100–200 mm post-shot cue ball positioning accuracy has been achieved by the autonomous system within a table area of $6 \times 5$ ft2. [ABSTRACT FROM PUBLISHER]

Based on the Split Hopkinson Pressure Bar (SHPB) device, a new combined compression and shear loading technique is developed by adding cushions with designed oblique surfaces. Employing steel as standard material, the technique is calibrated by a series of quasi-static and dynamic experiments. A reliable data processing method of the technique is proposed to decompose the normal stress ( σ ) and the shear stress ( τ ) on the oblique surface. The results show that the coupled compression and shear responses of steel exhibit obvious strain rate effect. Validation of the technique is confirmed by using Von Mises criterion in σ - τ plane to describe the coupled strength of steel. Thus, series of experiments are conducted to investigate the compression and shear behaviors of a granite under quasi-static loading (strain rates ∼ 3 × 10 −5  s −1 ) and impact loading with strain rates 50 s −1 and 100 s −1 . Five oblique angles, e.g. zero, 15, 30, 45, and 60 degrees, are involved in the experiments. Slopes of the decoupled normal and shear stress-strain curves exhibit obvious load-path dependency, which is known as the coupled compression and shear effect, and strain rate effect. These two effects become more important with oblique angle increasing. Failure criterion of granite specimen at different strain rates can be preliminarily described by the Drucker–Prager (D-P) model, and the strengths of granite exhibit obvious strain rate sensitivity and load-path dependency. The technique is helpful for the investigation of the dynamic properties of rock materials under complex stress states. [ABSTRACT FROM AUTHOR]

The dynamics of swinging bells is a timely problem considered when the bell's supporting structures are designed or monitored. The geometry of a yoke and the magnitude of an excitation force are crucial parameters determining a yoke–bell–clapper system response for a given shape and size of the bell. This paper presents the novel yoke–bell–clapper system with variable geometry and adjustable excitation force. A mathematical model based on the existing prototype is introduced. The mathematical model is validated, and then the influence of the yoke geometry and excitation force on the system response is assessed. The simulations are done using a sample-based approach. The system that undergoes investigation is non-linear, piecewise, and discontinuous. The derived mathematical model can reliably predict the ringing scheme of a bell and associated reaction forces in the supports. • We propose a novel model of the yoke–bell–clapper system. • We validate the model based on the prototype rig. • We investigate forces transmitted to the structure by the yoke–bell–clapper system. • We use the sample-based method to perform the numerical calculation to show the system's response in a wide range of system's parameters. • We prove that the model is robust and allows us to predict the dynamics of the yoke–bell–clapper system. [ABSTRACT FROM AUTHOR]

• Dynamic behaviors of impacting nanodroplets with oblique angles. • Reduction of contact time is noted for high oblique angles. • Two sliding regimes are distinguished in early and later impact processes. • Construction of the outcome phase diagram for oblique impact dynamics. In this study, the impact dynamics of water nanodroplets are investigated via MD simulations, aiming to examine scale effects during nanodroplets oblique impact. The MD results show that the significant interface slide can be observed at the nanoscale. Owing to the weakening of the adhesion effect between liquids and surfaces, asymmetric behaviors of oblique impacting nanodroplets vanish in spreading processes and are only observed in the retraction stage in the high oblique angle range (α > 45°). Additionally, the influence of increasing oblique angles on two feature parameters (i.e. the contact time and the sliding length) are detailed discussed, by reducing the former and enhancing the latter. Finally, the phase diagram in the parameter space of We n vs α is plotted, including adhesion, regular bouncing, and breakup bouncing. The outcome diagram can give a comprehensive insight into the oblique impact dynamics and further provide guidance for practical applications. [ABSTRACT FROM AUTHOR]