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The objective of this research work is to provide a systematic method to perform molecular dynamics simulation or evaluation for nano-scale interfacial friction between different materials in MEMS. A simplified model to simulate surface sliding between different kinds of material by molecular dynamics [MD] is proposed because the surface property is a dominant factor for the performance between two kinds of material in MEMS. The Newton's equations of motion are established by using the Morse potential function. An improved Verlet algorithm is employed to solve atom trajectories. Comparing the results of the computer simulation with experimental results in Ref. 1, the validity of the model is confirmed. The simulation results show that the preliminary stage and the last stage, when no interface is formed, the friction force fluctuates periodly and its peak value is smaller relatively, while at the intermediate stage, where the interface is formed, the friction force fluctuates periodly and its peak value is relatively bigger. The friction force is approximately proportional to the contact area. In the meantime, Cu sliding along Al with uniform speed and accelerated motion was also investigated, the mechanical properties between two surfaces were analyzed and a tentative computational simulation on the effect of the driving force was developed. The results lay a basis for future work.

We investigate the role of hidden terms at switching surfaces in piecewise smooth vector fields. Hidden terms are zero everywhere except at the switching surfaces, but appear when blowing up the switching surface into a switching layer. When discontinuous systems do surprising things, we can often make sense of them by extending our intuition for smooth system to the switching layer. We illustrate the principle here with a few attractors that are hidden inside the switching layer, being evident in the flow, despite not being directly evident in the vector field outside the switching surface. These can occur either at a single switch (where we will introduce hidden terms somewhat artificially to demonstrate the principle), or at the intersection of multiple switches (where hidden terms arise inescapably). A more subtle role of hidden terms is in bifurcations, and we revisit some simple cases from previous literature here, showing that they exhibit degeneracies inside the switching layer, and that the degeneracies can be broken using hidden terms. We illustrate the principle in systems with one or two switches.

When a flow suffers a discontinuity in its vector field at some switching surface, the flow can cross through or slide along the surface. Sliding along the switching surface can be understood as the flow along an invariant manifold inside a switching layer. It turns out that the usual method for finding sliding modes — the Filippov convex combination or Utkin equivalent control — results in a degeneracy in the switching layer whenever the flow is tangent to the switching surface from both sides. We derive the general result and analyze the simplest case here, where the flow curves parabolically on either side of the switching surface (the so-called fold–fold or two-fold singularities). The result is a set of zeros of the fast switching flow inside the layer, which is structurally unstable to perturbation by terms nonlinear in the switching parameter, terms such as ${(\mathrm{\text{sign}}x)}^2$ [where the superscript does mean “squared”]. We provide structurally stable forms, and show that in this form the layer system is equivalent to a generic singularity of a two timescale system. Finally we show that the same degeneracy arises when a discontinuity is smoothed using standard regularization methods.

Differential equations that switch between different modes of behavior across a surface of discontinuity are used to model, for example, electronic switches, mechanical contact, predator–prey preference changes, and genetic or cellular regulation. Switching in such systems is unlikely to occur precisely at the ideal discontinuity surface, but instead can involve various spatiotemporal delays or noise. If a system switches between more than two modes, across a boundary formed by the intersection of discontinuity surfaces, then its motion along that intersection becomes highly sensitive to such nonidealities. If switching across the surfaces is affected by hysteresis, time delay, or discretization, then motion along the intersection can be affected by erratic variations that we characterize as “jitter”. Introducing noise, or smoothing out the discontinuity, instead leads to steady motion along the intersection well described by the so-called canopy extension of Filippov’s sliding concept (which applies when the discontinuity surface is a simple hypersurface). We illustrate the results with numerical experiments and an example from power electronics, providing explanations for the phenomenon as far as they are known.

Dry-friction contacts in mechanical oscillators can be modeled using nonsmooth differential equations, and recent advances in dynamical theory are providing new insights into the stability and uniqueness of such oscillators. A classic model is that of spring-coupled masses undergoing stick-slip motion on a rough surface. Here, we present a phenomenon in which multiple masses transition from stick to slip almost simultaneously, but suffer a brief loss of determinacy in the process. The system evolution becomes many-valued, but quickly collapses back down to an infinitesimal set of outcomes, a sort of “micro-indeterminacy”. Though fleeting, the loss of determinacy means masses may each undergo different microscopic sequences of slipping events, before all masses ultimately slip. The microscopic loss of determinacy is visible in local changes in friction forces, and in creating a bistability of global stick-slip oscillations. If friction forces are coupled between the oscillators then the effect is more severe, as solutions are compressed instead onto two (or more) macroscopically different outcomes.

The main purpose of this paper is to explore the bursting oscillations as well as the mechanism of a parametric and external excitation Filippov type system (PEEFS), in which different types of bursting oscillations such as fold/nonsmooth fold (NSF)/fold/NSF, fold/NSF/fold and fold/fold bursting oscillations can be observed. By employing the overlap of the transformed phase portrait and the equilibrium branches of the generalized autonomous system, the mechanisms of the bursting oscillations are investigated. Our results show that the fold bifurcation and the boundary equilibrium bifurcation (BEB) can cause the transitions between the quiescent states and repetitive spiking states. The oscillating frequencies of the spiking states can be approximated theoretically by their occurring mechanisms, which agree well with the numerical simulations. Furthermore, some nonsmooth evolutions are investigated by employing differential inclusions theory, which reveals that the positional relationship between the points of the trajectory interacting with the nonsmooth boundary and the related sliding boundary of the nonsmooth system may affect the nonsmooth evolutions.

A singularity is described that creates a forward time loss of determinacy in a two-timescale system, in the limit where the timescale separation is large. We describe how the situation can arise in a dynamical system of two fast variables and three slow variables or parameters, with weakly coupling between the fast variables. A wide set of initial conditions enters the $𝜖$-neighborhood of the singularity, and explodes back out of it to fill a large region of phase space, all in finite time. The scenario has particular significance in the application to piecewise-smooth systems, where it arises in the blow up of dynamics at a discontinuity and is followed by abrupt recollapse of solutions to “hide” the loss of determinacy, and yet leave behind a remnant of it in the global dynamics. This constitutes a generalization of a “micro-slip” phenomenon found recently in spring-coupled blocks, whereby coupled oscillators undergo unpredictable stick-slip-stick sequences instigated by a higher codimension form of the singularity. The indeterminacy is localized to brief slips events, but remains evident in the indeterminate sequencing of near-simultaneous slips of multiple blocks.

While surface patterns are effective in improving tribological properties, nevertheless they alter the surface wettability, which will in turn affect the surface–lubricant interactions. When there is a shortage of lubricant on a patterned surface, the lubricant stored inside the cavities will be extracted to compensate the surface lubricant dissipation. Additionally, the lubricant retention effect provided by the cavities is competing with the release of the lubricant. With weak surface–lubricant interaction, the retention is limited. Therefore, the lubrication will have a sudden failure, giving a dramatic transition to abrasive wear. To improve the performance of polar lubricants on hydrophobic polymer surfaces, both topographical and selective surface modifications were incorporated on injection molded polypropylene surfaces. Distinctive lubrication improvement was observed when the surface structure density for the lubricant storage was high, and the release of the lubricant was controlled by the interaction with the selectively modified surfaces.

A dynamic test method for the measurement of the underwater sliding properties of model boats has been developed. Surface-modified model boats were examined to assess how the surface wettability properties affect sliding. Along with the surface properties, the influence of the boat shape was considered. We studied various coatings in the contact angle range of 3–162${}^{\circ }$ with two model boat shapes. The hydrophobicity of the surfaces influenced the sliding speed of the model boat depending on the boat shape. The method is applicable to study sliding properties of model boats with different surfaces in variable flow conditions.

This paper deals with the rocking and sliding behavior of a monolithic stone block or a system of stone blocks under earthquakes, a problem commonly observed for ancient temples in Greece and Southern Italy. The analysis for the above monolithic or multi-drum columns is conducted by a simple process based on generally accepted simplifications. The effects of column geometry, earthquake characteristics and restitution ratio due to impact are also studied herein. Furthermore, an analytical approach for the solution of the complete nonlinear equations of motion (including the one for the vertical earthquake excitation) for the subject considered is proposed. Finally, characteristic representative examples are presented with useful conclusions drawn. It was found that the stability criteria based on static conditions are reliable, while the corresponding dynamic criteria may lead to erroneous results.

This work focuses on analyzing the dynamical behavior of a mechanical system consisting of a double spatial pendulum in contact with a movable obstacle. The pendulum’s ability to move in space is achieved by the use of special Cardan–Hook joints as the links of the pendulum. The mechanical system is equipped with a special movable obstacle, i.e. a rotating circular plate situated below the pendulum, which limits the space of admissible positions. A significant part of this work is devoted to the modeling of the contact between the pendulum and the obstacle. In this regard, a special class of reduced models is derived with the resultant friction force and moment acting on the finite size of the contact area along with a compliant model of impact based on the Hertz stiffness. Finally, the effective model suitable for fast and realistic numerical simulations is obtained. The contact model is tested numerically and the effect of its parameters on the system bifurcation dynamics is investigated.

A system of stacked rigid blocks can be found in many applications of non-structural components: a statue resting on the top of a table is such an example. Previous studies usually assume that the friction at contact interface is so large that only rocking motion can be activated. However, this assumption may not be realistic when assessing the seismic response of unanchored non-structural components. Motivated from this constraint, this paper contributes to the state-of-the-art research of the classical rocking problem by presenting a numerical model within which sliding, rocking and sliding-rocking response of stacked rigid blocks can be computed by the time-history analysis. The exact fully nonlinear equations of motion, transition criteria for different response modes and treatment to handle the impact are presented in detail. The accuracy of the developed model is validated. A case study is also provided to investigate the overall failure probability of the stacked rigid blocks with realistic friction coefficient. In this particular case study, it is also shown that increasing the friction coefficient makes the stacked rigid blocks more susceptible to failure.

The relatively uncontrolled dynamic behavior of a rigid block resting on a flat surface under ground motion has been well studied. In contrast, a block with a gently inclined V- or W-shaped sliding key would ensure dynamic self-centering or resetting performance under various seismic conditions. To better understand the nonlinear responses of rigid blocks having this type of interface where both rocking and sliding movements are possible, an event-based algorithm is put forward to cover various types of motions, including the transition stages between different types of motions. A comprehensive study is carried out to examine the dynamic responses of blocks of different sizes and aspect ratios. Moreover, the simplified pure rocking model and pure sliding model are also adopted to obtain rough estimates of dynamic response for comparison. The results show that the simplified models are reliable for some special cases only, e.g. squat blocks and slender blocks. The study also evaluated the influence of the coefficient of friction and slope inclination on the resetting capabilities of typical sliding-prone and rocking-prone systems. For those cases that are prone to toppling or excessive sliding under strong earthquakes, the provision of vertical post-tensioning can effectively ensure stability and resetting performance. Such findings provide insight into the performance of precast segmental bridge columns with resettable sliding joints.

The dynamic response of a vertical breakwater to breaking waves has been studied by the authors with prototype tests on two breakwaters in Genoa Voltri and one in Brindisi. The tests were interpreted by Mass Spring Dash-pot elements connected among them in order to represent the Array structure typical of a breakwater (MSDA model). The model is similar to the classical MSD one, except that it also considers the force exchanged by adjacent caissons through the foundation.

The objective of this note is to present an analysis of the caisson interaction and to study and compare the different responses to breaker impacts on average European and Japanese caisson breakwaters. These represent typical section shapes using two areas with scaling rules relating caisson dimensions to the incident design significant wave height. Inertia, foundation stiffness and added masses are quite different for the two types of structures and their effect is analyzed.

The dynamic response is presented in terms of a static equivalent response factor given as a function of the ratio between impact load duration and the main structure oscillation period, of the ratio between caisson length and width and of the fraction of the total mass represented by foundation added mass (the latter being the essential difference between European and Japanese design).

Although the modeling of the array structure is essential to interpret the oscillations measured in the prototype, and is obviously important to study the effects of a load that varies along the breakwater, the prediction of the classical approach is similar in terms of maximum load on the foundations whenever the applied forcing is longitudinally homogeneous.

Shore protection projects require the prediction of coastal storm damage and economic loss but the damage processes are not well understood. An exploratory experiment consisting of 11 tests was conducted in a wave flume with a sand beach to examine the movement of 10 wooden blocks (floatable objects) placed on the foreshore and berm as well as on short and long pilings. The still water level was varied to create accretional and erosional profile changes. The cross-shore wave transformation on the beach and the wave overtopping and overwash of the berm were measured in 101 runs of irregular waves where each run lasted 400s. The initial block elevation above the sand surface had little effect on the hydrodynamics, sediment transport, and profile evolution in this experiment with widely-spaced blocks. The block floating and sliding on the sand surface and the block falling from the pilings depended on the swash hydrodynamics and block clearance above the foreshore and berm whose profile varied during each test. A simple probabilistic model is developed to estimate the immersion, sliding, and floating probabilities for the blocks in the swash zone. The predicted probabilities are compared with the observed cross-shore variation of the block response on or above the accretional and erosional beach profiles. The accurate prediction of the block response is shown to require the accurate prediction of the beach profile change.

The paper pertains to a study in which the waterfront retaining wall has been analyzed for its stability when it is exposed to the forces jointly coming from an earthquake and tsunami. Closed form solutions following the simple limit equilibrium principles have been proposed. For the calculation of the seismic passive earth pressure and the wall inertia force, pseudo-dynamic approach has been considered, while the hydrodynamic and the tsunami wave pressures have been calculated using different approximating solutions available in literature. The results presented in the sliding and overturning modes of failure of the wall show that the stability of the wall gets seriously challenged when it gets jointly exposed to the effects of the tsunami and earthquake. About 92% decrease is observed in the value of the factor of safety in sliding mode of failure of the wall as the ratio of tsunami wave height to the upstream still water height increases from 0 to 1.5. Also, the critical mode of failure of the wall has been found to be that of the overturning. Effect of different parameters involved in the analysis has also been studied and it has been observed that quite a few of them like k_h, k_v, ϕ, δ, r_u have a significant effect on the stability of the wall. Comparison with a previously existing methodology using pseudo-static approach suggests that the present pseudo-dynamic approach is more realistic and comparatively less conservative and hence can be used as a handy simple economic method for the design of the waterfront retaining walls exposed to the combined effects of earthquake and tsunami.

Grain boundary (GB) dynamics plays an important role in the mechanical and physical properties of nanocrystalline metals. In this study, we investigate the temperature effect on GB deformation transition using molecular dynamics simulations of [100] symmetric tilt GBs in Au bicrystals. Different deformation behaviours were revealed in GBs with the same structures at varied temperatures. GB sliding occurs as the predominant deformation mechanism at elevated temperatures, while GB migration dominates at low temperatures. The temperature-dependent critical stresses for GB migration and GB sliding were compared, revealing that temperature alters the critical GB misorientation at which GB migration transitions to GB sliding. Our study provides new insight into GB-mediated plastic deformation in nanocrystalline materials.