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The unsafe zone in machining is a region of the parameter space where steady-state cutting operations may switch to regenerative chatter for certain perturbations, and vice versa. In the case of milling processes, this phenomenon is related to the existence of an unstable quasi-periodic oscillation, the in-sets of which limit the basin of attraction of the stable periodic motion that corresponds to the chatter-free cutting process. The mathematical model is a system of time-periodic nonlinear delay differential equations. It is studied by means of a nonlinear extension of the semidiscretization method, which enables the estimation of the parameter ranges where the unsafe (also called bistable) zones appear. The theoretical results are checked with thorough experimental work: first, step-by-step parameter variations are adapted to identify hysteresis loops, then harmonic burst excitations are used to estimate the extents of the unsafe zones. The hysteresis loops are accurately distinguished from the dynamic bifurcation phenomenon that is related to the dynamic effect of slowly varying parameters. The experimental results confirm the existence of the bistable parameter regions. This article is part of the theme issue ‘Nonlinear dynamics of delay systems’.

Bistable logos accept two different interpretations, where each interpretation can be conditioned by the area of the image that is being observed. Thus, ocular fixations can affect their final perception. To determine if the eye fixation areas influence the perception, 20 volunteers observed a bistable logo in front of a fixed eye-tracker, reference Tobii T-120. The results indicate that the reported percepts are related to ocular fixation areas. It is concluded that there are areas that affect the identification of the possible percepts of the bistable logo, which leads to essential considerations for graphic designers to optimize graphic brand communication. Els logotips biestables accepten dues interpretacions que poden estar condicionades per làrea que estigui sent observada. Així, les fixacions oculars poden afectar la percepció final. Per determinar si les zones de fixació ocular influeixen en la percepció, 20 voluntaris van observar un logotip biestable davant d'un eye-tracker fix (Tobii T-120). Els resultats indiquen que les percepcions reportades estan relacionades amb les àrees de fixació ocular. Es conclou que hi ha àrees que incideixen en la identificació de les possibles percepcions del logotip biestable, la qual cosa deriva en implicacions per als dissenyadors gràfics de cara a optimitzar la comunicació marca. Los logotipos biestables aceptan dos interpretaciones que pueden estar condicionadas por el área que esté siendo observada. Así, las fijaciones oculares pueden afectar la percepción final. Para determinar si las zonas de fijación ocular influyen en la percepción, 20 voluntarios observaron un logotipo biestable frente a un eye-tracker fijo (Tobii T-120). Los resultados indican que las percepciones reportadas están relacionadas con las áreas de fijación ocular. Se concluye que existen áreas que inciden en la identificación de las posibles percepciones del logotipo biestable, lo cual deriva en implicaciones para los diseñadores gráficos de cara a optimizar la comunicación de marca.

Bistable logos accept two different interpretations, where each interpretation can be conditioned by the area of the image that is being observed. Thus, ocular fixations can affect their final perception. To determine if the eye fixation areas influence the perception, 20 volunteers observed a bistable logo in front of a fixed eye-tracker, reference Tobii T-120. The results indicate that the reported percepts are related to ocular fixation areas. It is concluded that there are areas that affect the identification of the possible percepts of the bistable logo, which leads to essential considerations for graphic designers to optimize graphic brand communication.

Transition waves that sequentially switch bistable elements from one stable configuration to another have received significant interest in recent years not only because of their rich physics but also, for their potential applications, including unidirectional propagation, energy harvesting, and mechanical computation. Here, we exploit the propagation of transition waves in a bistable one-dimensional (1D) linkage as a robust mechanism to realize structures that can be quickly deployed. We first use a combination of experiments and analyses to show that, if the bistable joints are properly designed, transition waves can propagate throughout the entire structure and transform the initial straight configuration into a curved one. We then demonstrate that such bistable linkages can be used as building blocks to realize deployable three-dimensional (3D) structures of arbitrary shape.

Bistable morphing composites have shown promising applications in energy harvesting due to their capabilities to change their shape and maintain two different states without any external loading. In this review article, the application of these composites in energy harvesting is discussed. Actuating techniques used to change the shape of a composite structure from one state to another is discussed. Mathematical modeling of the dynamic behavior of these composite structures is explained. Finally, the applications of artificial-intelligence techniques to optimize the design of bistable structures and to predict their response under different actuating schemes are discussed.

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered nuances regarding sequence–ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine and the suggestion that well-mixed sequences form a range of conformations, including globules, conformations with ensemble averages that are reminiscent of ideal chains, or self-avoiding walks. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely, globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intrachain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. We also identify differences between aspartate- and glutamate-containing sequences, whereby the shorter aspartate side chain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

This work designs and analyzes a metastructure-based vibration isolation model to improve small-scale equipment's isolation effectiveness under low-frequency excitations. The feature of the proposed model is the high static and low dynamic stiffness characteristics, also called quasi-zero-stiffness (QZS), possessed by the metastructure under vertical load. The metastructure consists of four parallelly arranged unit cells, and the QZS property is realized in each unit cell by the snap-through behavior of the cosine beam system and the bending-dominated behavior of semicircular arches. The static characteristics of the metastructure are studied analytically and numerically and validated with experimental results. Based on the static analysis results, the dynamic equation of the proposed metastructure is set up in the form of Duffing's equation. The harmonic balance method is used to calculate the frequency response and motion transmissibility of the metastructure at steady state for a harmonic load. The time and frequency responses under the sinusoidal base excitation are examined analytically and numerically, and their results are compared. The simulation results revealed that the proposed QZS metastructure obtains lower transmissibility and wider effective isolation range compared to the equivalent linear model. The parametric study shows that in the low-frequency excitation region, the motion transmissibility increases with decreasing damping ratio, whereas for the effective isolation range, the motion transmissibility increases with increasing damping ratio. Finally, stability analysis is performed to study the unstable region in the frequency response curve. The parametric study indicates that the unstable region reduces with the increase in damping ratio and remains unaffected with varying excitation amplitude.

Multistable mechanical metamaterials are a type of mechanical metamaterials with special features, such as reusability, energy storage and absorption capabilities, rapid deformation, and amplified output forces. These metamaterials are usually realized by series and/or parallel of bistable units. They can exhibit multiple stable configurations under external loads and can be switched reversely among each other, thereby realizing the reusability of mechanical metamaterials and offering broad engineering applications. This paper reviews the latest research progress in the design strategy, manufacture and application of multistable mechanical metamaterials. We divide bistable structures into three categories based on their basic element types and provide the criterion of their bistability. Various manufacturing techniques to fabricate these multistable mechanical metamaterials are introduced, including mold casting, cutting, folding and three-dimensional/4D printing. Furthermore, the prospects of multistable mechanical metamaterials for applications in soft driving, mechanical computing, energy absorption and wave controlling are discussed. Finally, this paper highlights possible challenges and opportunities for future investigations. The review aims to provide insights into the research and development of multistable mechanical metamaterials. The design principle and advantages of multistable mechanical metamaterials were introduced. The most advanced manufacture techniques of multistable mechanical metamaterials were reviewed. Multistable mechanical metamaterials have attractive applications, such as wave control, soft actuator and energy absorption. Perspectives and challenges on multistable mechanical metamaterials were provided.

The collection of clean power from ambient vibrations is considered a promising method for energy harvesting. For the case of wheel rotation, the present study investigates the effectiveness of a piezoelectric energy harvester, with the application of stochastic resonance to optimize the efficiency of energy harvesting. It is hypothesized that when the wheel rotates at variable speeds, the energy harvester is subjected to on-road noise as ambient excitations and a tangentially acting gravity force as a periodic modulation force, which can stimulate stochastic resonance. The energy harvester was miniaturized with a bistable cantilever structure, and the on-road noise was measured for the implementation of a vibrator in an experimental setting. A validation experiment revealed that the harvesting system was optimized to capture power that was approximately 12 times that captured under only on-road noise excitation and 50 times that captured under only the periodic gravity force. Moreover, the investigation of up-sweep excitations with increasing rotational frequency confirmed that stochastic resonance is effective in optimizing the performance of the energy harvester, with a certain bandwidth of vehicle speeds. An actual-vehicle experiment validates that the prototype harvester using stochastic resonance is capable of improving power generation performance for practical tire application.

Effective reduction of micro-amplitude vibration has always been a serious challenge. The nonlinear energy sink (NES) has been proven to be able to reduce vibration at a wide frequency. However, the energy threshold of the NES prevents it from suppressing micro-vibrations. In this paper, a bistable nonlinear energy sink (BNES) based on a buckling beam oscillator is constructed. The threshold of the NES is lowered by the nonlinear dynamic behavior of jumping between wells of the bistable oscillator. The motion equations of the discrete–continuous system are derived by using Hamilton's principle. The approximate analytical solution is obtained and verified numerically. The results show that even when the primary system has a micro-amplitude resonance, the nonlinear cross-well vibration of the BNES can still reduce the vibration. The robustness of the BNES is stronger than that of the tuned mass damper (TMD). The optimal parameters of the BNES are obtained with particle swarm optimization (PSO) algorithm. The result of parameter optimization shows that the energy threshold of the nonlinear energy sink can be effectively lowered. In short, the method based on nonlinear dynamics in this paper provides an effective reduction strategy for micro-vibration in engineering. Graphical abstract