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This research examines the free vibration characteristics of composite ring-like structures enhanced with carbon nanotubes (CNTs), taking into account the effects of CNT agglomeration. The structural framework comprises two concentric composite rings linked by elastic springs, creating a coupled beam ring (CBR) system. The first-order shear deformation theory (FSDT) is applied to account for transverse shear deformation, while Hamilton’s principle is employed to formulate the governing equations of motion. The effective mechanical properties of the composite material are assessed with regard to CNT agglomeration, which has a significant impact on the elastic modulus and the overall dynamic behavior of the structure. The numerical analysis explores the influence of porosity distribution, boundary conditions (BCs), and the stiffness of the springs on the natural vibration frequencies (NVFs). The results demonstrate that an increase in CNT agglomeration leads to a reduction in the stiffness of the composite, consequently decreasing the NVFs. Furthermore, asymmetric porosity distributions result in nonlinear fluctuations in NVFs due to irregularities in mass and stiffness, whereas uniform porosity distributions display a nearly linear relationship. This study also emphasizes the importance of boundary conditions and elastic coupling in influencing the vibrational response of CBR systems. These findings offer significant insights for the design and optimization of advanced composite ring structures applicable in aerospace, nanotechnology, and high-performance engineering systems.

A passive solid cannot do work on its surroundings through any quasistatic cycle of deformations. This property places strong constraints on the allowed elastic moduli. In this Article, we show that static elastic moduli altogether absent in passive elasticity can arise from active, non-conservative microscopic interactions. These active moduli enter the antisymmetric (or odd) part of the static elastic modulus tensor and quantify the amount of work extracted along quasistatic strain cycles. In two-dimensional isotropic media, two chiral odd-elastic moduli emerge in addition to the bulk and shear moduli. We discuss microscopic realizations that include networks of Hookean springs augmented with active transverse forces and non-reciprocal active hinges. Using coarse-grained microscopic models, numerical simulations and continuum equations, we uncover phenomena ranging from auxetic behaviour induced by odd moduli to elastic wave propagation in overdamped media enabled by self-sustained active strain cycles. Our work sheds light on the non-Hermitian mechanics of two- and three-dimensional active solids that conserve linear momentum but exhibit a non-reciprocal linear response. Active, non-conservative interactions can give rise to elastic moduli that are forbidden in equilibrium and enter the antisymmetric part of the stiffness tensor. The resulting solids function as distributed elastic engines that can perform work on their surroundings through quasistatic strain cycles.

We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground springs at locations determined by projecting from a circle onto an underlying periodic system. A family of periodic and quasiperiodic structures is obtained by smoothly varying a parameter defining such projection. Numerical simulations show the existence of vibration modes that first localize at a boundary, and then migrate into the bulk as the projection parameter is varied. Explicit expressions predicting the change in the density of states of the bulk define topological invariants that quantify the number of modes spanning a gap of a finite structure. We further demonstrate how modulating the phase of the ground springs distribution causes the topological states to undergo an edge-to-edge transition. The considered configurations and topological studies provide a framework for inducing localized modes in continuous elastic structural components through globally spanning, deterministic perturbations of periodic patterns defined by the considered projection operations.

The exploration of physical degrees of freedom of light with infinite dimensionality, such as orbital angular momentum (OAM) and frequency, has profoundly reshaped the landscape of modern optics, with representative photonic functional devices including optical vortex emitters and frequency combs. In nanophotonics, whispering gallery mode microresonators naturally support applications based on the OAM of light and have been employed as on-chip emitters of monochromatic optical vortices. On the other hand, whispering gallery mode microresonators can serve as a highly efficient non-linear optical platform for producing light at different frequencies, that is, microcombs. Here we combine optical vortices and microcombs by demonstrating an optical vortex comb on a III–V integrated non-linear ring microresonator. The angular grating-dressed non-linear microring simultaneously emits spatiotemporal light springs consisting of 50 OAM modes, with each frequency of the microcomb carrying a distinct OAM value. We also experimentally generate optical pulses with time-varying OAM by carefully endowing the spatiotemporal light springs with a specific intermodal phase relation. We expect our work to favour the development of integrated non-linear and quantum photonics for exploring fundamental optical physics and advancing photonic quantum technology. Microring-based vortex combs with each comb line carrying a distinct orbital angular momentum generate light springs with time-varying orbital angular momenta.

It has been recently shown that it is possible to design simple artificial swimmers at low Reynolds number that possess only one degree of freedom and, nevertheless, can overcome Purcell’s celebrated scallop theorem. One of the few examples is given by Montino and DeSimone, Eur. Phys. J. E, vol. 38, 2015, who consider the three-sphere Swimmer of Najafi and Golestanian, replacing one active arm with a passive elastic spring. We further generalize this idea by increasing the number of springs and show that it is possible to invert the swimming direction using the frequency of the single actuated arm. Il a récemment été prouvé qu’il était possible de créer des modèles simples de nageurs artificiels à bas nombre de Reynolds avec un seul degré de liberté, mais qui réussissaient cependant à sortir du cadre du fameux théorème de la coquille Saint-Jacques de Purcell. Un des exemples notables est le nageur de Montino et DeSimone, Eur. Phys. J. E, vol. 38, 2015, qui étudient le nageur à trois sphères de Najafi et Golestanian, en remplaçant un des bras actifs par un ressort passif. Nous généralisons cette idée en augmentant le nombre de ressorts et en montrant qu’il est possible de contrôler la direction du nageur en jouant sur la fréquence d’oscillation du bras actif.

Crystalline metals can have large theoretical elastic strain limits. However, a macroscopic block of conventional crystalline metals practically suffers a very limited elastic deformation of <0.5% with a linear stress–strain relationship obeying Hooke’s law. Here, we report on the experimental observation of a large tensile elastic deformation with an elastic strain of >4.3% in a Cu-based single crystalline alloy at its bulk scale at room temperature. The large macroscopic elastic strain that originates from the reversible lattice strain of a single phase is demonstrated by in situ microstructure and neutron diffraction observations. Furthermore, the elastic reversible deformation, which is nonhysteretic and quasilinear, is associated with a pronounced elastic softening phenomenon. The increase in the stress gives rise to a reduced Young’s modulus, unlike the traditional Hooke’s law behaviour. The experimental discovery of a non-Hookean large elastic deformation offers the potential for the development of bulk crystalline metals as high-performance mechanical springs or for new applications via “elastic strain engineering.” Engineering metals often suffer from a small elastic deformation with a linear stress-strain relationship obeying Hooke’s law. Here the authors observe a large nonlinear tensile elastic deformation with a strain of >4.3% in a bulk Cu alloy that offers potential for elastic strain engineering.

In biological and engineered systems, an inherent trade-off exists between the force and velocity that can be delivered by a muscle, spring, or combination of the two. However, one can amplify the maximum throwing power of an arm by storing the energy in a bow or sling shot with a latch mechanism for sudden release. Ilton et al. used modeling to explore the performance of motor-driven versus spring-latch systems in engineering and biology across size scales. They found a range of general principles that are common to animals, plants, fungi, and machines that use elastic structures to maximize kinetic energy. Science , this issue p. eaao1082 Combining motors, springs, and latches offers many routes to optimization of mechanical power in biological and engineered systems. Mechanical power limitations emerge from the physical trade-off between force and velocity. Many biological systems incorporate power-enhancing mechanisms enabling extraordinary accelerations at small sizes. We establish how power enhancement emerges through the dynamic coupling of motors, springs, and latches and reveal how each displays its own force-velocity behavior. We mathematically demonstrate a tunable performance space for spring-actuated movement that is applicable to biological and synthetic systems. Incorporating nonideal spring behavior and parameterizing latch dynamics allows the identification of critical transitions in mass and trade-offs in spring scaling, both of which offer explanations for long-observed scaling patterns in biological systems. This analysis defines the cascading challenges of power enhancement, explores their emergent effects in biological and engineered systems, and charts a pathway for higher-level analysis and synthesis of power-amplified systems.

Microscale organisms and specialized motile cells use protein-based spring-like responsive structures to sense, grasp and move. Rendering this biomechanical transduction functionality in an artificial micromachine for applications in single-cell manipulations is challenging due to the need for a bio-applicable nanoscale spring system with a large and programmable strain response to piconewton-scale forces. Here we present three-dimensional nanofabrication and monolithic integration, based on an acrylic elastomer photoresist, of a magnetic spring system with quantifiable compliance sensitive to 0.5 pN, constructed with customized elasticity and magnetization distributions at the nanoscale. We demonstrate the effective design programmability of these ‘picospring’ ensembles as energy transduction mechanisms for the integrated construction of customized soft micromachines, with onboard sensing and actuation functions at the single-cell scale for microrobotic grasping and locomotion. The integration of active soft springs into three-dimensional nanofabrication offers an avenue to create biocompatible soft microrobots for non-disruptive interactions with biological entities. Here, 3D nanofabrication and elasticity programming of monolithic soft microrobots equipped with magnetic springs with strain response at piconewton forces capable of deformation on micrometre length scales is demonstrated for applications in cell force sensing, cell manipulation and soft actuation.

Quasi-zero stiffness (QZS) isolators can achieve superior performance in vibration isolation; however, this superiority is often effective only for an excitation with the small excitation amplitude due to the narrow QZS region around the static equilibrium positions. A QZS isolator with multi-pairs of oblique springs can increase the QZS region, but its isolation frequency band is still narrow owing to the large static deflection. This article presents an improved isolator with two pairs of oblique springs by setting an initial position to be located between the supporting points of the upper pair of oblique springs and the equilibrium position so that the static deflection is significantly decreased, and thus, the isolation frequency band can be considerably increased. New formulations of stiffness and displacement transmissibility are derived for the improved QZS isolator. A prototype is designed, fabricated and tested to verify benefits of the present QZS isolator for vibration mitigation. Numerical results of the present isolator predicted by experiment and theory are compared with those of the corresponding linear isolator and previous QZS isolator to show advantages of the innovated design for vibration isolation.

Droplet rebound is ubiquitous on super-repellent surfaces. Conversion between kinetic and surface energies suggests that rebound suppression is unachievable due to negligible energy dissipation. Here, we present an effective approach to suppressing rebounds by incorporating bubbles into droplets, even in super-repellent states. This suppression arises from the counteractive capillary effects within bubble-encapsulated hollow droplets. The capillary flows induced by the deformed inner-bubble surface counterbalance those driven by the outer-droplet surface, resulting in a reduction of the effective take-off momentum. We propose a double-spring system with reduced effective elasticity for hollow droplets, wherein the competing springs offer distinct behavior from the classical single-spring model employed for single-phase droplets. Through experimental, analytical, and numerical validations, we establish a comprehensive and unified understanding of droplet rebound, by which the behavior of single-phase droplets represents the exceptional case of zero bubble volume and can be encompassed within this overarching framework. So far, attempts to prevent droplet rebound rely on augmenting energy dissipation. Here, the authors present that the rebound of hollow droplets is suppressed even on super-repellent surfaces, reminiscent of zero-surface-tension liquid droplets.