The evolving designs and requirements of aircraft structural components has recently created an increased interest in application of nonlinear modelling techniques. While the finite element (FE) methods already incorporate the necessary mechanics to model nonlinear behavior in structures, a major drawback is the considerably higher computation cost in comparison to the linear counterparts. Reduced order modelling (ROM) techniques offer a solution to counter this limitation. The work presented here is focused on the Koiter-Newton (K-N) model reduction technique which is based on a cubically nonlinear mechanical model. The K-N method utilizes existing FE models as a starting point to generate equivalent ROM parameters and thus, can be applied to obtain ROMs for generic structures. The model validity is assessed by conducting nonlinear dynamic analyses of two models with different boundary conditions. Nonlinear frequency response analyses are conducted to demonstrate hardening effects in both the test cases. Comparisons to full FE analyses show significant reduction in computational times.

We demonstrate that a quiet state and large-amplitude self-sustained oscillations can coexist in a carbon nanotube subject to time-independent drive. A feature of the bistability is that it would be hysteresis free in the absence of noise, and the oscillatory state would not be seen. It is revealed by random switching between the stable states, which we observe in the time domain. We attribute the switching to fluctuations in the system and show that it displays Poisson statistics. We propose a minimalistic model that relates the emergence of the bistability to a nonmonotonic variation of nonlinear friction with the vibration amplitude. This new type of dynamical regime and the means to reveal it are generic and are of interest for various mesoscopic vibrational systems.

Nonlinear dynamic simulations of mechanical resonators have been facilitated by the advent of computational techniques that generate nonlinear reduced order models (ROMs) using the finite element (FE) method. However, designing devices with specific nonlinear characteristics remains inefficient since it requires manual adjustment of the design parameters and can result in suboptimal designs. Here, we integrate an FE-based nonlinear ROM technique with a derivative-free optimization algorithm to enable the design of nonlinear mechanical resonators. The resulting methodology is used to optimize the support design of high-stress nanomechanical Si ₃N ₄ string resonators, in the presence of conflicting objectives such as simultaneous enhancement of Q-factor and nonlinear Duffing constant. To that end, we generate Pareto frontiers that highlight the trade-offs between optimization objectives and validate the results both numerically and experimentally. To further demonstrate the capability of multi-objective optimization for practical design challenges, we simultaneously optimize the design of nanoresonators for three key figure-of-merits in resonant sensing: power consumption, sensitivity and response time. The presented methodology can facilitate and accelerate designing (nano) mechanical resonators with optimized performance for a wide variety of applications. (Figure presented.)

Synchronization plays a crucial role in the dynamics of living organisms. Uncovering the mechanism behind it requires an understanding of individual biological oscillators and the coupling forces between them. Here, a single-cell assay is developed that studies rhythmic behavior in the motility of E. coli cells that can be mutually synchronized. Circular microcavities are used to isolate E. coli cells that swim along the cavity wall, resulting in self-sustained oscillations. Connecting these cavities by microchannels yields synchronization patterns with phase slips. It is demonstrated that the coordinated movement observed in coupled E. coli oscillators follows mathematical rules of synchronization which is used to quantify the coupling strength. These findings advance the understanding of motility in confinement, and open up new opportunities for engineering networks of coupled oscillators in microbial active matter.

Cantilevers find a wide range of applications in the design of scientific equipment and large-scale engineering structures such as aircraft wings. Analysis techniques based on linearization approximations are unable to capture the large amplitude oscillation behaviour of such structures and thus, necessitates development of dedicated nonlinear methods. In this work, the recent developments in the Koiter-Newton model reduction method are utilized to obtain nonlinear reduced order models (ROMs) from full finite element structural models in order to simulate large amplitude dynamics of cantilevers. The method describes a nonlinear system of governing equations comprising quadratic and cubic terms which are obtained as higher order derivatives of the in-plane strain energy. To ensure that the large rotations in cantilevers and the resultant foreshortening effect is also accounted for, a ROM updating algorithm is adopted where the ROM parameters are varied with the structural deflections. Linear eigenmodes of the structure are utilized to form the reduction subspace. To validate the methodology, the ROM solution is compared against experimental results and a convergence study is conducted to identify the number of modes needed to replicate the nonlinear response. Finally, a composite wingbox structure is considered for which time domain simulations are conducted and frequency response curves, obtained through a frequency sweep, are presented.

The quality factor (Q factor) of nanomechanical resonators is influenced by geometry and stress, a phenomenon called dissipation dilution. Studies have explored maximizing this effect, leading to softly-clamped resonator designs. This paper proposes a topology optimization methodology to design two-dimensional nanomechanical resonators with high Q factors by maximizing dissipation dilution. A formulation based on the ratio of geometrically nonlinear to linear modal stiffnesses of a prestressed finite element model is used, with its corresponding adjoint sensitivity analysis formulation. Systematic design in square domains yields geometries with comparable Q factors to literature. We analyze the trade-offs between resonance frequency and quality factor, and how these are reflected in the geometry of resonators. We further apply the methodology to optimize a resonator on a full hexagonal domain. By using the entire mesh—i.e., without assuming any symmetries—we find that the optimizer converges to a two-axis symmetric design comprised of four tethers.

Nanomechanical resonances of two-dimensional (2D) materials are sensitive probes for condensedmatter physics, offering new insights into magnetic and electronic phase transitions. Despite extensive research, the influence of the spin dynamics near a phase transition on the nonlinear dynamics of 2D membranes has remained largely unexplored. Here, we investigate nonlinear magneto-mechanical coupling to antiferromagnetic order in suspended FePS3-based heterostructure membranes. By monitoring the motion of these membranes as a function of temperature, we observe characteristic features in both nonlinear stiffness and damping close to the Néel temperature TN. We account for these experimental observations with an analytical magnetostriction model in which these nonlinearities emerge from a coupling between mechanical and magnetic oscillations, demonstrating that magneto-elasticity can lead to nonlinear damping. Our findings thus provide insights into the thermodynamics and magneto-mechanical energy dissipation mechanisms in nanomechanical resonators due to the material’s phase change and magnetic order relaxation.

The unique properties of two-dimensional (2D) materials bring great promise to improve sensor performance and realise novel sensing principles. However, to enable their high-volume production, wafer-scale processes that allow integration with electronic readout circuits need to be developed. In this perspective, we review recent progress in on-chip 2D material sensors, and compare their performance to the state-of-the-art, with a focus on results achieved in the Graphene Flagship programme. We discuss transfer-based and transfer-free production flows and routes for complementary metal-oxide-semiconductor integration and prototype development. Finally, we give an outlook on the future of 2D material sensors, and sketch a roadmap towards realising their industrial and societal impact.

Recent investigations pertaining to high aspect ratio wings have demonstrated the influence of geometric nonlinearities on structural and aeroelastic response when large deflections occur [1,2]. While utilization of nonlinear analyses techniques is beneficial for more realistic predictions of large deflection behaviour, it is accompanied with the drawback of high computational costs since finite element (FE) solvers are based on iterative predictor-corrector models. Nonlinear reduced order modelling can be an effective tool for conducting efficient analyses in such cases. In the proposed study we aim to exploit the recent developments in the Koiter-Newton (K-N) model reduction technique [3] for nonlinear dynamic response analysis of a high aspect ratio wing and thus, demonstrate the achievable reduction in computational costs in comparison to full FE simulations. The K-N reduction is a FE-based formulation which describes a system of nonlinear governing equations comprising quadratic and cubic stiffness terms. The higher order stiffness terms are evaluated as derivatives of the in-plane strain energy. To ensure that the effect of large rotations is accounted for, the reduced order model (ROM) is updated at fixed load intervals. Linear eigenmodes of the deformed structure are used to formulate the reduction subspace at the different load steps. The test structure chosen in this work is a variant of the Pazy wing [4] which is an experimental benchmark wing designed for nonlinear aeroelastic studies. The Pazy wing variant is based on the dimensions of the original design with minor modifications in the inner geometry. The FE model is constructed entirely using shell elements with 21,712 grid points and 130,272 degrees of freedom. For the initial validation, we conduct a nonlinear static analysis with a concentrated follower force, and compare it to FE solution from MSC Nastran. It is seen that by using just a single degree of freedom ROM, the nonlinear static solution is reproducible within a 2 % error margin for up to 40 % tip deflections. Subsequently, a nonlinear dynamic response analysis is conducted where the wing is subjected to large amplitude transient loads. The preliminary studies show a reduction in simulation time of over 95 % without significant loss in solution accuracy. References [1] Riso, Cristina, and Carlos E. Cesnik. "Low-Order Geometrically Nonlinear Aeroelastic Modeling and Analysis of the Pazy Wing Experiment." AIAA SciTech 2022 Forum. 2022. [2] Hilger, Jonathan, and Markus Raimund Ritter. "Nonlinear aeroelastic simulations and stability analysis of the Pazy wing aeroelastic benchmark." Aerospace 8.10 (2021): 308. [3] Sinha, Kautuk, et al. "Koiter–Newton Based Model Reduction for Large Deflection Analysis of Wing Structures." AIAA Journal (2023): 1-10. [4] Avin, Or, et al. "Experimental aeroelastic benchmark of a very flexible wing." AIAA Journal 60.3 (2022): 1745-1768.

Multi-material direct ink writing (DIW) of smart materials opens new possibilities for manufacturing complex-shaped structures with embedded sensing and actuation capabilities. In this study, DIW of UV-curable piezoelectric actuators is developed, which do not require high-temperature sintering, allowing direct integration with structural materials. Through particle size and ink rheology optimization, the highest d₃₃^*g₃₃ piezoelectric constant compared to other DIW fabricated piezo composites is achieved, enabling tunable actuation performance. This is used to fabricate ultrasound transducers by printing piezoelectric vibrating membranes along with their support structures made from a structural ink. The impact of transducer design and scaling up transducer dimensions on the resonance behavior to design millimeter-scale ultrasound transducers with desired out-of-plane displacement is explored. A significant increase in output pressure with increasing membrane dimensions is observed. Finally, a practical application is demonstrated by using the printed transducer for accurate proximity sensing using time of flight measurements. The scalability and flexibility of the reported DIW of piezo composites can open up new advancements in biomedical, human-computer interaction, and aerospace fields.

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here, we introduce a methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a manufacturing process to create ultra-large graphene drums with diameters of up to 1000 μm. We solve the inverse problem of a Föppl–von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced methodology allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.

Although strain engineering and soft-clamping techniques for attaining high Q-factors in nanoresonators have received much attention, their impact on nonlinear dynamics is not fully understood. In this study, we show that nonlinearity of high-Q Si₃N₄ nanomechanical string resonators can be substantially tuned by support design. Through careful engineering of support geometries, we control both stress and mechanical nonlinearities, effectively tuning nonlinear stiffness of two orders of magnitude. Our approach also allows control over the sign of the Duffing constant resulting in nonlinear softening of the mechanical mode that conventionally exhibits hardening behavior. We elucidate the influence of support design on the magnitude and trend of the nonlinearity using both analytical and finite element-based reduced-order models that validate our experimental findings. Our work provides evidence of the role of soft-clamping on the nonlinear dynamic response of nanoresonators, offering an alternative pathway for nullifying or enhancing nonlinearity in a reproducible and passive manner.

Through molecular dynamics simulations, we demonstrate the possibility of internal resonances in single-walled carbon nanotubes. The resonant condition is engineered with a lack of symmetry in the boundary condition and activated by increasing the energy exchange with a coupled thermal bath. The critical temperature threshold for initiating modal interaction is found to be chirality-dependent. By applying the proper orthogonal decomposition algorithm to molecular dynamics time responses, we show how the thermal fluctuations influence the vibrational behaviour of the nanotube leading to both flexural–flexural and flexural–longitudinal resonances. Understanding the interaction between nanotube resonators and the thermal bath is crucial for designing and optimizing their performance for various nanoscale sensing, actuation, and signal processing applications.

Resonators based on two-dimensional (2D) materials have exceptional properties for application as nanomechanical sensors, which allows them to operate at high frequencies with high sensitivity. However, their performance as nanomechanical sensors is currently limited by their low quality ( Q )-factor. Here, we make use of micro-electromechanical systems (MEMS) to apply pure in-plane mechanical strain, enhancing both their resonance frequency and Q-factor. In contrast to earlier work, the 2D material resonators are fabricated on the MEMS actuators without any wet processing steps using a dry-transfer method. A platinum clamp, which is deposited by electron beam-induced deposition, is shown to be effective in fixing the 2D membrane to the MEMS and preventing slippage. By in-plane straining the membranes in a purely mechanical fashion, we increase the tensile energy, thereby diluting dissipation. This way, we show how dissipation dilution can increase the Q -factor of 2D material resonators by 91%. The presented MEMS actuated dissipation dilution method does not only pave the way toward higher Q -factors in resonators based on 2D materials, but also provides a route toward studies of the intrinsic loss mechanisms of 2D materials in the monolayer limit.

The ultimate isolation offered by levitation provides new opportunities for studying fundamental science and realizing ultra-sensitive floating sensors. Among different levitation schemes, diamagnetic levitation is attractive because it allows stable levitation at room temperature without a continuous power supply. While the dynamics of diamagnetically levitating objects in the linear regime are well studied, their nonlinear dynamics have received little attention. Here, we experimentally and theoretically study the nonlinear dynamic response of graphite resonators that levitate in permanent magnetic traps. By large amplitude actuation, we drive the resonators into nonlinear regime and measure their motion using laser Doppler interferometry. Unlike other magnetic levitation systems, here we observe a resonance frequency reduction with amplitude in a diamagnetic levitation system that we attribute to the softening effect of the magnetic force. We then analyze the asymmetric magnetic potential and construct a model that captures the experimental nonlinear dynamic behavior over a wide range of excitation forces. We also investigate the linearity of the damping forces on the levitating resonator, and show that although eddy current damping remains linear over a large range, gas damping opens a route for tuning nonlinear damping forces via the squeeze-film effect.

Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degree-of-freedom models have been used to account for experimentally observed nonlinear effects, it is shown that these models quickly deviate from experimental findings when multiple modes influence the nonlinear response. Here, we present a nonlinear reduced-order modeling methodology based on finite-element method simulations for capturing the global nonlinear dynamics of nanomechanical resonators. Our physics-based approach obtains the quadratic and cubic nonlinearities of resonators over a wide frequency range that spans 70 MHz. To qualitatively validate our approach, we perform experiments on a graphene nanodrum driven optothermally and show that the model can replicate diverse ranges of nonlinear phenomena, including multistability, parametric resonance, and different internal resonances without considering any empirical nonlinear fitting parameters. By providing a direct link between microscopic geometry, material parameters, and nonlinear dynamic response, we clarify the physical significance of nonlinear parameters that are obtained from fitting the dynamics of nanomechanical systems, and provide a route for designing devices with desired nonlinear behavior.

Bacteria that are resistant to antibiotics present an increasing burden on healthcare. To address this emerging crisis, novel rapid antibiotic susceptibility testing (AST) methods are eagerly needed. Here, we present an optical AST technique that can determine the bacterial viability within 1 h down to a resolution of single bacteria. The method is based on measuring intensity fluctuations of a reflected laser focused on a bacterium in reflective microwells. Using numerical simulations, we show that both refraction and absorption of light by the bacterium contribute to the observed signal. By administering antibiotics that kill the bacteria, we show that the variance of the detected fluctuations vanishes within 1 h, indicating the potential of this technique for rapid sensing of bacterial antibiotic susceptibility. We envisage the use of this method for massively parallelizable AST tests and fast detection of drug-resistant pathogens.

Wing structures subjected to large deflections are prone to nonlinear load-deflection behavior. Geometric nonlinearities can arise due to the accompanying large rotations and in-plane deflections that manifest in the form of stiffening effects in the nonlinear static response. To account for these nonlinearities, reduced-order modeling techniques in combination with nonlinear finite element formulations have been previously proposed. However, these methods often have a limited range of validity due to linear eigenmode-based formulations with assumptions of small rotations. In this paper, a large deflection analysis framework based on the Koiter–Newton model reduction technique is presented. It is demonstrated that the reduced model in its basic form is ineffective for large deflection analysis. To resolve this, an incremental updating procedure is used for the reduced-order model that incorporates the necessary nonlinear effects. The model updating enables the computation of nonlinear response for a large range of deflections.

Mechanical resonators that possess coupled modes with harmonic frequency relations have recently sparked interest due to their suitability for controllable energy transfer and non-Hermitian dynamics. Here we show coupling between high-𝑄-factor (greater than 104) resonances with a nearly 1:1 frequency relation in spatially symmetric microresonators. We develop and demonstrate a method to analyze their dynamical behavior based on the simultaneous and resonant detection of both spectral peaks, and validate this with experimental results. The frequency difference between the peaks modulates their ringdown, and creates a beat pattern in the linear decay. This method applies to both the externally driven regime and the Brownian-motion (thermal) regime, and allows characterization of both linear and nonlinear parameters. The mechanism behind this method renders it broadly applicable to both optical and electrical readout, as well as to different mechanical systems. This will aid studies using near-degenerate mechanical modes, for example, optomechanical energy transfer, synchronization, and gyroscopic sensors.

This study examines the nonlinear dynamics in tapping-mode atomic force microscopy (AFM) with tip-surface interactions that include van der Waals and Derjaguin-Muller- € Toporov contact forces. We investigate the periodic solutions of the hybrid system by performing numerical pseudo-arclength continuation. Through the use of bifurcation locus maps in the set of parameters of the discontinuous model, the overall dynamical response scenario is assessed. We demonstrate the influence of various dissipation mechanisms that are related with the AFM touching or lacking contact with the sample. Local and global analyses are used to investigate the stability of the stable solution in the repulsive regime. The impacting nonsmooth dynamics framed within a higher-mode Galerkin discretization is able to capture windows of irregular and complex motion.