We uncover a chain of nonlinear modal interactions in softly clamped nanostring resonators. The process involves the sequential coupling of five mechanical modes, during frequency sweeps, yielding a broad nonlinear response with nearly constant amplitude. We demonstrate that soft clamping enables this cascaded energy transfer and amplifies the effective geometric nonlinearity of the driven mode by an order of magnitude. Analytical and finite element-based reduced-order models capture the key features of the coupling cascade and clarify its underlying mechanism. The phenomenon is generic in nonlinear vibrational systems and can be tailored through soft-clamping design strategies.

High-frequency stability is crucial for the performance of graphene resonators in sensing and timekeeping applications. However, the extreme miniaturization and high mechanical compliance that make graphene attractive also render it highly susceptible to nonlinearities, degrading frequency stability. Here, we demonstrate that graphene parametric oscillators provide an alternative nonlinear operating regime, where short-term frequency stability can be enhanced despite strong nonlinearity. By operating graphene resonators in a phase-locked loop, we experimentally demonstrate that parametric oscillations in the postbifurcation regime achieve lower Allan deviation at fast integration times than Duffing oscillations at identical amplitudes. This improvement originates from strong nonlinear damping inherent to parametric oscillators, which suppresses amplitude-to-frequency noise conversion at large amplitudes. A minimal theoretical model captures observed phase diffusion and identifies nonlinear damping as the dominant mechanism governing phase noise reduction. These results highlight the role of nonlinear dissipation in enabling precision sensing beyond conventional limits of graphene oscillators.

Mechanical cantilevers are central to nanotechnology, where low bending rigidity makes stability the fundamental challenge. Here, we introduce a wrinkle-induced stiffening approach that enhances the bending rigidity of monolayer graphene by several orders of magnitude, enabling the fabrication of mechanically robust graphene cantilevers. When suspended over microcavities, these wrinkled membranes exhibit significant increases in both in-plane and out-of-plane stiffness, as confirmed by nanoindentation and resonance measurements, which also reveal that enhanced bending rigidity strongly influences their vibrational response. This behavior marks a transition from tension-dominated mechanics to a regime where bending effects become prominent, even in a single atomic layer. By sculpting these structures, we realize graphene cantilevers with measured bending rigidities between 10⁶–10⁷ eV, while maintaining femtogram-scale mass. These findings establish a mechanical stabilization mechanism for realizing ultrathin cantilevers and highlight their potential for applications where high compliance is of importance.

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.

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.)

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.

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.

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.

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.

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.