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.)

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.

The resonance frequency of ultra-thin layered nanomaterials changes nonlinearly with the tension induced by the pressure from the surrounding gas. Although the dynamics of pressurized nanomaterial membranes have been extensively explored, recent experimental observations show significant deviations from analytical predictions. Here, we present a multi-mode continuum model that captures the nonlinear pressure-frequency response of pre-tensioned membranes undergoing large deflections. We validate the model using experiments conducted on polysilicon nanodrums excited opto-thermally and subjected to pressure changes in the surrounding medium. We demonstrate that considering the effect of pressure on the nanodrum tension is not sufficient for determining the resonance frequencies. In fact, it is essential to also account for the change in the membrane’s shape in the pressurized configuration, the mid-plane stretching, and the contributions of higher modes to the mode shapes. Finally, we show how the presented high-frequency mechanical characterization method can serve as a fast and contactless method for determining Young’s modulus of ultra-thin membranes.

Owing to their atomic thickness and low bending rigidity, suspended two-dimensional (2D) materials are prone to wrinkle formation. Here, we use molecular dynamics (MD) simulations to probe the effect of these wrinkles on the nonlinear elasticity of atomically thin graphene membranes. We observe a stress-strain response that consists of two linear regions that are separated by a transition. It is found that this transition is sharp in membranes where wrinkles are formed by uneven stresses at the boundaries. However, when wrinkles are formed by crystal defects, this nonlinear transition is seen to be more gradual. To capture these effects, we use a phenomenological model based on experimentally measurable quantities. We demonstrate the model's fidelity by fitting it to the MD simulated nonlinear response of many graphene membranes providing evidence that the sharpness of the transition between the linear regions in the stress-strain response is a measure of the type of wrinkles and can be quantified by our model.