The design and the combination of innovative metamaterials are attracting increasing interest in the scientific community because of their unique properties that go beyond the ones of natural materials. In particular, auxetic materials and phononic crystals are widely studied for their negative Poisson’s ratio and their bandgap opening properties, respectively. In this work, auxeticity and phononic crystals bandgap properties are properly combined to obtain a single phase periodic structure with a tridimensional wide tunable bandgap. When an external tensile load is applied to the structure, the auxetic unit cells change their configurations by exploiting the negative Poisson’s ratio and this results in the tuning, either hardening or softening, of the frequencies of the modes limiting the 3D bandgap. Moreover, the expansion of the unit cell in all the directions, due to the auxeticity property, guarantees a fully 3D bandgap tunability of the proposed structure. Numerical simulations and analytical models are proposed to prove the claimed properties. The first experimental evidence of the tunability of a wide 3D bandgap is then shown thanks to the fabrication of a prototype by means of additive manufacturing.

Parametric amplification, resulting from intentionally varying a parameter in a resonator at twice its resonant frequency, has been successfully employed to increase the sensitivity of many micro- and nano-scale sensors. Here, we introduce the concept of self-induced parametric amplification, which arises naturally from nonlinear elastic coupling between the degenerate vibration modes in a micromechanical disk-resonator and is not externally applied. The device functions as a gyroscope wherein angular rotation is detected from Coriolis coupling of elastic vibration energy from a driven vibration mode into a second degenerate sensing mode. While nonlinear elasticity in silicon resonators is extremely weak, in this high quality-factor device, ppm-level nonlinear elastic effects result in an order-of-magnitude increase in the observed sensitivity to Coriolis force relative to linear theory. Perfect degeneracy of the primary and secondary vibration modes is achieved through electrostatic frequency tuning, which also enables the phase and frequency of the parametric coupling to be varied and we show that the resulting phase and frequency dependence of the amplification follow the theory of parametric resonance. We expect that this phenomenon will be useful for both fundamental studies of dynamic systems with low dissipation and for increasing signal-to-noise ratio in practical applications such as gyroscopes.

This paper is devoted to a detailed analysis of the appearance of frequency combs in the dynamics of a micro-electro-mechanical systems (MEMS) resonator featuring 1:2 internal resonance. To that purpose, both experiments and numerical predictions are reported and analysed to predict and follow the appearance of the phononic frequency comb arising as a quasi-periodic regime between two Neimark-Sacker bifurcations. Numerical predictions are based on a reduced-order model built thanks to an implicit condensation method, where both mechanical nonlinearities and electrostatic forces are taken into account. The reduced order model is able to predict a priori, i.e. without the need of experimental calibration of parameters, and in real time, i.e. by solving one or two degrees-of-freedom system of equations, the nonlinear behaviour of the MEMS resonator. Numerical predictions show a good agreement with experiments under different operating conditions, thus proving the great potentiality of the proposed simulation tool. In particular, the bifurcation points and frequency content of the frequency comb are carefully predicted by the model, and the main features of the periodic and quasi-periodic regimes are given with accuracy, underlining that the complex dynamics of such MEMS device is effectively driven by the characteristics of the 1:2 internal resonance.

This paper reports the developments toward an integrated, tri-axial, frequency-modulated, consumergrade, and microelectromechanical system (MEMS) gyroscope. A custom low-power (160 μA), low-phase-noise integrated circuit is designed specifically for frequencymodulated operation. Both yawand pitch-rate sensing systems are demonstrated by coupling the circuit with two novel micromachined structures fabricated with a 24-μmthick industrial process. In operation, both gyroscopes show a repeatable and stable scale factor, with less than 0.55% of part-to-part variability, obtained with no any calibration, and 35 ppm/°C of variability over a 25-70 °C temperature range.

MEMS loudspeakers are emerging as very promising solutions to meet the ever-increasing requirements for modern audio devices to become smaller, lighter and potentially more power efficient. The piezoelectric actuation principle, thanks to the relatively large driving force achievable at low voltages, represents the most promising implementation of loudspeakers at the microscale. Despite a significant number of new structures have been proposed in the last years, research work is still needed both at the design level, in order to obtain full-range microspeakers with good sound quality, and at the simulation level, to accurately capture the linear and nonlinear responses of these type of devices. We here propose the design, modeling and characterization of a high performance piezoelectric MEMS speaker for in-ear applications, based on a piston-like movement of the microspeaker central component, connected to the actuators through a set of folded springs. The device features a Sound Pressure Level (SPL) greater than 107from 500onwards for actuation voltages of 30 V $_{\text{pp}}$ and a compact footprint of product-units = power4.5 x 4.5. A Total Harmonic Distortion (THD) smaller than 1% has also been observed at 1at 94dBSPL. Therefore, even if at the prototype stage, the proposed device represents a promising solution towards a new set of high performances piezo-MEMS speakers that do not require further additional closing membranes to minimize acoustic losses. An excellent numerical-experimental matching in terms of SPL was also proved, thus opening the path to a new systematic design procedure for this class of MEMS structures. 2023-0113

Micro-Electro-Mechanical Systems revolutionized the consumer market for their small dimensions, high performances and low costs. In recent years, the evolution of the Internet of Things is posing new challenges to MEMS designers that have to deal with complex multiphysics systems experiencing highly nonlinear dynamic responses. To be able to simulate a priori and in real-time the behavior of such systems it is thus becoming mandatory to understand the sources of nonlinearities and avoid them when harmful or exploit them for the design of innovative devices. In this work, we present the first numerical tool able to estimate a priori and in real-time the complex nonlinear responses of MEMS devices without resorting to simplified theories. Moreover, the proposed tool predicts different working conditions without the need of ad-hoc calibration procedures. It consists in a nonlinear Model Order Reduction Technique based on the Implicit Static Condensation that allows to condense the high fidelity FEM models into few degrees of freedom, thus greatly speeding-up the solution phase and improving the design process of MEMS devices. In particular, the 1:2 internal resonance experienced in a MEMS gyroscope test-structure fabricated with a commercial process is numerically investigated and an excellent agreement with experiments is found.