Micromechanical resonators, which have become feasible due to advanced manufacturing techniques, have shown several interesting phenomena including mode coupling in a range of applications that span metrology and sensing. Conventional fabrication methods of these resonators have been used throughout the field. However, fabrication of micromechanical resonators by femtosecond laser ablation which could accelerate prototyping, access to three dimensional resonators and reduce clean room use, has received little attention.

In this study, a protocol for fabricating and measuring laser cut micromechanical resonators using computational analysis and experimental techniques has been developed and validated through comparison with previous works by characterising doubly clamped beam resonators. The fabricated prototype is demonstrated to exhibit autoparametric resonance and coupling showcasing the potential of the new approach in engineering and fast prototyping of coupled micromechanical resonators.

The predominant influence of geometry and tensile stress on the Q factor of nanomechanical resonators is a phenomenon commonly described as dissipation dilution. In recent years, a variety of studies has looked into maximizing this effect, resulting in an assortment of softly-clamped resonator designs. This paper proposes a methodology that uses topology optimization (TO) to design nanomechanical structures with very high Q factors, by maximizing the effects of dissipation dilution. A novel equation, based on the tensile and bending energies of a prestressed finite element model, is proposed to capture this effect. Through adjoint sensitivity analysis, the sensitivity of this function with respect to (changes in) element-level design parameters was determined, which is a capability that is not available in commercial finite element packages. Furthermore, the absence of information required a priori to the optimization makes the proposed methodology versatile and easy to use. After verification of the equation and its sensitivity, it is used as an objective in TO to optimize resonator geometries inspired by state-of-the-art resonator designs. Given a thickness of 340nm and prestress of 1GPa, the final designs show a numerical Q × f0 that competes with optimized designs found in literature.

Mode coupling has extensive use in the MEMS field, including frequency division, vibration direction conversion, and energy transfer. In practice, these applications can be used to improve the performance of various devices such as sensors and energy harvesters. Nonlinear spring also has a wide application in MEMS field. Various nonlinear spring mechanisms, such as fixed-angle bows, bistable rotational mechanisms, H-shaped springs, and topology-optimized planar springs, have been proposed and utilized. Nevertheless, there is a lack of non-electric design elements specifically designed for mode coupling. This thesis proposes a simple system demonstrating the feasibility of using a nonlinear spring to achieve mode coupling. The system incorporates a spring-mass system with two mass blocks, two linear stages, and a unique nonlinear spring compliant mechanism. The integrated components can be fabricated using 3D printing resin or high-precision femtosecond laser-cutting of silicon wafers. Additionally, a new crank-slider structure and a spline-shaped nonlinear spring are developed and studied for this system. Each has advantages and disadvantages, and is suitable for systems of different sizes and materials respectively. Their load-displacement relationship roughly satisfies the cubic relationship, but still has a linear term. The proposed system holds potential for enhancing the performance of sensors, energy harvesters, and other MEMS devices.