This dissertation presents theoretical and experimental investigations into the dynamical behavior of Micro electromechanical systems (MEMS) resonators and their exploitation for filtering, sensing, and logic applications. The dissertation is divided into two parts: MEMS coupled structures and MEMS dynamic logic devices. First, a theoretical and experimental investigation is presented on both electrostatically and mechanically coupled resonator. Static and dynamic analysis is presented for weakly electrostatically coupled silicon microbeams and also for strongly mechanically coupled polyimide microbeams. The static analysis focuses on revealing pull-in characteristics, while the dynamic analysis focuses on the frequency response of the system and its exploitation for potential applications in filtering and amplification. Next, the phenomenon of mode localization is explored theoretically and experimentally on both electrostatically and mechanically weakly coupled resonators. Eigenvalue analysis is conducted and the dynamic response of the coupled system under different external perturbations is investigated. It is observed, that the exploitation of mode localization depends on the choice of the resonator to be under direct excitation, its stiffness to be perturbed, and which resonator is used to record the output results. These understandings will potentially help improve the performance of MEMS mode-localized sensors. Finally, three techniques to realize cascadable MEMS logic devices are presented. MEMS logic device vibrates at two steady states; a high on-resonance state (1) and a low off-resonance state (0). First, a MEMS logic device is presented capable of performing the AND/NAND logic gate and a tri-state logic gate using mixed-frequency excitation. This work is based on the concept of activation (1) and deactivation (0) of combination resonances due to the mixing of two or more input signals. Second, exploitation of subharmonic resonance under an AC only excitation to perform AND logic operation is presented. Finally, another MEMS logic device is presented working on the principal of activation (1) and deactivation (0) of second resonant mode of a clamped-clamped microbeam. This device is capable of performing OR, XOR and NOT gate. Experimental demonstration of the cascadability is shown for this case cascading OR and NOT gate to perform a logically complete NOR logic gate.

<p dir="ltr">Structural instability, traditionally deemed undesirable in engineering, can be leveraged for beneficial outcomes through intelligent design. One notable instance is elastic buckling, often leading to structures with two stable equilibria (bistable). Connecting bistable elements to form multistable mechanical metamaterials can enable the discretization and offer tunability of mechanical properties without the need for continuous energy input.<i> </i>In this work, we study the physics of these multistable metamaterials and utilize their state and property alterations along with snap-through instabilities resulting from state change for engineering applications. These materials hold potential for diverse applications, including mechanical and thermo-mechanical defrosting, energy absorption, energy harvesting, and mechanical storage and computation.</p><p dir="ltr">Focusing on defrosting, we find that the energy-efficient mechanical method using embedded bistable structures in heat exchanger fins significantly outperforms the thermal methods. The combination of manufacturing methods, material choice, boundary conditions, and actuation methodologies is systematically investigated to enhance defrosting performance. A purely mechanical strategy is effective against solid, glaze-like ice accumulations; however, performance is substantially diminished for low-density frost. To address this limitation, we study frost formation on the angular shape morphing fins and subsequently introduce a thermo-mechanical defrosting strategy. This hybrid approach focuses on the partial phase transition of low-density frost to solid ice through thermal methods, followed by mechanical defrosting. We experimentally validate this approach on a multistable heat exchanger fin pack.</p><p dir="ltr">Recent advancements have led to a new paradigm of reusable energy-absorbing materials, known as Phase Transforming Cellular Materials (PXCM) that utilize multiple negative stiffness elements connected in series. We explore the feasibility of this multistable metamaterial as frequency up-conversion material and utilize these phase transformations for energy harvesting. We experimentally demonstrate the energy-harvesting capabilities of a phase-transforming unit-cell-spring configuration and investigate the potential of multicell PXCM as an energy harvesting material.</p><p dir="ltr">The evolution towards intelligent matter, or physical intelligence, in the context of mechanical metamaterials can be characterized into four distinct stages: static, responsive, adaptive, and intelligent mechanical metamaterials. In the pursuit of designing intelligent mechanical metamaterials, there has been a resurgence in the field of mechanical computing. We utilize multistable metamaterials to develop mechanical storage systems that encode memory via bistable state changes and decode it through a global stiffness readout. We establish upper bounds for maximum memory capacity in elastic bit blocks and propose an optimal stiffness distribution for unique and identifiable global states. Through both parallel and series configurations, we realize various logic gates, thereby enabling in-memory computation. We further extend this framework by incorporating viscoelastic mechano-bits, which mimic the decay of neuronal action potentials. This allows for temporal stiffness modulation and results in increased memory storage via non-abelian behavior, for which we define a fundamental time limit of detectability. Additionally, we investigate information entropy in both elastic and viscoelastic systems, showing that temporal neural coding schemes can extend the system’s entropy beyond conventional limits. This is experimentally validated and shown to not only enhance memory storage but also augment computational capabilities.</p><p dir="ltr">The work in this thesis establishes multistability as a key design principle for developing responsive, adaptive, and intelligent materials, opening new avenues for future research in the field of multistable metamaterials.</p>