Ultra-thin drums play a crucial role in sensing applications due to their slender construction and relatively low bending rigidity. These properties render them highly sensitive to external forces. The emergence of graphene and other 2D materials has profoundly impacted the development of these devices, allowing for the creation of exceptionally thin membranes, even as thin as a single atomic layer. However, the extreme thinness of these structures introduces challenges, such as susceptibility to large deformations and nonlinear behaviour, making linear models unsuitable for mechanical analysis.

To fully harness the potential of ultra-thin resonators in practical applications, it is thus essential to comprehend their nonlinear mechanical behaviour thoroughly. Consequently, mathematical modelling and numerical simulations play a pivotal role in studying the nonlinear mechanics governing the motion and resonant behavior of these devices. This doctoral thesis investigates the nonlinear mechanics of ultra-thin membranes. Its primary objective is to develop analytical and numerical methodologies that will facilitate the future design and analysis of these structures for various applications...@en

Plants have been discovered to emit acoustic signals when experiencing drought stress. These acoustic emissions originate from sudden tension releases in the xylem vessels, which transport water within the plant. The rate at which the plants emit these signals increases in the initial stages of the desiccation process, but will reduce later on. Instead of monitoring these acoustic emissions, drought stress can also be identified by actively sending acoustic signals through the stem. This method is applied by Plense Technologies, who develop sensors that transmit ultrasound signals through the plant stem and aim to identify drought stress in an early stage. This can be used as a tool to improve crop irrigation management. However, knowledge on the vibratory dynamics of plant stems and xylem vessels is lacking due to the complexity of the material and frequency spectra, which makes the identification of drought stress in the stems difficult.

State-of-the-art research shows that stem characterization can be performed through modal analysis using Laser Doppler Vibrometry. This method has been performed on both stems and leaves and has been proven to accurately depict the effective properties of the material. This method is suitable for obtaining the vibratory dynamics of the bulk material of the stem, while the acoustic measurements can be implemented to capture xylem vibrations. In addition, computational modeling of the dynamics of plant stems and xylem vessels has rarely been performed, as observed from the state-of-the-art literature. The experiments using Laser Doppler Vibrometry and acoustics, combined with computation modeling of the stems and xylem vessels, form the research gap of this project.

In this thesis, the desiccation behavior of chrysanthemum stems is identified from its elastic and dynamic properties. Chrysanthemums are one of the largest commercial flowers and were selected for their straight stems and usability in the experiments. Experimental modal analysis was performed on the 38 stem over a period of 3 weeks, using a laser Doppler vibrometer and the acoustic sensor developed by Plense Technologies. The goal of these methods was to obtain empirical data on the vibratory dynamics of the stems and xylem vessels over time, respectively. In addition, the mass and diameters of the stems were captured and used to calculate the density of the stems. These parameters were analyzed to determine whether they show desiccation behavior. The laser Doppler vibrometry method was validated through a 3-point bending test to see whether the eigenfrequency is suitable to derive the elastic properties of the stems. The eigenfrequency and bending stiffness were analyzed to determine whether they are suitable parameters for identifying desiccation. Microscopic imaging of the cross sections of the stems was performed to obtain the diameters of the xylem vessels and to get an idea of the inner structure of the stems. Finally, a desiccation experiment was performed in parallel to the mentioned experiments, where 10 plants were measured for a duration of 6 weeks. The parameters suitable for identifying and monitoring desiccation were the mass, density and bending stiffness of the stems. The diameter and eigenfrequency were observed not to be statistically significant enough to monitor desiccation.

Three computational models were designed to simulate the vibratory dynamics of the stems, with three different geometries. The geometries of the models were a cylinder, an elliptical cylinder and a frustum. An optimization script was designed, which minimizes the error between empirically obtained and simulated eigenfrequencies of the stems and computes the related Young's modulus. This optimization was performed on both the first and second bending modes and from the results it was concluded that the frustum model had the best performance. The Young's moduli obtained from all three models were observed to be statistically significant, indicating that it is a suitable parameter to identify desiccation behavior. The xylem vessels were modeled using computational models designed by Dutta et al., 2022, which were adjusted to be implemented in this study. A section of the data obtained from the acoustic modal analysis contained clipped signals, which could not be used for the analysis. A resonance peak was identified, but could not be determined with certainty to be a eigenfrequency of the xylem vessels, due to the lack of knowledge on this matter. However, it was investigated what type and order of eigenmode it would be if it was a resonance of the xylem. It turned out to be a third-order bending mode and this was simulated, accordingly. The results from the model showed significantly higher eigenfrequencies, related to the third eigenmode. Further research on vessels and vascular tissue is required to improve the results.

Synchronization is a universal phenomenon observed across various natural systems, from fireflies flashing in unison to pacemaker cells that create heartbeats. In recent experiments, it was found that E. coli cells could be trapped in circular microcavities, exhibiting oscillatory motion. When two adjacent cavities were connected with microchannels, the cells showed synchronous motion. The objective of this thesis is to uncover the mechanism behind this synchronous motion. A model is developed based on hydrodynamic interactions between the cells due to the fluid in the channel, which resembles the Adler model, one of the simplest models of synchronization. To include the effect of real-world influences, noise is added to the model and stochastic simulations capture the experimental observations more closely. However, the presence of noise greatly affects the synchronization of the E. coli oscillators, making it hard to observe sustained synchrony. To counteract this, a proposal is made to use an external drive such that synchronous oscillations can be sustained. These advancements could pave the way toward the engineering of desired dynamics in confined active matter.

Model Order Reduction is an essential tool in analysis of structures exhibiting nonlinear dynamic behaviour. In this work the model order reduction method of Modal Derivatives, which is an extension of the linear Modal Truncation method into the nonlinear regime, is implemented in an automated scheme starting from a Finite Element discretization based on a Kirchhoff-Love shell element. After validation of the implementation, multiple thin-walled examples are analyzed and the results of the reduced-order model are compared to results from literature.

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.

Micro- and nanoelectromechanical (MEM/NEM) resonators are used in numerous fields of engineering and are crucial for time keeping, synchronization, and sensing applications. These systems are subjected to energy dissipation, which is a limiting factor in the performance. Extensive understanding is essential when nonlinearities show up in both stiffness and dissipation, to design appropriately. Focusing on dissipative mechanisms, this paper explores the vibrational behavior of a suspended clamped-clamped beam fabricated from silicon-nitride in the nonlinear regime. This study reveals a notorious decay in ringdown, when the resonator is decoupled from its vibrational power. A sustained amplitude is observed for up to 8 seconds. Though the exact source of this anomaly remains elusive, it is suggested that it might include modal coupling and/or optomechanical effects

Nanomechanical resonators made of two-dimensional (2D) materials are the subject of intensive research due to their remarkable properties, allowing them to operate at high frequencies with high sensitivity. However, dissipation losses and manufacturing issues have prevented them from reaching their full potential. This thesis aims to overcome these challenges by dry-transferring 2D materials onto a MEMS and clamping them using electron beam-induced deposition. By in-plane straining the membranes using MEMS, the tensile energy is increased, thereby diluting intrinsic losses. This approach increased the Q-factor of 2D material resonators by 91% and allowed measuring forces down to sub-piconewtons, outperforming commercially available silicon-based force sensors.

Bacterial identification is crucial for addressing infectious diseases and enabling effective treatment strategies. Conventional bacteria identification methods like MALDI-TOF, while efficient, lack the capability for screening the effectiveness of antibiotics. On the other hand, existing antimicrobial resistance (AMR) tests, despite being reliable, suffer from time inefficiency and lack concurrent identification capabilities. In response to these challenges, the present study employs the recent advancements in single-cell nanomotion detection using graphene drums to address these limitations. We integrate nanomotion detection with Machine Learning (ML) algorithms which enables us to simultaneously identify bacteria phenotype and their resistance to antibiotics. Bacterial time signals are transformed into time-frequency spectrograms, which then serve as inputs for machine learning algorithms. Through pattern recognition, these algorithms identify features within the images, facilitating the development of robust classification models. Utilizing single-cell nanomotion signals, differentiation is achieved between the species Escherichia coli, Staphylococcus aureus, and Klebsiella pneumoniae, as well as in detecting antibiotic-resistant and -susceptible strains, achieving an accuracy of 98.57% in the latter. This research marks the first instance of ML integrated with nanomotion detection for bacterial species identification and antibiotic susceptibility testing. It provides a basis for advanced diagnostic tools, expediting the provision of vital data regarding bacterial identification and antibiotic susceptibility, contributing significantly to medical diagnostics.

Life at low-Reynolds numbers regime is intriguing. Single motile bacteria are known to exhibit erratic behaviour; they swim in what is known as a random walk, alternating between periods of swimming straight and abrupt moments of re-orientation. Yet in dense populations, cells of E.coli have been reported to exhibit weak synchronization and self-organize into collective oscillatory motion patterns. However, the origin of this rhythmic behaviour remains largely unknown. Here, we present a method of inducing self-sustained oscillations over minute timescales in single E.coli cells by trapping them in circular microcavities. By engineering the size of these microwells, we show that the velocity of single E.coli can be tuned between speeds ranging from a few to 20 um/s. Furthermore, we show that by connecting the microwells via on-chip channels, E.coli tend to coordinate their motion through hydrodynamic interaction and exhibit collective dynamics. Using analytical modeling, we extract the coupling strength and design the channels to mediate synchronized oscillation between two bacterial oscillators. Our work not only advances our understanding of the collective dynamics of swarming bacteria but also provides the first evidence for single-cell bacterial oscillators, paving the way to using micro-organism-inspired oscillations in applications as varied as antibiotic screening, scientific computing and micro-swimmers.

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.

Two-dimensional (membrane) materials have been receiving much scientific attention due to their unique material properties that can be used to study the smallest physical phenomena. One such material is graphene, perceived as the holy grail in material physics, due to its unique material properties. Its aspect ratio diminishes the bending rigidity and allows wrinkles, ripples and other morphological imperfections to dominate the mechanical behaviour. Applying tension is a necessity to control these geometrical imperfections and simultaneously opens up pathways to study physical phenomena such as magnetism, superconductivity, optics and much more. Typically, this tension is applied using electrostatic forces, which alters amongst others, the electric properties of the material. Mechanically applied tension offers a solution to this problem but comes at the cost of difficult manufacturability. In this work, a new method to incorporate 2D materials with N/MEMS is presented. The dynamics of mechanically tensioned graphene are probed in linear and nonlinear regimes. The former regime finds the exact opposite of what is observed in electrostatically tensioned membranes. The latter shows exotic nonlinear effects that can be tuned by applying tension. Furthermore, it is identified that the dynamics of the MEMS device are coupled to that of the resonating membrane despite their mass and stiffness being roughly five orders of magnitude apart. The bottleneck of this project is the adhesion force between the two is insufficiently strong to apply significant strain allowing slippage to occur.

Antibiotic susceptibility test (AST) shows the efficacy of antibiotics against different strains and is frequently applied in finding new antibiotics, bacteria identification, and clinical analysis. The tests provide scientific evidence for finding pathogens and avoiding the misuse of antibiotics.

The first AST was invented by Alexander Fleming in the 1920s, right after the invention of antibiotics. Since then, methods of antibiotic testing have developed and improved. The nanomotion method is one of the auspicious methods in antibiotic susceptibility tests (AST). It features detecting the vibration of single living bacteria on the graphene drum before and after being treated with antibiotics. However, such a method is restricted in laboratory conditions currently. The aim of this thesis is to make the nanomotion method compatible with clinical requirements. As a result, a new set of designs including chips and their cartridge is fabricated and validated in this thesis.

In this research, a review including the traditional and up-to-date AST methods shows that in the nanomotion method, only one measurement is carried out simultaneously. As the research question, this novel design is supposed to carry out a few measurements with different parameters including concentration and antibiotic category.
To realize this purpose, concept designs analyzing the requirements are carried out on three components, fluid system, ventilation and sealing. More parameters regarding the material and fabrication are discussed in order to ensure its requirements including durability, printing quality and more.
In the end, the design is validated and tested in the setup. The result is compared to the original nanomotion method and the traditional AST method. We hope the thesis provides the possible direction of improvements for the nanomotion method.

While nonlinear phenomena in mechanical systems are well understood, strategies for designing structures that exhibit certain nonlinear responses have received little attention. Design optimization is a systematic and iterative process aimed at improving the performance and efficiency of a system. It involves exploring various design choices and parameters to find the best possible solution that meets specific criteria or objective, such as maximizing or minimizing nonlinearity. The use of design optimization techniques for tuning nonlinear dynamics has important implications for the development of micro- and nano-scale devices. By optimizing the nonlinear response of these devices, it is possible to achieve enhanced performance, and better control over their nonlinear behaviour.

In my thesis, I have devised a novel methodology that empowers us to optimize the nonlinear vibration characteristics of devices. My work extends to the development of a versatile routine capable of defining complex geometries and facilitating design within a Finite Element Method (FEM) framework. This routine operates in tandem with optimization algorithms, enabling us to identify and refine the most optimal designs in terms of strength of nonlinearity, minimizing or maximizing it when desirable.

Micro and nanomechanical resonators are essential to the state-of-the-art communication, data processing, timekeeping, and sensing systems. The discovery of graphene and other two-dimensional (2D) materials has been a profound source of inspiration for the next generation of these devices, owing to their exceptional mechanical, electrical, and thermal properties. However, alongside their advantages, the atomically thin nature of these resonators also presents its own unique challenges, as the dynamic response of these resonators rapidly becomes nonlinear, where nonlinear coupling and dissipation processes manifest. To unleash the full potential of these resonators, a comprehensive understanding of the emerging nonlinear phenomena is crucial. In this pursuit, this thesis studies nonlinear dissipation pathways in 2D material resonators that arise from the coupling of their internal mechanical modes to each other as well as to theirmicroscopic physics. The thesis consists of six chapters.@en

Micro and nanomechanical resonators are essential to the state-of-the-art communication, data processing, timekeeping, and sensing systems. The discovery of graphene and other two-dimensional (2D) materials has been a profound source of inspiration for the next generation of these devices, owing to their exceptional mechanical, electrical, and thermal properties. However, alongside their advantages, the atomically thin nature of these resonators also presents its own unique challenges, as the dynamic response of these resonators rapidly becomes nonlinear, where nonlinear coupling and dissipation processes manifest. To unleash the full potential of these resonators, a comprehensive understanding of the emerging nonlinear phenomena is crucial. In this pursuit, this thesis studies nonlinear dissipation pathways in 2D material resonators that arise from the coupling of their internal mechanical modes to each other as well as to theirmicroscopic physics. The thesis consists of six chapters.@en

Micro and nanomechanical resonators are essential to the state-of-the-art communication, data processing, timekeeping, and sensing systems. The discovery of graphene and other two-dimensional (2D) materials has been a profound source of inspiration for the next generation of these devices, owing to their exceptional mechanical, electrical, and thermal properties. However, alongside their advantages, the atomically thin nature of these resonators also presents its own unique challenges, as the dynamic response of these resonators rapidly becomes nonlinear, where nonlinear coupling and dissipation processes manifest. To unleash the full potential of these resonators, a comprehensive understanding of the emerging nonlinear phenomena is crucial. In this pursuit, this thesis studies nonlinear dissipation pathways in 2D material resonators that arise from the coupling of their internal mechanical modes to each other as well as to theirmicroscopic physics. The thesis consists of six chapters.@en

Micro and nanomechanical resonators are essential to the state-of-the-art communication, data processing, timekeeping, and sensing systems. The discovery of graphene and other two-dimensional (2D) materials has been a profound source of inspiration for the next generation of these devices, owing to their exceptional mechanical, electrical, and thermal properties. However, alongside their advantages, the atomically thin nature of these resonators also presents its own unique challenges, as the dynamic response of these resonators rapidly becomes nonlinear, where nonlinear coupling and dissipation processes manifest. To unleash the full potential of these resonators, a comprehensive understanding of the emerging nonlinear phenomena is crucial. In this pursuit, this thesis studies nonlinear dissipation pathways in 2D material resonators that arise from the coupling of their internal mechanical modes to each other as well as to theirmicroscopic physics. The thesis consists of six chapters.

Micro and nanomechanical resonators are essential to the state-of-the-art communication, data processing, timekeeping, and sensing systems. The discovery of graphene and other two-dimensional (2D) materials has been a profound source of inspiration for the next generation of these devices, owing to their exceptional mechanical, electrical, and thermal properties. However, alongside their advantages, the atomically thin nature of these resonators also presents its own unique challenges, as the dynamic response of these resonators rapidly becomes nonlinear, where nonlinear coupling and dissipation processes manifest. To unleash the full potential of these resonators, a comprehensive understanding of the emerging nonlinear phenomena is crucial. In this pursuit, this thesis studies nonlinear dissipation pathways in 2D material resonators that arise from the coupling of their internal mechanical modes to each other as well as to theirmicroscopic physics. The thesis consists of six chapters.

Micro and nanomechanical resonators are essential to the state-of-the-art communication, data processing, timekeeping, and sensing systems. The discovery of graphene and other two-dimensional (2D) materials has been a profound source of inspiration for the next generation of these devices, owing to their exceptional mechanical, electrical, and thermal properties. However, alongside their advantages, the atomically thin nature of these resonators also presents its own unique challenges, as the dynamic response of these resonators rapidly becomes nonlinear, where nonlinear coupling and dissipation processes manifest. To unleash the full potential of these resonators, a comprehensive understanding of the emerging nonlinear phenomena is crucial. In this pursuit, this thesis studies nonlinear dissipation pathways in 2D material resonators that arise from the coupling of their internal mechanical modes to each other as well as to theirmicroscopic physics. The thesis consists of six chapters.