Micro- and nanomechanical resonators are compliant systems that can exhibit nonlinear behaviour at relatively low actuation levels. Accurately identifying the governing modal parameters of such nonlinear systems remains a significant challenge. Here, we present a deep learning-based methodology for nonlinear system identification that predicts modal parameters from a single frequency sweep. By training neural networks on non-dimensionalised data, the approach is scale-invariant and broadly applicable to resonators ranging from the nano- to the macroscale. To generate training data efficiently, we introduce a parallel time-integration scheme for rapid frequency-sweep simulation, implemented in the open-source Python package Poscidyn. The methodology is validated on a two-degree-of-freedom benchmark system exhibiting 1:2 internal resonance with nonlinear modal coupling. The results demonstrate accurate parameter prediction and highlight the potential of the approach for data-driven identification of nonlinear systems. This work demonstrates a new route for nonlinear system identification that can easily be extended to systems with higher degrees of freedom and more complex nonlinear interactions. ... Read more

In this thesis, a multi-scale approach to the characterization of mechanical properties of coatings is performed. Coating plays a vital role in protecting of materials and increasing their performance in many applications. By moving from a macro-scale approach to a nano-scale, it is proposed that at this level a more fundamental understanding of how coatings perform is gained. And, by doing this, that it is possible to more reliably predict their behavior and ultimately produce longer lasting and better performing coatings. This thesis aims to contribute to this by first looking at the macro-scale behavior of weathered coating samples and analyzing the dynamic mechanical properties for progressively weathered samples. It further facilitates the nano-scale implementation of mechanical straining in combination with an Atomic Force microscope by designing a custom straining device. ... Read more

Miniaturized resonant sensors can reach exceptional resolution, but their reduced mass also makes them more vulnerable to frequency noise. In many state-of-the-art devices, nonlinearities emerge at low oscillation amplitudes, coupling amplitude and resonance frequency, thus, enabling amplitude fluctuations to convert into frequency fluctuations. This amplitude-to-frequency (A-F) conversion limits the frequency stability. Consequently, operation in the linear regime is conventionally preferred, constraining the achievable signal-to-noise ratio, and forming a key bottleneck for further improvements in resonant sensing.
This thesis extends the theoretical understanding of closed-loop frequency stability limits for nonlinear resonator operation and explores how nonlinear effects can be exploited rather than avoided. The work studies two mechanisms in particular: nonlinear damping and parametric resonance. The results show that nonlinear damping can substantially suppress A-F conversion at amplitudes beyond the onset of nonlinearity, and it relaxes the conditions required to benefit from established optimal operating points such as the zero-dispersion and amplitude-detachment points. In addition, the thesis demonstrates that parametric drive can improve frequency stability beyond previously derived limits, indicating a route to enhanced sensing performance. ... Read more

Modern aircraft designs aim to enhance overall performance and reduce fuel consumption, thereby minimising costs. The growing interest in high-aspect-ratio wings stems from the potential gains in aerodynamic performance. Concurrently, the utilisation of composite materials in the aircraft primary structure for weight reduction is increasing. Both aspects influence wing flexibility and may result in larger wing deflections than those of existing aircraft during operational conditions. Under appropriate loading conditions, the wing deflections can be large enough to surpass the threshold of geometrically linear analyses. This adds complexity to both structural and aeroelastic analyses.

The primary challenge in nonlinear structural analyses arises due to the replacement of the scalable linear methods with the iterative predictor-corrector methods. This can significantly exacerbate the required computational effort. The same limitation also extends to aeroelastic analyses. Beyond the computational aspects, the larger wing deflections introduce aeroelastic effects that cannot be modelled using the linear methods. Prior studies have demonstrated the influence of geometric nonlinearities on aeroelastic characteristics. Notably, a majority of numerical models used to investigate these effects so far rely on variants of geometrically exact beam theory for incorporating nonlinear structural kinematics. While this approach makes the analyses computationally efficient, it involves transforming finite element models into equivalent beam models..... ... Read more

From levitating living organisms to developing high-Q resonators, diamagnetic levitation has become a powerful technique to mechanically isolate objects. Its ability to work at room temperature without power consumption and simple setups has found many applications in precision measurements, including accelerometers, MEMS devices, mass sensors, and motion stages. By using the strong diamagnetic properties of materials like pyrolytic graphite, both micro- and macro-scale objects can be stably levitated. This allows for systems that reduce mechanical losses and provide high isolation. Therefore, diamagnetic levitation is ideal for creating ultra-low dissipation mechanical systems with high quality factors (Q-factor). However, a key challenge remains, the damping caused by eddy currents that occur due to motion through a changing magnetic fields. These currents dissipate energy and limit the performance of these levitated systems by lowering their Q-factor.
This thesis explores the optimization of pyrolytic graphite-based composite resonators to enhance the Q-factor. By combining finite element method (FEM) simulations with Multi-Objective Particle Swarm Optimization (MOPSO), we investigate how plate geometry and segmentation can suppress eddy currents and reduce damping. Composite plates with insulating epoxy are fabricated and levitated over a 2x2 array of NdFeB permanent magnets. Experimental validations demonstrate a significant increase in Q-factor, particularly when combining segmentation and optimised shape, reaching values up to 420,000. This work contributes to the advancement of high-Q levitating resonators and highlights the importance of geometry and materials in achieving ultra-low dissipation. ... Read more

Diamagnetic levitation offers a contactless, room-temperature platform for creating high-quality mechanical resonators. This study investigates the dynamic behavior of levitated diamond particles as potential high Q resonators. Using a cone shaped pole-piece magnet assembly, we achieve stable levitation of single crystalline diamond particles and clusters up to 400 μm in diameter. By leveraging diamond's extremely low electrical conductivity (∼ 10^-13 S/m), eddy current damping is nearly eliminated, leaving air resistance as the dominant dissipation mechanism. Resonant modes—including transverse, radial, and rotational—are characterized using laser Doppler vibrometry, with actuation enabled via electrostatic forces. Frequency response and Q factor measurements across a range of pressures reveal that while a Q factor up to 4250 is achieved, it remains below theoretical limits due to additional damping, likely caused by inter-particle friction and mode coupling in clusters.  Furthermore, frequency shifts with decreasing pressure suggest that ambient air contributes to effective stiffness, in addition to damping. These findings demonstrate the potential of diamond for next-generation, high Q, room-temperature levitated resonators, while highlighting the challenges posed by cluster dynamics and external perturbations. ... Read more

Water-borne coatings are increasingly used in industrial and consumer applications because of their low volatile organic compound (VOC) content and reduced environmental impact compared with solvent-borne systems. However, their mechanical integrity and durability remain key challenges, particularly under cyclic thermal or environmental loading. Therefore, understanding how these viscoelastic properties evolve with thermal aging is essential for predicting the durability of these water-borne coatings. The effect of thermal aging on the mechanical and nanomechanical behavior of water-borne coatings was investigated using a combination of bulk and nanoscale characterization techniques. Based on industry standard tests, two accelerated aging protocols were performed, the cold check test and the water uptake and freeze stability test, to simulate cyclic thermal stress. The progression of viscoelastic material properties over multiple aging cycles has been investigated based on industry standards using Dynamic Mechanical Analysis (DMA), revealing an increase in the storage modulus with progressive aging. Two Atomic Force Microscopy (AFM) methods were employed to assess local mechanical changes using both on- and off-resonance AFM techniques. The AFM measurements showed a corresponding increase in stiffness at the nanoscale, along with the development of surface cracks and other topographical features. Off-resonance AFM measurements on these features demonstrated that the local storage modulus, a measure of stiffness, in and around the surface cracks remained comparable to that of the surrounding matrix, whereas local cylindrical rods showed an increased storage modulus. These findings contribute to a better understanding of the mechanical and structural evolution of water-borne coatings under thermal cycling, linking stiffening to nanoscale defect formation, surfactant removal, additional crosslinking, and oxidation, all of which reduce polymer chain mobility to increase stiffness. The observed changes underscore the coupled chemical, mechanical, and morphological nature of the aging process in water-borne coatings. This thesis provides insights into thermally induced coating failure and coating degradation mechanisms, thereby potentially accelerating the development cycle of water-borne coatings. ... Read more

Interpreting the results of Atomic Force Microscopy on soft samples is a challenging task due to the coupling of the tip-sample forcing with the unobservable surface motion. Current analysis methods for soft samples are either slow and brittle to noise or require surface deformation to be provided explicitly and cannot converge onto the global optimum in equational reclaim. In this paper a machine learning algorithm called a Mixture of Expert neural network was successfully used with the goal of model classification between hard and soft samples in addition to estimating dynamic properties of those samples. In addition a separate autoencoder based machine learning approach is explored for the purposes of reconstructing the unobservable dynamics of the system in equational form. These results are obtained with the hope that they are implemented in Atomic Force Microscopy software for in-situ sample analysis. ... Read more

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.
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Most micro- and nanomechanical devices are designed to operate within the linear dynamic range by using simple geometries, primarily due to the limited knowledge in utilizing nonlinearity and constraints in fabrication techniques. However, it is anticipated that the scope of applications and fundamental research can be significantly expanded, if these tiny systems can be precisely engineered to account for and exploit their various nonlinear dynamic behaviors. This thesis provides a comprehensive study on the optimization of dynamical properties of high-Q nanomechanical resonators, spanning from linear to nonlinear dynamics and evolving from single-mode to multi-mode analysis.

We first give an introduction to the development of micro- and nanomechanical resonators in Chapter 1. We focus on their unique mechanics, including very low dissipation and strong nonlinearities. Furthermore, we elaborate on the motivation behind this thesis and the need for linking engineering optimization with micro- and nanomechanical resonators. Followed by Chapter 2, we elaborate on the methodology we use throughout this thesis, including fabrication techniques of nanomechanical Si3N4 devices, characterization approaches by optical measurements, and modeling procedures for structural dynamics. Among all methodologies, we highlight the Finite Element (FE)- based Reduced Order Models (ROMs) that can accurately capture the geometric details and boundary conditions, which facilitate the design of resonators with predictable dynamical properties.

We start from investigating linear dynamics of Si3N4 nanostrings in Chapter 3, where the tuning effects of their soft-clamping supports on resonance frequency and Q-factor are evaluated. We experimentally and theoretically reveal a trade-off between maintaining high stress and low stiffness of the supports in designing high-Q resonators fabricated with initial strain. By optimizing this trade-off with our soft-clamping design, we obtain a 50% enhancement of Q-factor compared to doubly-clamped string resonators. With stronger drive levels, in Chapter 4, we show that the nonlinear dynamics can also be substantially tailored by soft-clamping supports. Through careful engineering of support geometries, we introduce softening nonlinearity by stress-induced buckling, allowing precise control over the nonlinear dynamic responses in doubly supported nanostrings, which conventionally exhibit hardening behaviors.

Based on the accurate modeling of both linear and nonlinear dynamics that is validated by experiments, we integrate our FE-based ROM technique with a derivative-free optimization algorithm for the design of nonlinear mechanical resonators in Chapter 5. By optimizing the support’s geometry of our nanostrings, we show that the proposed methodology is not only capable of handling a single optimization goal, but also multiple conflicting objectives, such as the simultaneous enhancement of Q-factor and the Duffing constant. Besides, we generate Pareto frontiers that visualize the trade-offs among multiple optimization objectives, verify the optimized results with brute-force simulations and validate the numerical framework with experiments.

Apart from the dynamics in a single mode, we observe modal interactions between multiple vibrational modes of our nanostrings in the strong nonlinear regime. In Chapter 6, we demonstrate that soft-clamping techniques, commonly utilized to achieve high-Q resonators, can be employed to engineer mode coupling. We verify the analytically derived two-degree-of-freedom system between the lowest two out-of-plane modes by FE-based ROMs and experiments. We further reveal the significant impact of multi-mode interactions on the nanostrings’ frequency response, demonstrating additional opportunities to tailor the nonlinear dynamics of mechanical resonators facilitated by soft clamping. Moreover, we highlight the design potential of soft-clamping supports through the geometric optimization of two-mode coupling, showcasing the effective Duffing constant of the driven mode can be increased by 70%, as well as the onset of mode coupling can be geometrically programmed to either facilitate or inhibit its occurrence.

We conclude all works presented for achieving the optimization of nonlinear dynamics in nanomechanical resonators, and give an outlook for future directions in Chapter 7.
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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... ... Read more

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. ... Read more

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. ... Read more

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. ... Read more

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. ... Read more

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 ... Read more

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. ... Read more

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. ... Read more

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. ... Read more

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. ... Read more