This thesis investigates crumpled thin-sheet bellows as a more compliant alternative to traditional corrugated bellows in vibrationally isolated mechatronic systems (ASML lithography machines). While conventional bellows rely on carefully engineered corrugations, the crumpled foil bellows studied here achieve compliance through an irregular, crumpled morphology, making their dynamic stiffness and vibrational transmissibility difficult to predict. The first part of the thesis is a stand-alone literature review into the diverse approaches employed to model wrinkled and crumpled thin sheets, with their structural dynamics of particular interest. The second part presents original research in which realistic crumpled bellow geometries are generated using explicit non-linear simulations via the dynamic relaxation method, and subsequently dynamically analysed using Hintz–Herting modal reduction. In this way, the static and frequency-dependent emergent stiffness can be extracted and examined as functions of compaction ratio and foil thickness. Experimental measurements of dynamic stiffness are used to validate the numerical trends and to identify the limitations of linearised models for these systems.

Vibration isolation is essential for spacecraft payloads, where both launch loads and on-orbit micro-vibrations can degrade performance. Passive isolators are favoured for their simplicity and reliability but face trade-offs between low-frequency performance, stiffness, and compactness. This thesis introduces a topology optimisation framework for designing passive viscoelastic vibration isolators that distributes aluminium and nearly incompressible rubber within the design domain, moving beyond conventional constrained-layer damping layouts used in literature.

The framework combines a modal design approach with a bi-material finite element formulation using selective reduced integration to handle incompressibility. Modal objectives are defined through rigid-body dominated eigenfrequencies of the combined isolator–payload system, with damping enforced via Q-factor constraints.

Each optimised layout consists of a main load-carrying structure that provides stiffness and smaller damping substructures that create localised regions of energy dissipation. They adapt their shape and location to the inertial properties of the setup and targeted vibration mode, strategically placing viscoelastic material where it contributes most to damping without compromising stiffness. In doing so, the framework enables novel damping mechanisms and tunable multi-directional performance, offering an insight for future passive isolation design in vibration-sensitive applications.

In industries such as oil and gas, power generation, and chemical processing, the structural integrity of piping systems is crucial for operational safety and reliability. Various factors such as corrosion, erosion, and manufacturing defects can result in a loss of wall thickness, potentially leading to catastrophic failures. Detecting and assessing the integrity of piping systems without causing disruption to operations or compromising their structural integrity is a challenge in asset management and maintenance.
Guided Wave Tomography (GWT) is a promising non-destructive testing (NDT) technique for assessing the integrity of a pipeline by mapping its wall thickness. Using tomographic algorithms that use forward wavefield extrapolators, based on the gradient of the misfit a defect reconstruction can be made. Although the forward model is computationally inexpensive, the currently implemented gradient calculation is costly due to the large number of simulations required for each inversion parameter. This study explores the feasibility of using the adjoint state method for gradient computation in GWT, requiring only a single forward simulation independent of the number of model parameters.
A nonlinear conjugate gradient optimization method is implemented to iteratively update the wall thickness based on the misfit between simulated and observed data. The inversion process makes use of the dispersion curves to establish the relationship between phase velocity, frequency, and wall thickness. The study specifically focuses on the $S_0$ mode, analysing its suitability for complex defect reconstruction. Numerical experiments demonstrate that the adjoint method effectively localizes defects in both noise-free and noise environments, provided that there is a sufficient contrast in the sensitivity kernel between the defect and its surroundings. The technique achieves a resolution of approximately $1$ to $1.5\lambda$, with frequency continuation and multimodal inversions improving reconstruction accuracy. However, challenges arise in handling noise and wall thickness interchanges, which can be mitigated using adaptive regularization strategies.
The results suggest that the adjoint method is a viable alternative to traditional finite-difference sensitivity calculations. Future research should focus on experimental validation with real-world or as noise-free alternative 3D elastodynamic data evaluating the method on complex defect geometries and varying pipe configurations. Finally, the algorithm can be enhanced by integrating Hessian-based optimization techniques, thereby implementing a second-order adjoint method.

Piezoelectric energy harvesters convert vibrational energy into electrical energy, thereby reducing the dependence of wireless devices on batteries. However, most existing harvesters have a limited bandwidth, generating usable power only within a narrow range of excitation frequencies. Buckled beam harvesters address this issue by intentionally introducing nonlinear behaviour, but systematic design strategies for such devices are still missing due to the absence of versatile models and limited understanding of their dynamics.
In this thesis, these challenges are addressed by developing a model that combines finite element analysis with lumped-parameter equations and validating it experimentally. The resulting framework captures higher-order vibration modes and nonlinear dynamic phenomena such as secondary resonances and softening behaviour. It is demonstrated that these effects can be exploited to optimize the design and broaden the bandwidth of buckled beam piezoelectric energy harvesters. Based on the improved physical understanding, several practical design improvements are proposed.

Surface acoustic wave (SAW) is widely used in biological research and sensor applications, acomprehensive understanding of SAW propagation and visualization on suspended 2D membranes is crucial for the manipulation of nanoparticles in biological research and sensitivity improvement of SAW sensors based on 2D material. The initial step of this project involved exciting a standing SAW field on the SAW device and attempting to use Digital Holography Microscopy (DHM) for imaging the standing SAW field on the substrate. This attempt was very challenging and unfortunately was not successful. We used an Atomic Force Microscope (AFM) as an alternative solution for SAW field imaging. Initially, AFM was used to image the SAW field on the SAW device substrate, and the impacts of input frequency and power on the amplitude of the SAW field were investigated. Subsequently, microcavities were fabricated on the SAW device to record images of the SAW field within the microcavities and their surrounding areas, aiming to investigate the impact of microcavities on the SAW field. Finally, the prepared graphene membrane was transferred to the microcavities, the SAW propagation was recorded on the suspended membrane and the influence of the suspended membrane on SAW propagation was analyzed.