In this study, a dynamic Mindlin–Reissner-type plate is developed based on a simplified version of Mindlin’s form-II first-strain gradient elasticity theory. The governing equations of motion and the corresponding boundary conditions are derived using the general virtual work variational principle. The presented model contains, apart from the two classical Lame constants, one additional microstructure material parameter g for the static case and one micro-inertia parameter h for the dynamic case. The formal reduction of this model to a Kirchhoff-type plate model is also presented. Upon diminishing the microstructure parameters g and h, the classical Mindlin–Reissner and Kirchhoff plate theories are derived. Three points distinguish the present work from other similar published in the literature. First, the plane stress assumption, fundamental for the development of plate theories, is expressed by the vanishing of the z-component of the generalized true traction vector and not merely by the zz-component of the Cauchy stress tensor. Second, micro-inertia terms are included in the expression of the kinetic energy of the model. Finally, the detailed structure of classical and non-classical boundary conditions is presented for both Mindlin–Reissner and Kirchhoff micro-plates. An example of a simply supported rectangular plate is used to illustrate the proposed model and to compare it with results from the literature. The numerical results reveal the significance of the strain gradient effect on the bending and free vibration response of the micro-plate, when the plate thickness is at the micron-scale; in comparison to the classical theories for Mindlin–Reissner and Kirchhoff plates, the deflections, the rotations, and the shear-thickness frequencies are smaller, while the fundamental flexural frequency is higher. It is also observed that the micro-inertia effect should not be ignored in estimating the fundamental frequencies of micro-plates, primarily for thick plates, when plate thickness is at the micron scale (strain gradient effect).

This thesis investigates the high cycle fatigue (HCF) life prediction of materials under variable amplitude loading conditions, essential for aerospace and engineering applications. The study compares two common methodologies: the Basquin-type stress-life relations, and a Stress Intensity Factor variant, Aérospatiale's Internal Quality Factor (IQF) technique. Basquin-type methods, grounded in empirical S-N data, use fatigue strength coefficients and exponents to predict life based on stress amplitudes but often lack precision under non-standard conditions. SIF methods offer a nuanced analysis by incorporating geometric and material-specific factors, enhancing predictive accuracy for complex structures such as notched and bolted assemblies. The IQF method, an extension of SIF methodologies, integrates various loading conditions and material responses, providing a thorough fatigue life prediction framework. The research begins by identifying the limitations of traditional Basquin-type stress-life relations, particularly their inability to accurately predict fatigue life under variable amplitude loading due to their reliance on empirical data and the omission of mean stress effects. The methodology involves adjusting the S-N curve based on modification factors, such as notch factors and stress concentration factors, to refine predictions. The IQF methodology, developed by Aérospatiale, integrates parameter descriptions, examples, and a systematic procedure for evaluating fatigue life under complex loading conditions. By applying this methodology to notched and bolted assemblies, the study assesses its effectiveness in predicting fatigue life, comparing its performance to the Basquin-type approach. The thesis details the assumptions, procedures, and steps involved in each methodology, emphasizing the importance of geometric parameters and load spectra in fatigue analysis. The research utilizes various assumptions, such as uniform load distribution and simplified geometric models, to streamline the analysis while maintaining relevancy to industrial standards. For example, CAD designs and S-N curves for different simplified geometries common in aerospace applications are combined with Ground-Air-Ground load spectrums with mean stress adjustment capabilities to create an open-source dataset for future research. Results from the fatigue tests indicate that the IQF methodology provides the most reasonable life predictions among other models, which is natural because the stress concentration factor in Basquin-type relations are integrated by IQF, and in an experimental procedure like this, it is inevitable to have incompatible cross-data such as kt affecting the results in this manner. Regardless, the requirement of sensitivity in correction parameters' calculations is primarily recognized. Future work should focus on refining the interchangeability of parameters across methodologies, incorporating more complex load conditions, and expanding the empirical data available to validate theoretical models further.

As technology advances, demand for higher speed, higher precision machine tools and assembly equipment drives research to meet this demand. Ball bonder machines create small wire bonds between a silicon die and an assembly package by moving a set of automatic bonding tools along a programmed path as fast as possible to create a complete semiconductor device. Recent industry trends have shown demand to reduce noise and vibration during XY motion table movement. Some existing methods to reduce noise and vibration in XY table systems have significant cost or moving mass implications, which can be undesirable for the moving masses in a high speed ball bonder machine. A tuned mass damper (TMD) is proposed as a solution method to reduce noise and vibration of a certain ball bonder machine XY table component. The relevant portions of the machine were characterized with experimental modal testing and finite element models. Satisfactory agreement was found between FEA and modal/acoustic testing. Optimal design parameters and their sensitivities for the proposed tuned mass dampers were investigated in simulation. Optimal parameters for a robust mass damper design were found to differ from traditional optimal design parameters. Multiple iterations of prototype TMDs were conceptualized and fabricated to fit within packaging constraints, material limitations, and environmental factors. The performance of these prototypes were tested on a complete ball bonder machine. The prototypes showed satisfactory performance to the target mode, but did not show broadband noise or vibration reduction.