Not available / text

Parametric excitation is a fundamental feature of dynamical systems arising across the applied sciences. In this thesis we study the structure of parametric res- onance and its in uence of the global nonlinear dynamics in a number of oscillating systems which arise in engineering contexts. The parametrically excited Helmholtz oscillator and the elliptically excited pen- dulum are two systems where the interaction of regular and parametric excitation are important for a complete understanding of the dynamics. We examine the resonance structure of the Helmholtz oscillator and use the Melnikov function to demonstrate the e ect that the parametric excitation has on the nonlinear dynam- ics. The estimates produced in this analysis are then compared to a numerical study of the engineering integrity. For the elliptically excited pendulum we discuss the quantitative e ects of introducing ellipticity to the pro le of excitation. We go on to examine the e ect of periodic time varying mass in the Helmholtz oscillator and demonstrate that the resonance structure exhibits the phenomenon of coexistence. The evolution of the systems engineering integrity is examined and compared to the purely parametrically excited case. Finally we examine a system incorporating two pendulums on a rigid rig modelled by two linear springs. The parametric resonance in this case is mapped using numerical Floquet theory and the structure of the linear resonance is shown to organise solution space for the nonlinear system.

Measurement of stress - strain relationships in soil systems usually incorporate varying degrees of uncertainty. These uncertainties arise from laboratory testing mechanisms, sampling disturbances, errors performed by operators or technicians performing the tests, etc. Currently, deformation analyses have been modeled using several deterministic techniques. However, because of the uncertainties involved, there is a need to adapt these numerical methods into probabilistic models. This thesis develops a probabilistic constitutive model based on a variable moduli deterministic technique. First-order, second-moment stochastic methods are used to estimate a mean stress - strain curve and its ±1 standard deviation from raw data obtained on nearly identical, remolded sand samples. Probabilistic estimations for Bulk and Shear moduli are determined from the estimated mean curves and are used to develop a probabilistic constitutive model. Through the use of a probabilistic constitutive matrix, a stochastic equation is produced which can relate strains to any stress state imposed on a particular soil. This is verified through an example.

The strapdown dynamically tuned gyroscope (DTG) is a candidate for use as the angular motion sensor in s'trapdown inertial navigation systems and autopilots. However, the dynamic performance of the strapdown DTG is one of the limiting factors restricting usage of the instrument in these systems. This research project considers control strategies to enhance the strapdown DTG performance. The DTG equations of motion are derived, with damping terms, and angular speed components introduced about the spin axis. The DTG equations of motion are solved numerically using a 4th order Runge-Kutta method, and taking advantage of rotating reference frames to eliminate time varying elements in the system matrix. This approach reduces the number of computations per time step and improves numerical stability. The tuning conditions for a multigimbal DTG are derived. A modal analysis is carried out on the DTG system matrix for different tuning conditions. This work provides the basis for the reduction of the DTG equations of motion to a free rotor gyroscope form. A parameter estimation procedure is designed which reflects the sensitivity of the DTG dynamic characteristics to certain parameters. A comprehensive experimental programme is carried out to validate the DTG mathematical model and estimate the numerical value of critical DTG parameters. A control strategy which processes the torquer and demodulator signals of the strapdown DTG is formulated. This strategy, used on the strapdown DTG, improves the diagonal dominance of the system transfer function matrix. Throughout the bandwidth the amplitude of the nutation response is at least 20 dB down on the amplitude of the precession response, compared with only 6 dB down on an uncompensated strapdown DTG. The compensator-strap down DTG system bandwidth is extended, compared to the strapdown DTG. The increase in bandwidth and improvement in system diagonal dominance depends on the precise form of the compensator and the manner of implementation; analogue, digital or hybrid. The compensator is feed-forward and can therefore be integrated into a system without altering the strapdown loops. The flexibility of the strategy enables the system designer to balance conflicting requirements of performance allied with minimal, cost, hardware and processing increases. An analogue and hybrid version of the compensator has been added to a strapdown DTG with subsequent test results in close agreement with theoretical studies. The control strategy has potential applications wherever strapdown DTG's are used.

Not available / text

Not available / text

Not available / text

published_or_final_version / abstract / Civil Engineering / Master / Master of Philosophy

published_or_final_version / abstract / toc / Civil Engineering / Master / Master of Philosophy

published_or_final_version / Civil and Structural Engineering / Master / Master of Philosophy