The vibration of orthogonally stiffened skew plates is studied by using the pb-2 Rayleigh-Ritz method. By minimizing the Rayleigh quotient, the natural frequencies and mode shapes are obtained. The dimensionless natural frequencies of orthogonally stiffened skew plates with different boundary conditions are determined. Since this problem has not been previously studied, the conventional finite element method is used as a comparative check. Numerical results have been presented here for different skew angles, edge ratios, and stiffener height-plate thickness ratios. The results provide rich information to better understand the dynamics of existing orthogonally stiffened plate structures and provide design information.

A general method is proposed to model multi-axle tractor-trailer type vehicles. As an example, a three-axle vehicle is considered. The vehicle model consists of two rigid mass and six wheel masses with eleven degrees of freedom (DOF), which include heave, pitch, and roll motions. The equations of motion are derived with the use of the principle of virtual work. Newmark's method is used to predict the dynamic response of the vehicle.

Then a semi-analytical method is proposed to study the vibration of the bridge under moving vehicles with the use of mode superposition. The response is expressed as the sum of the contribution of different modes. The normal coordinates can be solved explicitly. An iterative approach has been developed to treat the coupling between the bridge and the vehicle.

The interaction problem concerning bridges subjected to dynamic vehicle loading has received considerable attention. The difficulty common to a tremendous amount of efforts involves finding a suitable way to treat the dynamic coupling between the bridge and the vehicle. To be more general, skew bridges subjected to multi-axle vehicles are considered in the dissertation.

An existing highway bridge, the Walnut Creek Bridge, is considered. By using the pb-2 Rayleigh-Ritz method, its natural frequencies and mode shapes are obtained and compared with test results. Simulations are conducted for the Walnut Creek Bridge due to moving vehicles. The dynamic amplification factors are computed and compared with test results. The bridge/vehicle interaction problem is further discussed with examination of the effects of the bridge entrance and surface roughness. In this study, different irregularities are used, including perfectly smooth, the measured profile at the Walnut Creek Bridge entrance, and four types of road surface roughness for very good, good, average and poor roads according to the International Organization for Standardization (ISO) specifications. Other factors examined are the vehicle characteristics including vehicle type, axle spacing, vehicle model and speed, and the bridge characteristics including damping, span length and skew angle. The effect of traffic condition is also investigated. Further research is recommended.