<p> This thesis describes the analytical study of the stability of the structural system under circulatory loading and/or parametric excitation. The model is a double pendulum, composed of two rigid weightless bars of equal length and two concentrated masses at the ends of each bar, on an oscillating base. The vertical oscillation of the base produces parametric excitation to the system. A circulatory force is applied at the free end. At the joints the restoring moments are produced by spring and damping. The damping coefficients are taken as positive, and the gravitational effects are included. </p> <p> The combined effect of the circulatory loading and parametric excitation on stability of the system is investigated. The problem is so formulated that the stability of the system is represented by coupled Mathieu equations. The effect of damping on the boundary of stability is also determined. </p> / Thesis / Master of Engineering (ME)

This thesis describes the analytical study of a structural system under the combined action of noncirculatory or circulatory loading and oscillating base motion. The model is a double inverted pendulum composed of two rigid weightless bars of equal length with two concentrated masses at the ends of each bar, on an oscillating base. Noncirculatory or circulatory loading is applied at the free end. At the hinges restoring moments are produced by spring and damping forces. Damping coefficients are taken as positive, and gravitational effects are considered. The stability of the system under the combined action of the noncirculatory or circulatory loading and the parametric excitation can be investigated by Hsu's method. This method is applied to solve the coupled Mathieu equations by the given system and determine the unstable resonance, a nonlinear analysis is used to find the steady state response. / Thesis / Master of Engineering (MEngr)