A combination of Newton's second law, a transformation using three consecutive Euler angles, and Taylor expansions is used to develop three nonlinear integro-differential equations describing the flexural-flexural-torsional vibration of metallic and composite beams. The twisting curvature is used to define a physical twisting variable which makes the equations of motion unique and independent of the rotation sequence of the Euler angles. A numerical-perturbation approach is used to analyze the response of metallic and composite beams to parametric and external excitations. First, the linear eigenfunctions and natural frequencies are calculated using a combination of the state-space concept and the fundamental-matrix method. Then, the method of multiple scales is used to construct a set of nonlinear autonomous first-order ordinary-differential equations describing the slow-time modulation of the amplitudes and phases of the interacting modes in the presence of one-to-one and/or two-to-one internal resonances. The inversion symmetry, D, symmetry, and 0(2) symmetry of the system are studied using the modulation equations. The solutions of the modulation equations may be fixed points, limit cycles, or chaotic solutions. / Ph. D.

Thin-walled beam structures are adopted as structural members in various fields of modem technology including aeronautical/aerospacial, naval, mechanical and civil ones. With the advent of advanced composite material systems, there is a vital need to reformulate the classical theory of thin-walled beams in a wider framework. This dissertation is intended to incorporate several essential effects which have a considerable importance for the rational design of composite thin-walled beam structures. These effects are the transverse shear deformation, the warping constraint, the secondary warping as well as the hygrothennal and the dynamic ones. The field equations of laminated composite thin-walled beams of either open or closed single and multicell cross-sections are derived through the application of Hamilton's variational principle. The Laplace Transform technique is used to obtain exact solutions. In this dissertation, the aero elastic divergence instability of aircraft wings modelled as thin-walled beams as well as the eigenfrequency problem of cantilevered composite thin-walled beams of closed cross-section are considered in the framework of a reformed theory incorporating non-classical effects. The numerical results reveal the great role played by non-classical effects as well as by the tailoring technique applied to the problems studied in this dissertation. / Ph. D.

An attempt is made to understand the phenomenon of aeroelasticity as applied to the helicopter rotors, specifically laminated composite rotor blades. Realizing the immense complexity of the problem, a beginning has been made by developing a structural model for a rotating composite beam. Present work has three objectives; 1) To carry out an extensive survey of research related to the aeroelastic analysis of rotor blades, 2) To expand an existing finite element model by introducing new degrees of freedom and validate the changes, 3) and, finally using this model to carry out a linear static and dynamic analysis for a rotating composite beam. It was found that the rotation and fiber orientations have a pronounced effect on the static deflections and the natural frequencies of vibration of the laminated beam. / Master of Science