| This dissertation documents an investigation of the mathematical modeling and dynamic response of flexible, segmented, cantilever beams with overlapping sections of varying length. This configuration is a reasonable approximation of physical structures such as a telescoping booms, extension ladders, and retractable satellite antennas. At the beginning these systems are characterized according to their physical configurations and constraints. Next, a modeling approach based upon Euler beam is formulated, along with appropriate abstractions for the system's internal and external load configurations. Equations of motion for two types of segmented overlapping cantilever beams are derived and frequency equation is expressed in a form of determinant equated to zero. The scheme to calculate the roots of this determinant are thoroughly discussed and the associated eigenproblems are solved for modal characteristics.; Special consideration is given to studies, which provide evidence that for the high modes, root finding algorithms may be subject to numerical instability due to the finite precision associated with software used for the analysis segmented overlapping beam configurations. The results obtained after extensive numerical computation and analysis, yield new insights into the prediction of the numerical instability for continuous systems consisting of an infinite number of eigenvalues.; In addition, this research presents comprehensive parametric studies, which yield invaluable insight into the interrelationships among modal characteristics, dynamic response, and design optimization of flexible segmented structures. The set of presented graphical outcomes illustrate how the beam configuration with three or more segments can be modified independently of the total length L, provided that internal segments can be separately controlled and how to modify the beam length to maintain a prescribed natural frequency. Nondimensional graphs provide using them for different beam geometrical and physical properties. |
