Elasticity-based vibrations of hollow anisotropic beams and an evaluation of the shape factor for hollow anisotropic sections - Lebsack, Michael J., author; Heyliger, Paul, advisor; Criswell, Marvin, committee member; Puttlitz, Christian, committee member (Colorado State University. Libraries, 2012)
This study considers the transverse vibrations and natural frequencies of hollow anisotropic beams free from end restraints using full three-dimensional elasticity solutions and common one-dimensional beam theory approximations. Calculations of the natural frequencies are made for a number of hollow beam dimensions using the one-dimensional Euler-Bernoulli, Rayleigh, and Timoshenko beam theories. Complete derivations of the elasticity solutions and beam theories are presented. The accuracy of the approximate methods is determined by comparison to elasticity solutions. Subsequent discussion on the limitations of each approximate beam theory in calculating natural frequencies is made. Mode shapes and cross-section deformations for the first five modes of vibration are presented. Additionally, the shape factor for the Timoshenko beam theory is analyzed for hollow-anisotropic sections.