Non-conservative dynamics of spinning beam systems with general boundary conditions.

摘要

This thesis uses analytical techniques to solve for the free and forced vibration response of non-conservative, spinning Timoshenko beams. The free vibration analytical method employs differential matrix operators and an appropriately defined state vector to reduce the partial differential equations to a system of ordinary differential equations. A series-type solution is used to solve the system of ordinary differential equations. The forced vibration analytical method requires an analysis of the adjoint system since the presence of distributed follower forces destroy physical symmetry, hence, making the problem non-self adjoint. The adjoint analysis yields eigenvalues and eigenvectors of the adjoint of the problem. Modal expansion over the real and adjoint system eigenvectors is used to determine the dynamic response of non-conservative, spinning Timoshenko beams.;The free vibration analysis is performed for six boundary condition cases. Each case is investigated for the influence of beam spin rate and magnitude of follower force upon the natural frequencies of the beams. Both the forward and backward precession frequencies are investigated. The forced vibration analysis is performed for the four boundary condition cases that do not include rigid body motion. Results are presented showing the response of each of the boundary condition cases to an exponentially decreasing transverse load for various follower force loadings.