Controlling the One-Dimensional Motion of Hybrid Vibrational Rod Systems

Abstract

A mathematical model of the one-dimensional controlled motion of a hybrid vibrational system is proposed. The plant includes an inhomogeneous elastic rod with loads concentrated at its endpoints. An analytical-numerical procedure for finding the eigenvalues (eigenfrequencies) and eigenfunctions is developed. A novel procedure to take into account the nonuniform distributed forces and forces concentrated at the endpoints using a modification of Grinberg’s approach is presented. Efficient statements and constructive approximate solutions of the problems for controlling the motion of a countably dimensional vibrational system with a complex distribution of eigenfrequencies are proposed.