Transverse Vibration of a Rectangularly Orthotropic Spinning Disk, Part 2: Forced Vibration and Critical Speeds

Abstract

The transverse forced vibration of a rectangularly orthotropic spinning disk is investigated. The disk is subjected to a constant stationary point-load. Although the deflection of an isotropic disk under these loading conditions is time-invariant in a space-fixed coordinate system, the orthotropic disk undergoes time-dependent oscillatory motion. This phenomenon occurs as a result of the continually changing orientation of material properties with respect to the load. The disk deflection under-the-load is determined as a function of time. Also the deflection along a disk radius and circle containing the load are determined at a fixed instant of time. The occurrence of critical speeds is also investigated. Without damping, virtually any angular speed of the orthotropic disk is found to be critical. This behavior is due to the occurrence of more than one Fourier component in each of the eigenfunctions of the free vibration problem. With damping included, a large amplitude response is found at a speed much less than the lowest classical critical speed of an isotropic disk.