Modal Analysis of a Rotating Thin Plate via Absolute Nodal Coordinate Formulation

Abstract

Modal analysis of a rotating thin plate is made in this paper through the use of the thin plate elements described by the absolute nodal coordinate formulation (ANCF). The analytical expressions of elastic forces and their Jacobian matrices of the thin plate elements are derived and expressed in a computationally efficient way. The static analysis of a cantilever thin plate and the modal analysis of a square thin plate with completely free boundaries are made to validate the derived formulations. The modal analysis of a rotating cantilever thin plate based on the ANCF is studied. The effect of rotating angular velocity on the natural frequencies is investigated. The eigenvalue loci veering and crossing phenomena along with the corresponding modeshape variations are observed and carefully discussed. Finally, the effects of dimensional parameters on the dimensionless natural frequencies of the thin plate are studied.