1ACTIVE MODAL CONTROL OF A FLEXIBLE ROTOR

This study explores the applicability of a novel approach by applying a dual-level control for modal vibration suppression of complex dynamic systems possessing rigid body, diver-gence, flutter, and/or repeated modes. Independent modal space control (IMSC) of undamped or proportionally dam-ped systems has been well established. However, the tech-nology was not correctly developed for non-classically dam-ped systems by the pioneer researchers. For systems with rigid body, divergence, and/or repeated modes, the problems of orthogonality and singularity must be treated in a different fashion to facilitate modal vibration control. The present approach applies a first level control to remove any combination of flutter, divergence, rigid body, and/or re-peated modes by enabling positive definiteness of the aug-mented system. A second level control is then applied for the augmented system with complex modes. Ordinary de-coupling procedure by using the orthogonality of the left and right eigenvectors can thus be applied for subsequent mo-dal control to suppress excessive vibration of the complex dynamic systems. Active modal control of a flexible rotor with repeated rigid body modes is used to demonstrate the concept. NOMENCLATURE A cross-sectional area of the rotor a element length {}d structural nodal displacement vector}{d & structural nodal velocity vector}{d& & structural nodal acceleration vector E Young's modulus of the rotor sE weighting matrix for the s-th modal control Input G shear modulus []G gyroscopic damping matrix I area moment of inertia of a rotor element []K structural stiffness matrix k shear coefficient L left modal matrix []M structural mass matrix N a row vector denoting shape functions TN transposition of the shape functions uQ modal control input sS Riccati matrix for the s-th mode (size 2 x 2) R right modal matrix W rotation speed ss real part of the s-th eigenvalue sw imaginary part of the s-th eigenvalue sl closed loop eigenvalue of the s-th mode 1