DYNAMICS OF A FLEXIBLE ROTATING BEAM INTERACTING WITH A FLAT RIGID SURFACE .1. MODEL DEVELOPMENT

The dynamics of a flexible Euler-Bernoulli beam attached to a uniforml y rotating hub and interacting at the tip with a plane rigid surface p arallel to the hub axis is analyzed. Lagrange's equations and a genera lized co-ordinates-eigenfunctions representation for the displacement fields are used to formulate the unconstrained motion equations. It is shown that one must account for the longitudinal displacements if dyn amical stiffening is to be observed. A quadratic approximation for the se displacements is used, and a computationally effective way of by-pa ssing the calculation of the volume integrals at every integration ste p, by matrix-vector multiplications is implemented. The energy dissipa ting constraint, which requires the tip of the filament to move on the surface, is imposed with a Lagrange multiplier and a generalized forc e column vector corresponding to dry friction. A procedure of evaluati ng the generalized friction force in terms of the generalized co-ordin ates and velocities is presented. The presence of dynamical stiffening is tested and the calculated values of the fundamental frequency are found to be in excellent agreement with data from literature. (C) 1996 Academic Press Limited