A PERTURBATION SOLUTION FOR THE FLEXIBLE ROTATING-DISK - NONLINEAR EQUILIBRIUM AND STABILITY UNDER TRANSVERSE LOADING

A singular perturbation solution is developed for the transversely loa ded, flexible rotating disk using the von Karman large deflection theo ry of thin plates. No solution exists for these equations in the limit of vanishing dimensionless bending stiffness, E. This fact, along wit h the desire to have the terms describing non-linear membrane stretchi ng appear in the leading order equations, motivates a perturbation exp ansion for displacement of the form w similar to epsilon(-1/2)w(0) + w (1) +....The dimensionless transverse loading term is retained in the leading order equations only if it is rescaled by epsilon(1/2). This r escaling of transverse load magnitude constitutes a similitude predict ion for unifying the equilibrium and stability measurements of differe nt flexible, rotating disks. Experimental measurements of the stabilit y of flexible rotating disks under transverse point loading support th is prediction. In addition, the numerically computed stability of the perturbation solution agrees quantitatively with the experimental meas urements.