Solution of the nonlinear equations for wake-induced flutter via the Krylov and Bogoliubov method of averaging

Abstract

Using the Krylov & Bogoliubov (1949, Introduction to Non-Linear Mechanics, Princeton: Princeton University Press) method of averaging, solutions have been obtained to the previously developed nonlinear equations of motion for wake-induced flutter of one circular cylinder in the wake of a fixed similar cylinder. The results obtained have been compared with previously obtained ones via numerical integration of the same equations; the agreement is excellent, but there is a considerable saving in computational time using the Krylov and Bogoliubov method. It has been reconfirmed that, when the windward cylinder is held fixed, increasing mechanical damping is not a very efficient way of decreasing the amplitude of oscillation of the leeward cylinder. Provided the same set of aerodynamic force coefficients are employed the nonlinear analysis predicts essentially the same lower flutter boundary as that obtained via a linearized analysis. There is, however, evidence that the leeward cylinder acts as a hard oscillator, resulting in a considerable difference in the upper flutter boundary obtained via the nonlinear analysis vis-a-vis the linearized theory.