DIRECT APPLICATION OF THE TRANSFER-MATRIX METHOD TO SOLVE NONLINEAR AUTONOMOUS BOUNDARY-VALUE-PROBLEMS WITH MULTIPLE BRANCHES

A direct transfer matrix method is developed to analyze the nonlinear, branched and one-dimensional autonomous boundary value problems. The method is applied to determine (1) the natural frequencies and modes a bout the initial state (vacuum), (2) the nonlinear steady-state deflec tions, (3) the natural frequencies and modes about the trimmed state, and (4) the aeroelastic stability of branched blades in hover. A quasi -steady strip theory is employed for calculation of the aerodynamic fo rces. A Newton-Raphson method based on a quasi-linearization of a nonl inear distributed boundary value problem is developed to solve the ste ady-state deflections of the blade. The formulation is validated by co mparing the results with those obtained by other methods in the litera ture.