La. Shultz et Vr. Murthy, DIRECT APPLICATION OF THE TRANSFER-MATRIX METHOD TO SOLVE NONLINEAR AUTONOMOUS BOUNDARY-VALUE-PROBLEMS WITH MULTIPLE BRANCHES, Computers & structures, 49(3), 1993, pp. 439-452
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.