A method, involving the use of an integrating matrix operator, is developed for calculating closed form numerical solutions to linear differential equations.The procedures developed yield the time history of the dependent variables due to any forcing function and initial values by simple
matrix multiplication. A closed form steady state solution is further shown for the special case of periodic coefficients and periodic forcing. The method is applied to the equations of motion of a two degree of freedom helicopter rotor blade. Due to the absence of physical restrictions on
the coefficients of the equations of motion (except that they may not be functions of the dependent variables), it is seen that the effects of Mach number and reversed flow may be handled in a nearly exact manner when linear conditions exist. The steady state solution to the complete nonlinear
equations is treated as a perturbation on a good linear approximation. An iterative scheme is shown for this solution. Illustrative numerical results are given showing the effects of several parameters on stability and the convergence of the nonlinear steady state solutions.
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Document Type: Research Article
Engineering Analysis, Kaman Aircraft Corporation, Bloomfield, Connecticut
Publication date: 1965-07-01
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