A class of nonlinear discrete systems with an arbitrary number of degrees of freedom is studied for their steady state vibrations. The coordinates are first transformed to the principal coordinates corresponding to the linear part of the system. An iteration scheme is used to obtain the desired solutions. Some special effects of the relations between the linear natural frequencies on the qualitative nature of the solutions are demonstrated. It is shown that if the linear natural frequencies do not possess certain re¬lations, the system can be treated in a manner similar to that for a system of a single degree of freedom. In other cases the procedure gets more complicated. The various solutions are then examined for their stability. Poincare's theory of singularities in the phase plane is used to study the stability of those problems that can be treated in a manner similar to that for a single degree of freedom system. In all other cases the stability is examined by applying the Routh-Hurwitz criterion to a transformed set of equations. Solution for one specific problem is obtained and checked against those obtained from an analog type computer.
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