Application of the arc-length method in nonlinear frequency response

In the last years, several iterative numerical techniques have been developed to solve nonlinear structural problems. Some of these methods are capable to trace complex paths in the space load/displacement. One of those most popular procedures are the are-length method of Crisfield, that possesses the capability to overcome inflection points, without having the necessity of determining them. A great similarity exists between curves of nonlinear load/displacement path obtained with the arc-length method, and curves of the frequency response of non-linear dynamic system. Both curves present limit points with snap-back and snap-through phenomena. This work consists of the description and the application of the arc-length method to solve a system of nonlinear equations obtaining as a result the nonlinear frequency response.