Method of multiple scales and identification of nonlinear structural dynamic systems

A procedure is developed to identify the parameters of a nonlinear structural dynamic system with a single degree of freedom. A cubic nonlinearity is assumed for purposes of illustration. In comparison to the direct identification procedures, which depend on either the availability of data on all four variables, namely, velocity, acceleration, displacement, and the input of the system, or the formulation of an algorithm that is used to numerically integrate differential equations at each iterative step, the developed procedure requires the data on only one of the field variables and no numerical integration at each step. The input to the system is also treated as an unknown. The results from the perturbation identification procedure are compared with the results from two direct identification procedures.