Data Reduction from Nonlinear Response Curves

In experimental research, the inverse problem of nonlinear vibration is often encountered. The most comprehensive and straightforward analysis is possible with systems having a nonlinear restoring force and a linear damping. With such systems the derivation of the restoring force can be separated from the determination of the damping and mass. This is possible by construction of the curve of natural frequencies pertinent to a given response curve. The shape of the curve of natural frequencies directly indicates the nature of the restoring force. All systems having the same linear damping and various nonlinear or linear restoring forces are related in a simple manner. The resonant amplitudes of all such systems are determined by a straight line passing through the origin. Also, two fairly general cases of nonlinear damping are considered (in addition to the nonlinear restoring force) in both one and many degrees-of-freedom.