A new method for measuring nonharmonic periodic excitation forces in nonlinear damped systems

The purpose of this study is to identify an external loading of long time duration, which is nonharmonic but periodic, acting on a nonlinear dynamic system with nonlinear restoring as well as nonlinear damping. A new procedure is proposed for the force identification through an inverse formalism. However, this involves a Volterra-type nonlinear integral equation of the first kind, which lacks solution stability. Therefore, the nonlinear dynamic system under investigation is transformed into a linear relation between forces and pseudo-displacements. The lack of solution stability is resolved by applying available regularization methods. The feasibility of the force identification is demonstrated through a numerical example.