Nonlinear system identification based on restoring force transmissibility of vibrating structures

In vibrating elastic structures, the motion at locations with no external load is induced by internal forces and due to transmissibility. This capability is utilized in this paper for parameter estimation of nonlinear structures in the absence of input measurements. It is demonstrated that the non-linearities are detectable at degrees of freedom away from the excitation with no need for input measurements and mass matrix information. To estimate the linear and nonlinear parameters within the physical equations of motion, the proposed approach is utilized in conjunction with a new data-driven subspace identification algorithm. The idea is to project the output measure-ments onto the basis function that is used for predicting the restoring force, and then separate the nonlinear dynamics from the underlying linear system. The proposed approach is implemented and examined for different structural nonlinearity types and compared to other methods. Moreover, the vibro-impact parameters of three parallel cantilever beams with non-equidistant gaps are experimentally investigated. The results address the feasibility range of the transmissibility-based subspace algorithm for the identification of a broad class of structural nonlinearities when the excitation loads are not measurable.