Measurement of nonlinear normal modes using mono-harmonic force appropriation: Experimental investigation

A structure undergoing large amplitude deformations can exhibit nonlinear behavior which is not predicted by traditional linear theories. Structures with some initial curvature offer an additional complication due to buckling and snap through phenomena, and can exhibit softening, hardening and, internal resonance. As a structure transitions into a region of nonlinear response, a structure’s nonlinear normal modes (NNMs) can provide insight into the forced responses of the nonlinear system. Mono-harmonic excitations can often be used to experimentally isolate a dynamic response in the neighborhood of a single NNM. This is accomplished with an extension of the modal indicator function and force appropriation to ensure the dynamic response of the structure is on the desired NNM. This work explores these methods using two structures: a nominally-flat beam and a curved axi-symmetric plate. Single-point force appropriation is used by manually tuning the excitation frequency and amplitude until the mode indicator function is satisfied for the fundamental harmonic. The results show a reasonable estimate of the NNM backbone, the occurrence of internal resonance, and couplings between the underlying linear modes along the backbone.