Identification of weak nonlinearities in MDOF systems based on reconstructed constant response tests

A novel strategy to characterize and identify structural nonlinearities in MDOF systems based on reconstructing constant response tests from constant excitation tests is developed in this paper. Constant displacement frequency response functions (FRFs) can be measured by a stepped sine test where the displacement is controlled at every frequency of interest. In these FRFs, the nonlinear restoring force is effectively linearized and natural frequencies can be estimated by linear modal analysis. Using a series of constant displacement tests, the relationship of equivalent stiffness versus displacement can be established by curve fitting, and hence, the nonlinear stiffness characterized. This paper proposes a method to reconstruct the constant displacement FRFs from stepped sine tests with constant excitation; this avoids the requirement to control either the response or force amplitude leads to a faster and more stable testing program. Similarly, damping nonlinearities in structures can be characterized and identified by constant velocity tests reconstructed in a similar way. This approach of FRF reconstruction is mathematically simple and suitable for structures with weak nonlinearities. The method is demonstrated on a framed structure with unknown weak nonlinearities, and the nonlinear stiffness and damping parameters of the structure are identified and validated. The results demonstrate the feasibility and effectiveness of the approach and also show the potential for practical applications in engineering.