Frequency response expansion strategy for nonlinear structures

Finite-element (FE) models of engineering structures are generally of high order to provide detailed descriptions of the structure's static and dynamic response. However, experimental testing of such structures can only obtain spatially-incomplete sets of response data. For linear structures, the response of unmeasured degrees-of-freedom (DOFs) can be estimated using linear expanded mode shapes and experimentally-extracted linear modal parameters. Nevertheless, such techniques cannot be directly applied to nonlinear structures when the responses are distorted when driven by high levels of excitation and modal superposition is no longer valid. This paper presents a novel strategy to expand spatially-incomplete measured data to the FE-modelled DOFs that is suitable for nonlinear structures. This strategy is an extension of the current linear expansion techniques; it starts with linear experimental modal analysis and conventional linear expansion technique to estimate the unmeasured responses of the underlying linear system using low-amplitude testing data. Then the nonlinear responses, measured during high-amplitude testing, are correlated with the measured underlying linear dynamics to extract the residuals, which are subsequently used to estimate the nonlinear stiffness and damping coefficients. Finally, the unmeasured nonlinear responses are expanded using the modal properties from linear experimental analysis and estimated nonlinear coefficients. The strategy is validated using two case studies: the first is a numerical two-beam example with a localised nonlinear spring; the second is an asymmetric diesis-like structure with geometrical nonlinearities, in which data from experimental testing are used.