Finite element model calibration of a nonlinear perforated plate. (31st March 2017) - Ehrhardt, David A.; Allen, Matthew S.; Beberniss, Timothy J.; Neild, Simon A.
Abstract: This paper presents a case study in which the finite element model for a curved circular plate is calibrated to reproduce both the linear and nonlinear dynamic response measured from two nominally identical samples. The linear dynamic response is described with the linear natural frequencies and mode shapes identified with a roving hammer test. Due to the uncertainty in the stiffness characteristics from the manufactured perforations, the linear natural frequencies are used to update the effective modulus of elasticity of the full order finite element model (FEM). The nonlinear dynamic response is described with nonlinear normal modes (NNMs) measured using force appropriation and high speed 3D digital image correlation (3D-DIC). The measured NNMs are used to update the boundary conditions of the full order FEM through comparison with NNMs calculated from a nonlinear reduced order model (NLROM). This comparison revealed that the nonlinear behavior could not be captured without accounting for the small curvature of the plate from manufacturing as confirmed in literature. So, 3D-DIC was also used to identify the initial static curvature of each plate and the resulting curvature was included in the full order FEM. The updated models are then used to understand how the stress distribution changes at large response amplitudes providing a possible explanation of failures observed during testing. Highlights: This work explores the use of nonlinear normal modes (NNMs) as a guide to the model calibration of geometrically nonlinear finite element models. Initial updates to the structure's modulus of elasticity are performed using the structure's linear normal modes of vibration and measured initial conditions. Further updates to the structure's boundary conditions are performed by comparing the center deflection of the plate predicted from the NNMs measured using high speed 3D digital image correlation and calculated from nonlinear reduced order models (NLROMs). The resulting time domain modal deformation predicted and measured matches well. Finally, the updated NLROMs are used to examine the stress distribution along the NNM providing a potential cause for observe experimental failures.