Deterministic and stochastic partial linearization approach for nonlinear reduced order models of structures

The large computational effort required for finite element analysis predictions of the dynamic response of thin aircraft panels in extreme aeroacoustic environments has led to significant research on the development of nonlinear reduced order models (ROMs). ROMs reduce the finite element model to a low-order system of nonlinear modal-like equations which can be integrated in the time domain. Although much more computationally efficient than finite element models, it may still be expensive to build and solve the ROM equations of motion for complex structures owing to the large number of nonlinear terms involved. To further reduce this computational cost, deterministic and stochastic partial linearization methodologies are introduced in this paper, in which the nonlinearity is retained only for the dominant modes of the basis. In the stochastic approach, the solution approximation error introduced by the partial linearization is recognized as an epistemic uncertainty, which is modeled by randomizing the linear stiffness terms of the non-dominant modes. The nonparametric stochastic approach is adopted for this modeling and its uncertainty level is estimated using maximum likelihood estimation. Both methods are verified on the ROM of a 96,000 degrees-of-freedom, 9-bay panel, where significant computational gains are observed for dynamic simulations. The response of the full nonlinear ROM in the verification study is within the 95% confidence bounds of the stochastic partially linearized model.