基于频域本征正交分解的几何非线性动力学降阶

In order to improve solving efficiency of a structural nonlinear dynamic system under large geometric deformation condition and study its dynamic behavior in a specified frequency range, the proper orthogonal decomposition (POD) method in frequency domain was used to study the dynamic order reduction problem of a geometrically nonlinear structure with a cantilevered plate taken as the study object. The geometrically nonlinear stiffness of the plate was solved using the cooperative rotation (CR) method. POD base vectors were generated with snapshots computed in a specified frequency domain, and Galerkin method was used to realize the order reduction of dynamic system. The nonlinear stiffness was added to the external force term in the form of increment, and the nonlinear behavior of the system was reflectedin the form of generalized external force. The POD order reduction analysis in frequency domain and comparison were done for the cantilevered plate.Results showed that (1) for a linear system, the POD order reduction analysis in frequency-domain has high precision, the error is less than 1%, and its solving time is far less than that for the full order system, the solving time for 1 order POD is less than 50% of that for the full order system; (2) for a nonlinear system, the error of 1 order POD analysis is less than 1.5%, and the error of 3 order POD analysis is less than 0.5%, the solving time for the two cases is less than 75% of that for the full order analysis under sine and step loads; (3) for a geometrically nonlinear dynamic system under multi-point random loads, if the first 6 orders POD base vectors are kept after order reduction in frequency domain, the reduced order system's analysis error is less than 0.5% and its solving time is just 79% of that for the full order system.