Geometrically Nonlinear Random Response of Stiffened Laminated Plates by Proper-Orthogonal-Decomposition-Based Reduced-Order Modeling

The geometrically nonlinear random vibration response of stiffened laminated plates under acoustic excitation is carried out by using the equivalent linearization (EL) technique combined with the reduced-order model and the finite element method. The nonlinear equations of motion of stiffened laminated plates are obtained based on large deflection finite element formulation. The proper orthogonal decomposition technique is used to select the modal basis, and a reduced-order model of the structures is established. Based on the force error minimization approach, the EL formulation for solving nonlinear random vibration response is derived. Then the EL technique is incorporated into finite element software NASTRAN by the direct matrix abstraction program, and the direct matrix abstraction program also realizes the iterative process of determining the modal equivalent linear stiffness matrix. Then, the statistical dynamic response results obtained by EL and linear method are compared and analyzed. It is verified that the proposed method has high accuracy and efficiency, and it can be applied to the geometric nonlinear random vibration response analysis of stiffened laminated plates. The results show that geometric nonlinearity plays an important role in the vibration response of stiffened laminated plates, especially under high sound pressure loads.

Automated summary

The study investigates the geometrically nonlinear random vibration response of stiffened laminated plates under acoustic excitation using the equivalent linearization technique combined with reduced-order model and finite element method. An EL formulation for solving nonlinear random vibration response is derived based on the force error minimization approach. The proposed method shows high accuracy and efficiency in analyzing the geometric nonlinear random vibration response of stiffened laminated plates.