Nonlinear Vibrations of Fiber-Metal Laminates Thin Plates Considering Both Geometric and Material Nonlinearity: Theoretical and Experimental

With the widespread application of fiber-metal laminates in various aerospace fields and the inherent presence of both material and geometric nonlinearities in composites, the prediction of nonlinear vibration characteristics of these structures holds particular importance. This study, based on the Jones–Nelson–Hui and von Kármán theories, utilizes the energy method and the orthogonal polynomial method to solve the differential equations and iteratively obtain the nonlinear natural frequencies and responses. Additionally, the complex modulus method is employed to calculate the nonlinear modal damping ratios. Experimental validation demonstrates the effectiveness of the proposed model, with a frequency error of less than 3.7%, a response error of less than 15.4%, and a damping error of less than 11.5% when compared with experimental results. Finally, the influence of elastic modulus, thickness, and ply configuration on the nonlinear vibration characteristics of the structure is investigated. The discussion reveals that titanium reduces vibrations but should not be too thick, while fiber thickness can be appropriately increased.