Nonlinear vibration study of fiber-reinforced composite thin plate with strain-dependent property based on strain energy density function method

The strain energy density function method is proposed to study the nonlinear vibration behavior of the fiber-reinforced composite thin plate with strain dependence. First, the material nonlinearity of the fiber-reinforced composite is extended to the vibration field. On the basis of Jones-Nelson nonlinear model, a theoretical model with the consideration of the strain-dependent nonlinearity is established to illustrate the theoretical principle of the strain energy density function method. In the model, the nonlinear elastic moduli in different fiber directions are expressed as a function of the strain energy density. The nonlinear natural frequencies are solved by Ritz method in conjunction with the classical laminated plate theory and Hamilton's principle, and the nonlinear vibration responses are calculated by Newton-Raphson iteration method. Moreover, a TC300 carbon/epoxy composite plate is taken as a research object. In order to determine the corresponding parameters in the theoretical model, the composite beam specimens are cut off to conduct the stress-strain measurement. The nonlinear natural frequencies and vibration responses of the composite plate under different excitation levels are obtained. The comparisons between the theoretical calculation and experimental test show that the maximum calculation error of the first six natural frequencies with considering the strain-dependent nonlinearity is less than 4.3%, and the maximum calculation error of the resonant responses is less than 12.0% for the third mode and the sixth mode, thus the practicability and reliability of the proposed method have been verified.