An Amplitude- and Temperature-Dependent Vibration Model of Fiber-Reinforced Composite Thin Plates in a Thermal Environment

A thermal environment has a complex influence on the dynamic characteristics of fiber-reinforced composite materials and structures. It is challenging to consider the effects of high temperature and external vibration energy simultaneously on their nonlinear vibration response. In this research, the material nonlinearities, due to both the excitation amplitudes and the high temperatures, are studied for the first time, and a new nonlinear vibration model of fiber-reinforced composite thin plates in a thermal environment is proposed by introducing the nonlinear thermal and amplitude fitting coefficients simultaneously. Then, based on the classical laminated plate theory, the complex modulus approach, and the power function and the Ritz methods, dynamic governing equations in high-temperature environments are derived to solve the nonlinear natural frequencies and vibration responses and damping parameters. Moreover, the three-dimensional fitting curves of the elastic moduli and loss factors, excitation amplitudes, and temperature values are obtained so that the key nonlinear fitting coefficients in the amplitude- and temperature-dependent model can be identified. To validate this model, the experimental tests on CF130 carbon/epoxy composite thin plates are undertaken. It is found that the 3rd and 5th natural frequencies, vibration responses, and damping results obtained from the nonlinear model are consistent with the experimental measurements, and the mechanism of nonlinear thermal vibration behaviour is revealed.