A Lumped Parameter Model of a Fibre-Reinforced Composite Plate with Temperature Dependence Based on Thermal Vibration Measurements

Background: Experimental modelling techniques are still rare for composite structures under complex thermal environments. Objective: In this paper, by taking a fibre-reinforced composite plate (FRCP) as an example, a lumped parameter model of the FRCP with temperature dependence is developed from an experimental perspective. Methods: Initially, a series of thermal vibration measurements are performed under different temperatures to characterize the temperature-dependent vibration behaviours of the FRCP, in which the natural frequencies and modal damping ratios are identified via the variational mode decomposition method. Then, according to the degree of freedom division criterion of the half-wave number, a mass-spring-damper lumped parameter model of this type of composite plate considering additional thermal stiffness is established. Finally, a novel method of determining the lumped stiffness and damping parameters in this model is proposed based on the above experimental data. Results: The developed model is verified by comparing the theoretical natural frequencies, modal shapes and resonant responses with the test results at 40, 120, 220 and 300 °C, for which the calculation errors are within an acceptable range. Conclusions: It has been found that the accuracy of this lumped parameter model can be further improved by applying a larger number of modes to inversely calculate the lumped stiffness and damping parameters. Meanwhile, the efficiency can also be increased by adopting an appropriate step size in the iterative calculation of the additional thermal stiffness.