Research On The Fractional Derivative Consititutive Model Of The Rubber Isolator And Its Dynamic Applications

Usually there was an isolator between APU and the airplane to isolate vibration and otherimpacts. High damping rubber material was a viscoelastic material, and was widely used in theisolator. It was very imprecise to predict the response of the dynamics of rubber with the traditionalviscoelastic model, and fractional derivative was widely used in dynamics modeling for rubber. In thispaper, the dynamics constitutive model of rubber was built, and dynamic characteristics was analyzedaround its constitutive model.The main research work and results of the paper were listed as follows:1) According to the basic theory of the Riemann-liouville fractional derivative, thefour-parameter fractional derivative model expression was derived and the3D fractional derivativeconstitutive model of the APU rubber isolator was derived based on the four-parameter fractionalderivative model.2) The test bench was designed with double shear rubber specimen, the dynamic stiffness wastested for the rubber specimen, and the test data were fitted with the least squares method. The resultshowed that the four-parameter fractional derivative model was more consistent with experimentaldata.3) Based on Grünwald fractional derivative theory and the four-parameter fractional derivativeconstitutive model, the program was written and the APU isolator was analyzed with the finiteelement method.4) The test data was collected for the response of the APU isolator, and results was compared andanalyzed for differences between the test results and finite element simulation. It was shown that thefinite element program could basically accurate predicted the dynamic response of the APU isolatorrubber.5) The fractional derivative differential equations of motion were built and solved numericallyconcerning with impact nonlinear. According to the results of the impact test, the fitting result showedthat the nonlinear model could accurately predicted the impact response of the APU isolator, makinguse of the method of least squares fitting for to determine the unknown parameters in the equation.The foundation was layed for study of the rubber materials dynamic characteristics, and themethod was supplied for to more accurately predict the dynamic response of the APU rubber isolator.