ON AN INTEGRATED DYNAMIC CHARACTERIZATION OF VISCOELASTIC MATERIALS BY FRACTIONAL DERIVATIVE AND GHM MODELS

Abstract

THE PASSIVE VIBRATION CONTROL OF MECHANICAL SYSTEMS UNDER UNWANTED VIBRATIONS CAN BE ACCOMPLISHED IN A VERY EFFICACIOUS WAY BY THE USE OF DEVICES INCORPORATING VISCOELASTIC MATERIALS. IN THESE CASES, THE DEVELOPMENT OF A VIBRATION CONTROL STRATEGY GENERALLY REQUIRES THE PREVIOUS AND WIDE KNOWLEDGE OF THE DYNAMIC PROPERTIES (THAT IS, THE DYNAMIC MODULUS OF ELASTICITY AND THE CORRESPONDING LOSS FACTOR) OF THE EMPLOYED VISCOELASTIC MATERIAL. THESE PROPERTIES ARE DETERMINED BY TESTING THE MATERIAL OF CONCERN IN BROAD RANGES OF FREQUENCY AND TEMPERATURE, WHICH ARE THE MOST IMPORTANT VARIABLES IN GENERAL APPLICATIONS. THEN, FROM THE RESULTING EXPERIMENTAL DATA, THE CORRESPONDING REDUCED FREQUENCY NOMOGRAM IS GENERATED (BASED ON THE FREQUENCY-TEMPERATURE SUPERPOSITION PRINCIPLE) AND AN ADEQUATE MATHEMATICAL MODEL IS FITTED, SUPPLYING THE INFORMATION REQUIRED AT THE DESIGN STAGE. AMONG THE AVAILABLE MATHEMATICAL MODELS, THE FRACTIONAL DERIVATIVE MODEL AND THE GHM MODEL, ALONG WITH EITHER THE WLF EQUATION OR THE ARRHENIUS EQUATION, ARE NOW VERY PROMINENT. THE CURRENT WORK INVESTIGATES THE USE OF THESE MODELS IN THE WIDE AND INTEGRATED DYNAMIC CHARACTERIZATION OF A TYPICAL AND THERMORHEOLOGICALLY SIMPLE VISCOELASTIC MATERIAL. IT IS TAKEN EXPERIMENTAL DATA COLLECTED FROM 0.1 TO 100 HZ AND –40 °C TO 50 °C, WHICH ARE SIMULTANEOUSLY MANIPULATED TO RAISE BOTH THE FREQUENCY AND THE TEMPERATURE DEPENDENCIES. IN THE CURVE FITTING PROCESS, A HYBRID APPROACH, COMBINING TECHNIQUES OF GENETIC ALGORITHMS AND NONLINEAR OPTIMIZATION, IS ADOPTED. THE ENSUING RESULTS ARE EVALUATED BY MEANS  OF OBJECTIVE FUNCTION VALUES, COMPARATIVE EXPERIMENTAL-PREDICTED DATA PLOTS AND ALSO BY THE AKAIKE’S INFORMATION CRITERION (AIC). IT IS SHOWN THAT THE FOUR PARAMETER FRACTIONAL DERIVATIVE MODEL PRESENTS EXCELENT CURVE FITTING RESULTS. AS TO THE GHM MODEL, ITS MODIFIED VERSION IS THE MOST ADEQUATE BUT A HIGHER NUMBER OF TERMS IS REQUIRED FOR A SATISFACTORY GOODENESS-OF-FIT. YET THE FRACTIONAL DERIVATIVE MODEL STANDS OUT.