Characterization of isotropic viscoelastic materials by the fractional derivative model considering frequency, temperature and static strain
Eduardo Gregorio Olienick Filho1; Carlos Alberto Bavastri2; Eduardo Marcio de Oliveira Lopes2
1 Universidade Tecnológica Federal do Paraná; 2 Universidade Federal do Paraná
doi:10.20906/CPS/CILAMCE2017-0089
Resumo
This work presents a methodology for the integrated dynamic characterization of thermo-rheologically simple viscoelastic materials, considering the influence of frequency, temperature and static deformation due to preload. Therefore, a technique based on the four-parameter fractional derivative model is proposed. The influence of the static deformation is introduced by standardized tests, held at different percentages of strain (5, 7, 10, 12 and 15% to the initial length of the test piece). For ranges of pre-set temperature, frequency and strain values, the Young's modulus complex is measured by keeping the dynamic excitation amplitude constant at 0.1mm (~0.01% of the length of the specimen). The experimental results with butyl rubber are used to identify the fundamental parameters of the fractional derivative model for the Young's modulus, which describe the effect of frequency, as well as to identify additional parameters, which account for the effects of temperature and static strain. The identification follows the concepts of inverse problem, minimizing the objective function assembled from the mean square error between the experimental Young's modulus and its analytical equivalent obtained through the employed model. That results in a three-dimensional matrix, since the influence of frequency, temperature and static strain is considered. At the end of the optimization process, all the desired parameters are obtained, which allows, among other actions, the Generation of standard nomograms for the complex Young modulus of the investigated material, which are essential for vibration control designs. The results show that for an adequate control design, particularly if it is of vibration isolation, it is important to have different nomograms (depending on frequency and temperature) for each preload.
Palavras-chave: viscoelastic materials; integrated dynamic characterization; fractional derivatives; nonlinear optimization technique