J. Srisertpol and A. Rodpai (Thailand)

Control Theory, Mechanics of Materials and Weighting Least Square Method

The study and analysis of mathematical models of linear viscoelastic materials is to investigate the relationship between input (stress or strain) on such materials and output (strain or stress) that occurs from the response of such materials. Generally, the mathematical models used for linear viscoelastic materials are the Maxwell model, the Kevin-Voigt model and the standard linear model in which all these models cannot accurately describe the properties of linear viscoelastic materials. For instance, the Maxwell model does not show the recovery behavior of materials, the Kevin-Volgt model does not demonstrate the stress relaxation and the standard linear model can be applied well only for solid materials that can be recovery 100 %. In the present paper, the study is aimed to identify the mathematical model of linear viscoelastic materials that is expressed in terms of transfer function that can accurately describe the properties of linear viscoelastic materials. The control theory can be used to find out the mathematical model of linear viscoelastic materials using the system identification method for which the storage modulus ( )G ω′ , loss modulus ( )G ω′′ and input frequency )(ω obtained from the measurement are used. To determine the transfer function coefficients, the least square method, the weighting least square method with input frequency, and the weighting least square method with variance are used. The study results will be used to develop more efficient experimental set-up.

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