Experimental identification of the material constitutive equation by means of forced sinusoidal excitation measurements

Experimental measurements of forced sinusoidal excitation and response are used to identify the material model equation of homogeneous uniform beam specimens in flexural conditions. The contribution of the measurement system structure to the specimen frequency response function is estimated to be used for calibration, and the stress strain relationship of the beam specimen is estimated by means of an optimization algorithm. A Standard Linear Solid material model is considered, so that a rational polynomial function, in the frequency domain, can be used for both the instrument frame and the material model. A physically sound model for the instrument frame is obtained by eliminating unphysical and unstable poles from the rational function model. Such model is then used for the identification of the beam material model parameters in order to filter the instrument contribution to the beam measurements. The use of different polynomial function bases such as Forsythe, Legendre and Chebyshev and its influence on the accuracy of the model results is investigated.