On the use of flexural wave propagation experiments for identification of complex modulus

In this paper, we investigate the nonparametric estimation of the frequency dependent complex modulus of a viscoelastic material. The strains due to flexural wave propagation in a bar specimen are registered at different cross sections. The time domain data is transformed into frequency domain using discrete Fourier transform and a nonlinear least squares algorithm is then employed to estimate the complex modulus at each frequency. Inherent numerical problems due to associated ill-conditioned matrices are treated with special care. An analysis of the quality of the nonlinear least squares estimate is also carried out. The validity of the theoretical results are confirmed by numerical studies and experimental tests.