Estimation of state and identification of complex modulus based on measurements om a bar traversed by waves

Sammanfattning: Estimation of state and identification of complex modulus based on measurements on non-uniform rods and beams have been studied theoretically and experimentally. Two principal cases were studied. In the first case, the material properties are fully known and the state at a section is to be estimated. In the second case, the complex modulus is to be identified (and optionally the state is to be estimated). Nothing needs to be known about supports, structures and loads outside the rod and beam segments under consideration. In particular, analytical expressions of the standard deviation of the non-parametric complex modulus were derived for a uniform rod.Experimental tests were performed with rods of polymethyl methacrylate (PMMA) and polypropylene (PP) and with beams of aluminium, PMMA and PP. Both parametric and non-parametric complex moduli were determined in the frequency domain. For a uniform rod, parametric complex moduli were determined also in the time domain.It was found that the identification of the non-parametric complex modulus and the estimation of state may be inaccurate at certain discrete frequencies. It was shown how such inaccuracies can be avoided in the frequency range of interest by use of more than the minimum number of measurement sections and a non-uniform distribution of them. If a parametric complex modulus is used, the results should be compared with those for a non-parametric modulus. The parametric complex moduli determined in the time domain deviated more than expected from the complex moduli determined in the frequency domain. The reasons for these deviations are not fully understood.