Identification of the Dynamic Properties of Linear Viscoelastic Materials by the Wave Propagation Testing

Sogabe, Yuji; Tsuzuki, Masayuki

doi:10.1299/jsme1958.29.2410

“…In the frequency domain this relationship looks like ( ) = ( ) ( ) (1) where ( ) and ( ) denotes the Fourier transformed stress and strain, respectively. Knowledge about the complex modulus is essential in understanding the materials behavior in a dynamic environment, and can be determined through different kinds of wave propagation experiments, as studied in for example [1,4,16].…”

Section: Introductionmentioning

confidence: 99%

“…The complex modulus of a viscoelastic material can be identified both nonparametrically, as in [5,8,10], or parametrically, as in [11,12,16]. In nonparametric identification, the value of the complex modulus is determined at a number of discrete frequency points .…”

Section: Introductionmentioning

confidence: 99%

Parametric identification of complex modulus

Rensfelt

¹

,

Söderström

²

2011

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This report treats three different approaches to parametric identification of the complex modulus of a viscoelastic material. In the first approach, a nonparametric estimate is used to fit the parametric model, while in the other two the model is fitted directly from data. In all three cases, theoretical expressions for the accuracy of the estimate are derived under the assumption that the measurement noise is white and that the signal-to-noise ratio is large. The expressions are validated against both simulated and experimental data. In the case of experimental data it is seen that the theoretical expression severely underestimates the variance of the identified parameters, and one of the expressions is therefore modified to cover the case of correlated noise with much better agreement as a result.

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“…In the frequency domain this relationship looks like ( ) = ( ) ( ) (1) where ( ) and ( ) denotes the Fourier transformed stress and strain, respectively. Knowledge about the complex modulus is essential in understanding the materials behavior in a dynamic environment, and can be determined through different kinds of wave propagation experiments, as studied in [1], [10] and [23]. In order to get good quality estimates, the collected data should contain as much valuable information as possible, and design parameters that influence the information content must thus be chosen carefully.…”

Section: Introductionmentioning

confidence: 99%

Optimal Excitation for Nonparametric Identification of Viscoelastic Materials

Rensfelt

¹

,

Söderström

²

2011

IEEE Trans. Contr. Syst. Technol.

5

0

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The problem of optimal excitation in nonparametric identification of viscoelastic materials is considered. The goal is to design the input spectrum in an optimal way, so that the average variance of the estimates is minimized. It is shown how the covariance matrix of the estimates can be expressed in terms of the input spectrum. This theory can also be used in order to identify the (unknown) excitation, used in a particular experiment, from measured strain data. Two scalar criteria connected to A-and D-optimal experiment design, are considered. The results indicate that the accuracy of the estimates can be greatly improved by applying an optimal input signal. Issues concerning the implementation of the achieved optimal input spectrum in live experiments are discussed briefly.

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“…A viscoelastic material is characterized by its complex modulus that relates stress and strain, and can be determined through wave propagation experiments, as studied in (Sogabe and Tsuzuki, 1986), (Blanc, 1993) and (Hillström et al, 2000). To get good quality estimates, the collected data should contain as much valuable information as possible, and design parameters that influence the information content must thus be chosen carefully.…”

Section: Introductionmentioning

confidence: 99%