Identification of Complex Modulus From Measured Strains on an Axially Impacted Bar Using Least Squares

Hillström, Lars; Mossberg, Magnus; Lundberg, Bengt

doi:10.1006/jsvi.1999.2649

Cited by 74 publications

(40 citation statements)

References 10 publications

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“…(4). In (14), È ( ) and AE ( ) are the unknown amplitudes of waves traveling in positive and negative Ü direction, respectively.…”

Section: Fitting a Parametric Model Directly From Datamentioning

confidence: 99%

“…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%

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Parametric identification of complex modulus

Rensfelt

Söderström

2011

Automatica

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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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“…(4). In (14), È ( ) and AE ( ) are the unknown amplitudes of waves traveling in positive and negative Ü direction, respectively.…”

Section: Fitting a Parametric Model Directly From Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Parametric identification of complex modulus

Rensfelt

Söderström

2011

Automatica

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“…This means that for the ear canal the impedance of the ear canal'sw all is included [15] to model sound propagation in the outer ear and in addition the acoustics of the middle and inner ear are represented by the impedance at the eardrum [16]. Further,the impedance of the MIRE microphone [17] is taken into account as well as the earplug's material [18] and the impedance of the entity earplugear canal [19]. Besides the impedance of the different structures, the effect of viscosity and heat conduction is included for the sound propagation in the earplug'schannels because their diameter is very small.…”

Section: Simulations Of the Transfer Functionsmentioning

confidence: 99%

Digital Filters for Accurately Verifying the Performance of Hearing Protectors in Use

Bockstael¹,

Deschrijver²,

Botteldooren³

et al. 2010

Acta Acustica united with Acustica

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SummaryThe performance of hearing protectors can be assessed in situ by measuring the sound pressure inside the ear canal following the Microphone In Real Ear (MIRE)p rotocol. Thus acustom-made earplug has been designed with an inner bore, allowing the insertion of the MIRE measurement microphone. However, the actual exposure levelcan only be accurately predicted if the relationship, henceforth called transfer function, between the sound levelatthe microphone and at the eardrum is known. Previous research has revealed that the transfer function can be precisely approximated with an individualized FDTD model, butasimplified method is needed for practical implementation due to the time-consuming nature of this numerical technique. In this matter,aone-dimensional analytical model appears inadequate, hence an approximation to the detailed FDTD model based on digital filter design is proposed instead. Twod i ff erent approaches have been applied to estimate the individualized filter coefficients: multiple linear regression and Multivariate Orthonormal Ve ctor Fitting (MOVF).I ng eneral, both methods can predict an individual'st ransfer function quite accurately if the length of the earplug'si nner bore and the length of the residual part of the ear canal behind the protector are known. However, MOVF seems more reliable for ears with alonger residual part.

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“…This work is based on the experimental data obtained in (Hillström et al, 2000), where the material PMMA (plexiglass) was studied. A rod of L = 2 m was axially impacted, and strain data collected at N = 4096 discrete time instances, with a sampling interval of 20 µs.…”

Section: Optimization Aspectsmentioning

confidence: 99%

“…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%