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In analyzing a structural member composed of two different materials with identical cross-sectional areas, it is crucial to understand how their distinct elastic properties affect the member's response under load. The analysis involves assessing stress and strain distributions using the transformed section concept, which accounts for variations in material properties.
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Inverse Material Identification in Coupled Acoustic-Structure Interaction using a Modified Error in Constitutive

James E Warner1, Manuel I Diaz1, Wilkins Aquino2

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Computational Mechanics
|October 24, 2014
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This study identifies material properties in coupled acoustic-structure interaction (ASI) systems using optimization. The method accurately reconstructs elastic moduli from measurement data, even with noise.

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Parameter estimationacoustic-structure interactionerror in constitutive equationinverse problem

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Area of Science:

  • Computational Mechanics
  • Inverse Problems
  • Acoustic-Structure Interaction (ASI)

Background:

  • Accurate material property identification is crucial for analyzing complex systems.
  • Frequency-domain analysis is essential for understanding dynamic behaviors in coupled physics.
  • Inverse problems in engineering often suffer from ill-posedness, requiring robust regularization techniques.

Purpose of the Study:

  • To develop and validate a novel methodology for identifying heterogeneous linear elastic moduli.
  • To apply the method to frequency-domain, coupled acoustic-structure interaction (ASI) problems.
  • To investigate the effectiveness of two distinct regularization strategies for ill-posed inverse problems.

Main Methods:

  • Formulating the identification problem as an optimization task, minimizing a modified error in constitutive equation (MECE) functional.
  • Incorporating measurement data (solid displacement or fluid pressure) as quadratic error terms within the MECE functional.
  • Implementing two regularization strategies: Morozov's discrepancy principle and an error-balance approach for selecting the weighting coefficient.

Main Results:

  • Successful recovery of elastic parameters in both 2D and 3D ASI systems using simulated measurement data.
  • Accurate reconstruction of material properties demonstrated even when measurement data is corrupted by noise.
  • Both regularization strategies proved effective, with the discrepancy principle offering near-optimal solutions and the error-balance approach providing a practical alternative without prior noise level information.

Conclusions:

  • The proposed MECE-based optimization framework is a robust and effective tool for identifying heterogeneous elastic moduli in ASI systems.
  • The developed regularization strategies successfully address the ill-posed nature of the inverse problem, ensuring reliable results.
  • The methodology's ability to handle noisy data makes it suitable for real-world applications where perfect measurements are unattainable.