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Acquiring elastic properties of thin composite structure from vibrational testing data

Vitalii Aksenov, Aleksey Vasyukov, Katerina Beklemysheva

TL;DR

This paper addresses nondestructive identification of elastic properties for a thin composite plate from vibrational AFC data under viscoelastic damping. A forward model based on Kirchhoff-Love plate theory is solved with Morley finite elements and corrected for accelerometer inertia, while the inverse problem is posed as a nonlinear least-squares problem solved via differentiable programming using automatic differentiation. The authors combine trust-region Newton methods for local convergence with differential evolution for robust global initialization, demonstrating accurate parameter recovery in isotropic tests and highlighting the importance of multiple AFC peaks for identifiability. The approach facilitates efficient experiment planning and can be extended to frequency-dependent moduli and time-domain data, with potential for GPU-accelerated scaling and improved loss formulations.

Abstract

The problem of acquiring elastic properties of a composite material from the data of the vibrational testing is considered. The specimen is considered to abide by the linear elasticity laws and subject to viscoelastic damping. The BVP for transverse movement of such a specimen under harmonic load is formulated and solved with finite-element method. The problem of acquiring the elastic parameters is then formulated as a nonlinear least square optimization problem. The usage of the automatic differentiation technique for stable and efficient computation of the gradient and hessian allows to use well-studied first and second order optimization methods, namely Newton and BFGS. The results of the numerical experiments on simulated data are analyzed in order to provide insights for the experiment planning.

Acquiring elastic properties of thin composite structure from vibrational testing data

TL;DR

This paper addresses nondestructive identification of elastic properties for a thin composite plate from vibrational AFC data under viscoelastic damping. A forward model based on Kirchhoff-Love plate theory is solved with Morley finite elements and corrected for accelerometer inertia, while the inverse problem is posed as a nonlinear least-squares problem solved via differentiable programming using automatic differentiation. The authors combine trust-region Newton methods for local convergence with differential evolution for robust global initialization, demonstrating accurate parameter recovery in isotropic tests and highlighting the importance of multiple AFC peaks for identifiability. The approach facilitates efficient experiment planning and can be extended to frequency-dependent moduli and time-domain data, with potential for GPU-accelerated scaling and improved loss formulations.

Abstract

The problem of acquiring elastic properties of a composite material from the data of the vibrational testing is considered. The specimen is considered to abide by the linear elasticity laws and subject to viscoelastic damping. The BVP for transverse movement of such a specimen under harmonic load is formulated and solved with finite-element method. The problem of acquiring the elastic parameters is then formulated as a nonlinear least square optimization problem. The usage of the automatic differentiation technique for stable and efficient computation of the gradient and hessian allows to use well-studied first and second order optimization methods, namely Newton and BFGS. The results of the numerical experiments on simulated data are analyzed in order to provide insights for the experiment planning.
Paper Structure (21 sections, 31 equations, 8 figures, 2 tables, 2 algorithms)

This paper contains 21 sections, 31 equations, 8 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Previous theoretical and experimental studies
  3. Experimental setup and physical assumptions
  4. Description of experimental stand
  5. Governing equations
  6. Mathematical model
  7. BVP for AFC
  8. Formulation of the inverse problem
  9. Numerical method for direct problem
  10. Finite Element Solution
  11. Correction of inertia terms due to accelerometer mass
  12. Optimization problem
  13. Automatic differentiation
  14. Trust-region methods
  15. Global optimization
  16. ...and 6 more sections

Figures (8)

  • Figure 1: Example AFC for the experimental setup, described below. Ratio of amplitudes and phase shift between driving vibration and response is plotted on the right and on the left, respectively.
  • Figure 2: Mesh for the numerical experiments with the isotropic strip. The right side is clamped, and the area, occupied by the accelerometer is highlighted in red.
  • Figure 3: AFCs, obtained with different approaches for modelling the influence of the accelerometer.
  • Figure 4: AFCs for symmetric and shifted positioning of the accelerometer.
  • Figure 5: AFCs before and after local optimization for $f_{max} = 600\ Hz$
  • ...and 3 more figures