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Experimental Verification of the Neural Network Optimization Algorithm for Identifying Frequency-Dependent Constitutive Parameters of Viscoelastic Materials

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Abstract

Purpose

The constitutive parameters of viscoelastic materials, such as storage modulus and loss factor, usually have frequency-dependent characteristics. The combination of polymers with different reinforcement and fillers usually exhibits various mechanical characteristics, which makes the identification of the material properties of viscoelastic materials a challenging task. The present study proposes an inverse identification technique based on a neural network optimization (NNO) algorithm to characterize the frequency-dependent material properties of a viscoelastic material.

Methods

To this end, a symmetric three-layered sandwich plate is considered having face layers of isotropic elastic material and a core layer of viscoelastic material. The experimental free vibration tests are performed using the impact hammer method to determine resonant frequencies and modal loss factors for various eigenmodes. In addition, a numerical model of the sandwich plate is developed to determine vibrational responses utilizing the finite element method. The vibration-based material parameter identification technique is implemented based on the NNO algorithm. The identified material parameters are then compared with the experimental dynamic mechanical analysis (DMA) test results. Furthermore, a numerical parametric study is performed considering the optimized viscoelastic material properties to investigate the influence of various geometrical and structural factors on the free vibration response of the sandwich plate.

Results

The identified results are in excellent agreement with the experimental DMA test results affirming the robustness of the proposed inverse technique. The parametric study not only investigates the effect of various structural and geometric parameters on the dynamic response of the sandwich plate but also verifies that the calibrated properties are both realistic and physically meaningful.

Conclusions

The proposed algorithm is a useful and efficient tool for inverse identification of the constitutive properties, and this approach can be extended for the calibration of other parameters (constitutive or not) for a variety of viscoelastic materials in any field of application. This study is a critical step forward in understanding viscoelastic materials and their frequency-dependent behaviorur.

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Data availability

The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

Abbreviations

NNO:

Neural network optimization

DMA:

Dynamic mechanical analysis

CLD:

Constrained layer damping

FLD:

Free layer damping

FRF:

Frequency response function

FFT:

Fast Fourier transform

ANN:

Artificial neural network

HPB:

Half power bandwidth

FCFF:

Clamped-free

FCFC:

Two opposite short sides clamped

SSSS:

All sides simply-supported

CCCC:

All sides clamped

a :

Length of plate

b :

Width of plate

\(h_{k}\) :

Thickness of each layer

\(u,v,w\) :

Linear displacements along x,y, and z directions

\(\theta\) :

Rotational displacement

\(\varepsilon_{kp}\) :

In-plane strain of face layers

\(\varepsilon_{kb}\) :

Bending strain of face layers

\(\gamma_{ks}\) :

Shear strain of face layers

\(\varepsilon_{2l}\) :

Longitudinal strain of core layer

\(\varepsilon_{2t}\) :

Transverse strain of core layer

\(\gamma_{2s}\) :

Shear strain of core layer

\(U\) :

Total strain energy

\(T\) :

Total kinetic energy

E :

Elastic modulus

G :

Shear modulus

\(K_{{\text{S}}}\) :

Shear correction factor

\(A_{kij}\) :

Coefficient matrices due to in-plane membrane deformation of face layers

\(D_{kij}\) :

Coefficient matrices due to bending of face layers

\(S_{kij}\) :

Coefficient matrices due to shear deformation of face layers

\(Q_{kij}\) :

Reduced stiffness matrices of face layers

\(A_{2ij1} ,A_{2ij2}\) :

Coefficient matrices due to in-plane membrane deformation of core layer

\(S_{2ij1} ,S_{2ij2}\) :

Coefficient matrices due to shear deformation of core layer

\(Q_{2ij}\) :

Reduced stiffness matrices of core layer

\(\left[ K \right]\) :

Global stiffness matrix

\(\left[ M \right]\) :

Global mass matrix

\(G_{{\text{v}}}\) :

Shear storage modulus of core material

\(\beta_{{\text{v}}}\) :

Loss factor of core material

\(\left[ B \right]\) :

Strain–displacement matrix

\(\left[ N \right]\) :

Shape function matrix

\(\delta\) :

Generalized displacement vector

\(\omega\) :

Natural frequency

\(\eta_{{\text{s}}}\) :

Modal loss factor

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Authors and Affiliations

  1. Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela, Odisha, 769008, India

    Jagesh Kumar Prusty & Sukesh Chandra Mohanty

  2. Department of Structural Engineering, National Technical University of Athens, Zografou, 15780, Athens, Greece

    George Papazafeiropoulos

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  1. Jagesh Kumar Prusty
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Correspondence to George Papazafeiropoulos.

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Prusty, J.K., Papazafeiropoulos, G. & Mohanty, S.C. Experimental Verification of the Neural Network Optimization Algorithm for Identifying Frequency-Dependent Constitutive Parameters of Viscoelastic Materials. J. Vib. Eng. Technol. 12, 2147–2173 (2024). https://doi.org/10.1007/s42417-023-00972-y

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