Analytical and ANN-based approaches for free vibration and nonlinear transient analysis of FG-GOEAM toroidal shell segments

This study investigates the free vibration and nonlinear transient response of functionally graded graphene origami (GOri)-enabled auxetic metamaterials (GOEAMs) toroidal shell segments under thermal conditions. The impact of the Winkler-Pasternak foundation, distributed in two configurations: cente...

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Bibliographic Details
Published in:Computers & structures Vol. 309; p. 107676
Main Authors: Hoang, Vu Ngoc Viet, Thanh, Pham Trung
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.03.2025
Subjects:
Artificial neural network
FG-GOEAM toroidal shell segments
Galerkin technique
Non-homogeneous Winkler-Pasternak foundation
Nonlinear dynamics
Nonlinear dynamics
FG-GOEAM toroidal shell segments
Artificial neural network
Non-homogeneous Winkler-Pasternak foundation
Galerkin technique
ISSN:0045-7949
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Summary:This study investigates the free vibration and nonlinear transient response of functionally graded graphene origami (GOri)-enabled auxetic metamaterials (GOEAMs) toroidal shell segments under thermal conditions. The impact of the Winkler-Pasternak foundation, distributed in two configurations: centered and at both ends of the shell, is thoroughly examined. The material properties with GOri distributions through the shell thickness are scrutinized using genetic programming-assisted micromechanical models. Nonlinear kinematic relationships are derived via Reddy's third-order shear deformation theory and von Kármán's geometric assumptions. The equations of motion are solved using Galerkin method. An Artificial Neural Network (ANN), trained with Bayesian regularization backpropagation algorithm, is developed to predict natural frequencies, using comprehensive training data validated against analytical results. The ANN achieves a target mean squared error (MSE) of 1×10−7, with error histograms showing minimal and evenly distributed errors. Regression plots confirm perfect correlations (R = 1) between predicted and actual values, indicating robust predictive accuracy. Additionally, increased GOri folding amplifies the negative Poisson's ratio, reduces Young's modulus in GOri/Cu composites, and consequently decreases shell stiffness, lowers natural frequencies, and increases vibration amplitudes. A center-concentrated foundation distribution yields higher natural frequencies and reduced vibration amplitudes compared to end-distributed configurations. The proposed approaches demonstrate high accuracy and generalization capability in predicting the dynamic responses of FG-GOEAM shells under thermal effects. The findings emphasize the critical role of GOri folding patterns and foundation distributions in tuning vibration characteristics, offering valuable insights for the design and optimization of advanced metamaterial structures. •Nonlinear dynamics of toroidal shell segments are analyzed using Galerkin's method.•Investigation of novel auxetic metamaterials with distinct properties, including a negative Poisson's ratio.•Analysis of Winkler-Pasternak foundation with central and end-positioned configurations along the shell's length.•Artificial neural network using the Bayesian Regularization algorithm effectively predict natural frequencies.•Effects of elastic substrates, material properties, geometry, and thermal environment on shells are examined.
ISSN:0045-7949
DOI:10.1016/j.compstruc.2025.107676