Vibration Analysis FGM Plate: A Hybrid Analytical and Machine Learning Approach

Abstract

This study investigates the free vibration characteristics of functionally graded material (FGM) plates through both analytical solutions and machine learning (ML) approaches. Starting with deriving equilibrium equations for FGM plates via Hamilton's principle, we accurately determine their natural frequencies under various conditions. Subsequently, we employ an Artificial Neural Network (ANN) model, trained on an extensive dataset from previous research, to predict these vibrational frequencies [1]. The ANN's predictions are meticulously compared with our analytical findings and corroborated against existing studies, showcasing the model's high level of precision and computational efficiency. Notably, the research reveals that the ANN model can significantly streamline the analysis process, handling complex patterns in data that traditional methods find challenging. This blend of analytical rigor and ML innovation offers a novel pathway for enhancing the structural analysis and design of FGM plates, potentially revolutionizing material science and engineering practices. The precision with which the ANN model predicts the natural frequencies across a diverse range of FGM plates underscores the power of data-driven approaches in engineering analysis. The integration of ML not only augments the accuracy of traditional methods but also introduces a level of adaptability and scalability previously unattainable. Our findings suggest that the convergence of computational mechanics and artificial intelligence holds immense promise for the future of material design and optimization, offering a more holistic understanding of the dynamic properties of FGM plates. Furthermore, this study sets a precedent for the application of ML in complex engineering problems, encouraging further exploration into hybrid methodologies that can bridge the gap between theoretical analysis and practical engineering solutions [2]. Through this innovative approach, we aim to contribute to the advancement of FGM technology, paving the way for the development of more resilient and efficient structural components.

Full text

The 3rd Internatonal Conference on Appled Mathematcs n Engneerng (ICAME’24)
26-28 June 2024, Ayvalık - Balıkesr, Türkye
http://icame.balikesir.edu.tr 224
Vbraton Analyss FGM Plate: A Hybrd Analytcal and Machne Learnng Approach
Emn Emre Özdlek1, Emrcan Gündoğdu2, Murat Çelk1, Erol Demrkan1
1 Istanbul Techn৻cal Un৻vers৻ty, C৻v৻l Eng৻neer৻ng Department, Istanbul, Turkey
2 Istanbul Techn৻cal Un৻vers৻ty, Computer Eng৻neer৻ng Department, Istanbul, Turkey
Abstract
Ths study nvestgates the free vbraton characterstcs of functonally graded materal (FGM) plates
through both analytcal solutons and machne learnng (ML) approaches. Startng wth dervng
equlbrum equatons for FGM plates va Hamlton's prncple, we accurately determne ther natural
frequences under varous condtons. Subsequently, we employ an Artfcal Neural Network (ANN)
model, traned on an extensve dataset from prevous research, to predct these vbratonal frequences
[1]. The ANN's predctons are metculously compared wth our analytcal fndngs and corroborated
aganst exstng studes, showcasng the model's hgh level of precson and computatonal effcency.
Notably, the research reveals that the ANN model can sgnfcantly streamlne the analyss process,
handlng complex patterns n data that tradtonal methods fnd challengng. Ths blend of analytcal
rgor and ML nnovaton offers a novel pathway for enhancng the structural analyss and desgn of FGM
plates, potentally revolutonzng materal scence and engneerng practces. The precson wth whch
the ANN model predcts the natural frequences across a dverse range of FGM plates underscores the
power of data-drven approaches n engneerng analyss. The ntegraton of ML not only augments the
accuracy of tradtonal methods but also ntroduces a level of adaptablty and scalablty prevously
unattanable. Our fndngs suggest that the convergence of computatonal mechancs and artfcal
ntellgence holds mmense promse for the future of materal desgn and optmzaton, offerng a more
holstc understandng of the dynamc propertes of FGM plates. Furthermore, ths study sets a precedent
for the applcaton of ML n complex engneerng problems, encouragng further exploraton nto hybrd
methodologes that can brdge the gap between theoretcal analyss and practcal engneerng solutons
[2]. Through ths nnovatve approach, we am to contrbute to the advancement of FGM technology,
pavng the way for the development of more reslent and effcent structural components.
Keywords: FGM Plates, Artfcal Neural Network, Plate Vbraton
References
[1] Çelik, M., Gündoğdu, E., Özdilek, E.E., Demirkan, E., Artan, R. (2024 Artificial Neural Network (ANN)
Validation Research: Free Vibration Analysis of Functionally Graded Beam via Higher-Order Shear
Deformation Theory and Artificial Neural Network Method. Applied Sciences, 14(1), 217.
[2] Vaishali, Karsh, P.K., Kushari, S., Kumar, R.R., Dey, S. (2023). Stochastic Free Vibration and Impact
Responses of Functionally Graded Plates: A Support Vector Machine Learning Model Approach. Journal of
Vibration Engineering & Technologies, 11, 2927-2943.
 Correspondng Author Emal: celkmur15@tu.edu.tr