Understanding the dynamic behavior of structural components is crucial for optimizing performance and ensuring structural integrity. This study presents a new method that combines a systematic experimental investigation of four distinct hole geometries (circular, square, compact rectangular, and long rectangular) with varying hole counts, all designed to maintain equal material removal, and the application of Gaussian Process Regression to model and predict natural frequencies from experimental modal analysis. Experimental modal testing was conducted on 36 beam specimens to evaluate changes in vibrational properties. The results demonstrate a clear relationship between hole geometry and the attenuation of natural frequencies: circular holes resulted in minimal reductions due to uniform stress distribution, whereas square and rectangular holes caused greater stiffness loss, with the most substantial attenuation observed in beams with long rectangular holes where the first natural frequency decreased by up to 44%. The proposed Gaussian Process Regression model achieved high predictive accuracy on the test set, with coefficients of determination (R2) of approximately 0.98 for the first natural frequency, 0.93 for the second, and 0.92 for the third. Sensitivity analysis identified the number of holes as the most influential parameter, contributing 67.8% to variations in the first natural frequency. These findings provide practical guidelines for structural design by identifying optimal hole geometries and counts to achieve weight reduction while maintaining stiffness, and demonstrate the utility of Gaussian Process Regression for reliable modeling of vibrational behavior in perforated beams.
| [1] |
P. Guéguen, M.-A. Brossault, P. Roux, and J. C. Singaucho, “Slow Dynamics Process Observed in Civil Engineering Structures to Detect Structural Heterogeneities,” Engineering Structures 202, no. 2020 (2020): 109833.
|
| [2] |
F. Guo, F. Hu, S. Wu, F. He, J. Liu, and X. Wu, “System Dynamics in Structural Strength and Vibration Fatigue Life Assessment of the Swing Bar for High-Speed Maglev Train,” International Journal of Mechanical System Dynamics 2, no. 2022 (2022): 178–189.
|
| [3] |
J. Ren and Q. Cao, “Assignment of Natural Frequencies and Mode Shapes Based on FRFs,” Aerospace 8, no. 2021 (2021): 262.
|
| [4] |
J. Yang, S. Liu, B. Yang, and Y. Liu, “Scattering of SH Waves in a Bi-Material Half Space With a Circular Hole and Periodic Type III Interfacial Cracks,” Mechanics of Advanced Materials and Structures 30, no. 2023 (2023): 2863–2871.
|
| [5] |
X. Zhang, X. Lu, C. Li, R. Tian, L. Chen, and M. Wang, “Design of Hyperbolic Quasi-Zero Stiffness Metastructures Coupled With Nonlinear Stiffness for Low-Frequency Vibration Isolation,” Engineering Structures 312, no. 2024 (2024): 118262.
|
| [6] |
D. O. Aikhuele and O. E. Diemuodeke, “Computational Analysis of Stiffness Reduction Effects on the Dynamic Behaviour of Floating Offshore Wind Turbine Blades,” Journal of Marine Science and Engineering 12, no. 2024 (2024): 1846.
|
| [7] |
K. Sabeel, M. Al-Greer, and I. Bashir, “Advancements in In-Vibration Testing: Effects on Thermal Performance and Degradation of Modern Batteries,” Batteries 11, no. 2025 (2025): 82.
|
| [8] |
G. Dessena, M. Civera, A. Yousefi, and C. Surace, “NExT-LF: A Novel Operational Modal Analysis Method via Tangential Interpolation,” International Journal of Mechanical System Dynamics, no. 2025 (2025).
|
| [9] |
C. Vadivelu, V. Prabaharan, and P. K. Akhas, “Flexural Behavior of Perforated Rectangular Hollow Section Cold-Formed Steel Beams: An Experimental and Numerical Study,” Results in Engineering 26, no. 2025 (2025): 104821.
|
| [10] |
T. O. Adeloye, “Dynamic Coefficient of Flexural Motion of Beam Experiencing Simple Support under Successive Moving Loads,” International Journal of Mechanical System Dynamics 4, no. 2024 (2024): 427–445.
|
| [11] |
Z. Hu, L. Wei, L. Yang, Y. Wang, and Y. Fan, “A Ball-Contacting Dynamic Vibration Absorber With Adjustable Stiffness and Nonlinear Characteristics,” Aerospace 11, no. 2024 (2024): 229.
|
| [12] |
A. Afshar, G. Nouri, S. Ghazvineh, and S. H. Hosseini Lavassani, “Machine-Learning Applications in Structural Response Prediction: A Review,” Practice Periodical on Structural Design and Construction 29, no. 2024 (2024): 03124002.
|
| [13] |
N. Gao, M. Wang, X. Liang, and G. Pan, “On-Demand Prediction of Low-Frequency Average Sound Absorption Coefficient of Underwater Coating Using Machine Learning,” Results in Engineering 25, no. 2025 (2025): 104163.
|
| [14] |
J. Guo, J. Zhang, Y. Feng, F. Wang, and C. Li, “Lightweight Implementation of Natural Vibration Frequency Adjustment of Satellite Structures by Varying the Structural Stiffness,” Aerospace Science and Technology 118, no. 2021 (2021): 107061.
|
| [15] |
G. Rinaldi, M. Packirisamy, and I. Stiharu, “Tuning the Dynamic Behaviour of Cantilever MEMS-Based Sensors and Actuators,” Sensor Review 27, no. 2007 (2007): 142–150.
|
| [16] |
H. Hang, K. Shankar, and J. C. S. Lai, “Effects of Distributed Structural Dynamic Modification With Reduced Degrees of Freedom,” Mechanical Systems and Signal Processing 23, no. 2009 (2009): 2154–2177.
|
| [17] |
L. Luschi and F. Pieri, “An Analytical Model for the Determination of Resonance Frequencies of Perforated Beams,” Journal of Micromechanics and Microengineering 24, no. 2014 (2014): 055004.
|
| [18] |
B. Huang, J. Wang, J. Du, T. Ma, Y. Guo, and Z. Qian, “Vibration Analysis of a Specially Orthotropic Composite Laminate With Rectangular Cutout Using Independent Coordinate Coupling Method,” Composite Structures 150, no. 2016 (2016): 53–61.
|
| [19] |
A. A. Abdelrahman, I. Esen, C. Özarpa, and M. A. Eltaher, “Dynamics of Perforated Nanobeams Subject to Moving Mass Using the Nonlocal Strain Gradient Theory,” Applied Mathematical Modelling 96, no. 2021 (2021): 215–235.
|
| [20] |
M. Bochenski, J. Gawryluk, and A. Teter, “Influence of Hole Localization on Local and Global Dynamic Response of Thin-Walled Laminated Cantilever Beam,” Materials 14, no. 2021 (2021): 7409.
|
| [21] |
T. Ozaki, N. Ohta, and M. Fujiyoshi, “Analytical Modeling of a MEMS Beam Resonator With Release-Etch Holes,” Journal of Micromechanics and Microengineering 32, no. 2022 (2022): 097001.
|
| [22] |
S. R. Bathini, R. R. Alavala, O. Beedalannagari, A. Dasore, M. Panchal, and M. S. Shaik, “Investigation of Vibration Characteristics of Stir-Cast Aluminum Reinforced SiC Composite Beam,” Journal of Composite & Advanced Materials/Revue des Composites et des Matériaux Avancés 33, no. 2023 (2023): 175–181.
|
| [23] |
H. Ziou and M. Guenfoud, “Modal Behaviour of Longitudinally Perforated Nanobeams,” Advances in Civil and Architectural Engineering 14, no. 2023 (2023): 143–159.
|
| [24] |
H. Biglari, H. Teymouri, and A. Shokouhi, “Dynamic Response of Sandwich Beam With Flexible Porous Core Under Moving Mass,” Mechanics of Composite Materials 60, no. 2024 (2024): 163–182.
|
| [25] |
S. Jajemizadeh, A. H. Rabiee, and M. Salamat-Talab, “Energy Harvesting for Damage Assessment: A Novel Approach for Detecting and Evaluating Structural Defects in Composite Laminates,” Journal of Composite Materials 2024 (2024): 00219983241309336.
|
| [26] |
A. Hossein Rabiee, V. Tahmasbi, and M. Qasemi, “Experimental Evaluation, Modeling and Sensitivity Analysis of Temperature and Cutting Force in Bone Micro-Milling Using Support Vector Regression and EFAST Methods,” Engineering Applications of Artificial Intelligence 120, no. 2023 (2023): 105874.
|
| [27] |
M. Safari, A. H. Rabiee, and J. Joudaki, “Developing a Support Vector Regression (SVR) Model for Prediction of Main and Lateral Bending Angles in Laser Tube Bending Process,” Materials 16, no. 2023 (2023): 3251.
|
| [28] |
M. Safari, V. Tahmasbi, and A. H. Rabiee, “Investigation into the Automatic Drilling of Cortical Bones Using ANFIS-PSO and Sensitivity Analysis,” Neural Computing and Applications 33, no. 2021 (2021): 16499–16517.
|
| [29] |
A. Tariq, A. Polat, and B. Deliktaş, “Boosting Machine Learning Algorithms for Predicting the Macroscopic Material Behavior of Continuous Fiber Reinforced Composite,” Journal of Reinforced Plastics and Composites, no. 2024 (2024): 07316844241292694.
|
| [30] |
A. Polat, A. Tariq, F. Okay, and B. Deliktaş, “Investigation of the Critical Buckling Load of a Column With Linearly Varying Moment of Inertia Using Analytical, Numerical, and Hybrid Machine Learning Approaches,” Journal of Strain Analysis for Engineering Design, no. 2025 (2025): 03093247251337987.
|
| [31] |
A. Tariq, B. Uzun, M. Akpinar, M. O. Yayli, and B. Deliktas, “Size-Dependent Dynamics of a Bi-Directional Functionally Graded Nanobeam via Machine Learning Methods,” Advances in Nano Research 18, no. 2025 (2025): 33–52.
|
| [32] |
R. Lourenço, A. Tariq, P. Georgieva, A. Andrade-Campos, and B. Deliktaş, “On the Use of Physics-Based Constraints and Validation KPI for Data-Driven Elastoplastic Constitutive Modelling,” Computer Methods in Applied Mechanics and Engineering 437, no. 2025 (2025): 117743.
|
| [33] |
A. Tariq and B. Deliktaş, “An Inverse Parameter Identification in Finite Element Problems Using Machine Learning-Aided Optimization Framework,” Experimental Mechanics 65, no. 2025 (2025): 325–349.
|
| [34] |
A. Tariq, B. Uzun, B. Deliktaş, and M. Ö. Yaylı, “An Investigation on Ensemble Machine Learning Algorithms for Nonlinear Stability Response of a Two-Dimensional FG Nanobeam,” Journal of the Brazilian Society of Mechanical Sciences and Engineering 46, no. 2024 (2024): 556.
|
| [35] |
Z. Sun, M. Mahmoodian, A. Sidiq, S. Jayasinghe, F. Shahrivar, and S. Setunge, “Optimal Sensor Placement for Structural Health Monitoring: A Comprehensive Review,” Journal of Sensor and Actuator Networks 14, no. 2025 (2025): 22.
|
| [36] |
J. Sukhnandan and G. A. Drosopoulos, “A Machine Learning Approach Used to Predict the Peak Displacement, Base Shear and Fundamental Frequency of Multi-Storey Steel Structures under Seismic Excitation,” Structures 73, no. 2025 (2025): 108367.
|
| [37] |
Y. Huang and J. Ding, “A Multiscale Differential-Algebraic Neural Network-Based Method for Learning Dynamical Systems,” International Journal of Mechanical System Dynamics 4, no. 2024 (2024): 77–87.
|
| [38] |
N. Gillich, C. Tufisi, C. Sacarea, et al., “Beam Damage Assessment Using Natural Frequency Shift and Machine Learning,” Sensors 22, no. 2022 (2022): 1118.
|
| [39] |
N. Mohanty, S. K. Sasmal, U. K. Mishra, and S. K. Sahu, “Experimental and Computational Analysis of Free In-Plane Vibration of Curved Beams,” Journal of Vibration Engineering & Technologies 11, no. 2023 (2023): 1777–1796.
|
| [40] |
W. A. Altabey, “Prediction of Natural Frequency of Basalt Fiber Reinforced Polymer (FRP) Laminated Variable Thickness Plates With Intermediate Elastic Support Using Artificial Neural Networks (ANNs) Method,” Journal of Vibroengineering 19, no. 2017 (2017): 3668–3678.
|
| [41] |
B. Y. Dagli, A. Ergut, and M. E. Turan, “Prediction of Natural Frequencies of Rayleigh Pipe by Hybrid Meta-Heuristic Artificial Neural Network,” Journal of the Brazilian Society of Mechanical Sciences and Engineering 45, no. 2023 (2023): 221.
|
| [42] |
S. Harsha, S. Hanumanthappa, S. B. Marulasiddappa, and S. R. Naganna, “Machine Learning Models for Damage Detection in Steel Beams,” International Journal of System Assurance Engineering and Management 14, no. 2023 (2023): 1898–1911.
|
| [43] |
S. B. Rane, R. A. Patil, N. Raykar, and S. B. Kumbhar, “A Machine Learning Approach for Investigation of the Natural Frequency of a Nitinol-Reinforced Composite Beam,” Engineering Research Express 6, no. 2023 (2023): 015003.
|
| [44] |
N. R. Clinkinbeard and N. N. Hashemi, “Supplementation of Deep Neural Networks With Simplified Physics-Based Features to Increase Accuracy of Plate Fundamental Frequency Predictions,” Physica Scripta 99, no. 2024 (2024): 056010.
|
| [45] |
L. Liu and A. A. Ibraheem, “Introducing Innovative Deep Neural Networks to Predict Natural Frequency of the Nanocomposites Reinforced Concrete Structures under External Loading,” Mechanics of Advanced Materials and Structures, no. 2024 (2024): 1–13.
|
| [46] |
M. Spodniak, M. Hovanec, and P. Korba, “A Novel Method for the Natural Frequency Estimation of the Jet Engine Turbine Blades Based on Its Dimensions,” Heliyon 10, no. 2024 (2024): e26041.
|
| [47] |
V. T. Vu, D. V. Thom, and T. D. Tran. 2024. “Identification of Damage in Steel Beam by Natural Frequency Using Machine Learning Algorithms.” Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science (2024): 09544062241255570.
|
| [48] |
S. Suman, K. Dwivedi, A. Raza, and H. Pathak, “Accelerating Composite Sandwich Plate Analysis: A Hybrid Higher-Order XFEM and ANN Approach for Natural Frequency Prediction,” Mechanics Based Design of Structures and Machines 53, no. 2025 (2025): 4711–4723.
|
| [49] |
A. H. Rabiee and A. M. Jalali, “A Hybrid Machine Learning and Particle Swarm System for Configuring Holes on Cantilever Beams to Achieve Desired Natural Frequencies,” Journal of Theoretical and Applied Vibration and Acoustics 10, no. 2 (2025): 51–64.
|
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2025 The Author(s). International Journal of Mechanical System Dynamics published by John Wiley & Sons Australia, Ltd on behalf of Nanjing University of Science and Technology.
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