Chaotic Vibration Prediction of a Laminated Composite Cantilever Beam
Source abstract
Abstract
The deep learning method of the recurrent neural network (RNN) is applied to predict the chaotic vibrations of a laminated composite cantilever beam. The RNN model converts time series data into a multi-step supervised learning format and normalizes it using MinMaxScaler. The cantilever structure is subjected to an evenly distributed load, and a series of chaotic vibrations are observed corresponding to different amplitudes and angular velocities of the load. Then, the RNN data-driven model is applied to predict chaotic vibrations, and the chaotic vibration prediction of RNN is evaluated. The prediction results are primarily evaluated using two metrics: mean absolute error (MAE) and root mean square error (RMSE). The analysis results show that the maximum MAE is 0.041 and the maximum RMSE is 0.067. Even under perturbed initial conditions, the RNN model maintained high prediction accuracy, with a maximum MAE of 0.022 and RMSE of 0.038, highlighting its robustness and reliability in predicting chaotic vibrations. The error analysis indicates that the RNN accurately predicts chaotic vibrations with a high degree of precision.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Structural Health Monitoring Techniques · Topology Optimization in Engineering
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
School of Environmental and Safety Engineering, Liaoning Petrochemical University, Fushun 113001, China
Funding
National Natural Science Foundation of China (NNSFC) · Liaoning Petrochemical University · Liaoning Provincial Education Department Basic Scientific Research Project for Youth
References (43)
Show source-provided references
1. Nonlinear eccentric bending and buckling of laminated cantilever beams actuated by embedded pre-stretched SMA wires10.1016/j.compstruct.2022.115211 ↗
2. Nonlinear dynamic behaviors of a deploying-and-retreating wing with varying velocity10.1016/j.jsv.2013.08.006 ↗
3. Sound-insulation prediction model and multi-parameter optimisation design of the composite floor of a high-speed train based on machine learning10.1016/j.ymssp.2023.110631 ↗
4. Kormanikova, E., Kotrasova, K., Melcer, J., and Valaskova, V. (2022). Numerical investigation of the dynamic responses of fibre-reinforced polymer composite bridge beam subjected to moving vehicle. Polymers, 14.10.3390/polym14040812 ↗
5. Deep learning-based analysis of interface performance between brittle engineering materials and composites10.1016/j.eswa.2024.124920 ↗
6. Predictability of weather and climate10.1029/2019EA000586 ↗
7. A generative adversarial network approach to (ensemble) weather prediction10.1016/j.neunet.2021.02.003 ↗
8. Global bifurcations and chaotic dynamics in nonlinear nonplanar oscillations of a parametrically excited cantilever beam10.1007/s11071-005-6435-3 ↗
9. Analytical and experimental investigations on large deflection analysis of composite cantilever beams10.1080/15376494.2020.1751901 ↗
10. Theoretical and experiment optimization research of a frequency up-converted piezoelectric energy harvester based on impact and magnetic force10.1088/2631-8695/ad62b9 ↗
11. Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates10.1016/j.matdes.2017.07.025 ↗
12. Influence of nonlinear terms on dynamical behavior of graphene reinforced laminated composite plates10.1016/j.apm.2019.10.030 ↗
13. Bending theory for laminated composite cantilever beams with multiple embedded shape memory alloy layers10.1177/1045389X19835954 ↗
14. Free vibration analysis of third-order shear deformable composite beams using dynamic stiffness method10.1007/s00419-008-0276-8 ↗
15. Nonlinear vibrations and viscoelasticity of a self-healing composite cantilever beam: Theory and experiments10.1016/j.compstruct.2022.115741 ↗
16. Nonlinear responses of a symmetric cross-ply composite laminated cantilever rectangular plate under in-plane and moment excitations10.1016/j.compstruct.2013.01.013 ↗
17. Liu, X., and Sun, L. (2023). Chaotic vibration control of a composite cantilever beam. Sci. Rep., 13.10.1038/s41598-023-45113-3 ↗
18. Influence of piezoelectric performance on nonlinear dynamic characteristics of MFC shells10.1155/2019/1970248 ↗
19. Chaotic snap-through vibrations of bistable asymmetric deployable composite laminated cantilever shell under foundation excitation and application to morphing wing10.1016/j.compstruct.2024.118261 ↗
20. Sun, L., Li, X.D., and Liu, X. (2024). Control of large amplitude limit cycle of a multi-dimensional nonlinear dynamic system of a composite cantilever beam. Sci. Rep., 14.10.1038/s41598-024-61661-8 ↗
21. Analytical investigation on the buckling and free vibration of porous laminated FG-CNTRC plates10.5937/vojtehg72-50469 ↗
22. A method to enhance the nonlinear magnetic plucking for vibration energy harvesters10.1007/s11012-024-01856-5 ↗
23. Hao, Y.X., Sun, K.C., and Li, H. (2025). Nonlinear dynamics of the GPR porous cantilever twisted plate near veering regions. Mech. Based Des. Struct. Mach., 1–27.10.1080/15397734.2025.2477649 ↗
24. A neural network-based distributed parameter model identification approach for microcantilever10.1177/0954406215615626 ↗
25. Bayesian estimation of discrepancy in dynamics model prediction10.1016/j.ymssp.2019.01.014 ↗
26. Data driven nonlinear dynamical systems identification using multi-step CLDNN10.1063/1.5100558 ↗
27. Inferring the dynamics of oscillatory systems using recurrent neural networks10.1063/1.5096918 ↗
28. Huang, B., Zheng, H., Guo, X., Yang, Y., and Liu, X. (2022). A Novel Model Based on DA-RNN Network and Skip Gated Recurrent Neural Network for Periodic Time Series Forecasting. Sustainability, 14.10.3390/su14010326 ↗
29. Dynamical time series embeddings in recurrent neural networks10.1016/j.chaos.2021.111612 ↗
30. Temporal convolutional networks with RNN approach for chaotic time series prediction10.1016/j.asoc.2022.109945 ↗
31. Forecasting of noisy chaotic systems with deep neural networks10.1016/j.chaos.2021.111570 ↗
32. Chaotic time series prediction of nonlinear systems based on various neural network models10.1016/j.chaos.2023.113971 ↗
33. Robust recurrent neural networks for time series forecasting10.1016/j.neucom.2023.01.037 ↗
34. A new hybrid PSO-YUKI for double cracks identification in CFRP cantilever beam10.1016/j.compstruct.2023.116803 ↗
35. An efficient improved Gradient Boosting for strain prediction in Near-Surface Mounted fiber-reinforced polymer strengthened reinforced concrete beam10.1007/s11709-024-1079-x ↗
36. ConvLSTM-based spatiotemporal and temporal processing models for chaotic vibration prediction of a microbeam10.1016/j.cnsns.2024.108411 ↗
37. Enhancing damage detection using reptile search algorithm-optimized neural network and frequency response function10.1007/s42417-024-01545-3 ↗
38. Osmani, A., Shamass, R., Tsavdaridis, K.D., Ferreira, F.P.V., and Khatir, A. (2025). Deflection predictions of tapered cellular steel beams using analytical models and an artificial neural network. Buildings, 15.10.3390/buildings15060992 ↗
39. Reddy, J.N. (2003). Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, Taylor & Francis.10.1201/b12409 ↗
40. Sun, L., Hou, F.L., and Liu, X.P. (2025). Nonlinear vibration control of a high-dimensional nonlinear dynamic system of an axially-deploying elevator cable. Mathematics, 13.10.3390/math13081289 ↗
41. Nonlinear transverse vibrations of angle-ply laminated composite piezoelectric cantilever plate with four-modes subjected to in-plane and out-of-plane excitations10.1016/j.engstruct.2019.109501 ↗
42. Nonlinear dynamics analysis of a graphene laminated composite plate based on an extended Rayleigh–Ritz method10.1016/j.tws.2023.110673 ↗
43. Randomising the Simple Recurrent Network: A lightweight, energy-efficient RNN model with application to forecasting problems10.1007/s00521-023-08775-8 ↗