Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever Beam
In this study, the natural frequencies and roots (Eigenvalues) of the transcendental equation in a cantilever steel beam for transverse vibration with clamped free (CF) boundary conditions are estimated using a long short-term memory-recurrent neural network (LSTM-RNN) approach. The finite element m...
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MDPI AG
2023-02-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/13/5/2887 |
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| author | Madiha Bukhsh Muhammad Saqib Ali Abdullah Alourani Khlood Shinan Muhammad Usman Ashraf Abdul Jabbar Weiqiu Chen |
| author_facet | Madiha Bukhsh Muhammad Saqib Ali Abdullah Alourani Khlood Shinan Muhammad Usman Ashraf Abdul Jabbar Weiqiu Chen |
| author_sort | Madiha Bukhsh |
| collection | DOAJ |
| description | In this study, the natural frequencies and roots (Eigenvalues) of the transcendental equation in a cantilever steel beam for transverse vibration with clamped free (CF) boundary conditions are estimated using a long short-term memory-recurrent neural network (LSTM-RNN) approach. The finite element method (FEM) package ANSYS is used for dynamic analysis and, with the aid of simulated results, the Euler–Bernoulli beam theory is adopted for the generation of sample datasets. Then, a deep neural network (DNN)-based LSTM-RNN technique is implemented to approximate the roots of the transcendental equation. Datasets are mainly based on the cantilever beam geometry characteristics used for training and testing the proposed LSTM-RNN network. Furthermore, an algorithm using MATLAB platform for numerical solutions is used to cross-validate the dataset results. The network performance is evaluated using the mean square error (MSE) and mean absolute error (MAE). Finally, the numerical and simulated results are compared using the LSTM-RNN methodology to demonstrate the network validity. |
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| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-11T07:32:17Z |
| publishDate | 2023-02-01 |
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| series | Applied Sciences |
| spelling | doaj.art-d6e187adc35c44108d8fdbefab1044e72023-11-17T07:16:23ZengMDPI AGApplied Sciences2076-34172023-02-01135288710.3390/app13052887Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever BeamMadiha Bukhsh0Muhammad Saqib Ali1Abdullah Alourani2Khlood Shinan3Muhammad Usman Ashraf4Abdul Jabbar5Weiqiu Chen6Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, ChinaCollege of Electrical Engineering, Institute of Power Electronics, Zhejiang University, Hangzhou 310027, ChinaDepartment of Computer Science and Information, College of Science in Zulfi, Majmaah University, Al-Majmaah 11952, Saudi ArabiaDepartment of Computer Science, College of Computer in Al-Lith, Umm Al-Qura University, Makkah 24382, Saudi ArabiaDepartment of Computer Science, GC Women University, Sialkot 51310, PakistanCollege of Computer Science, Zhejiang University, Hangzhou 310027, ChinaKey Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Department of Engineering Mechanics, Zhejiang University, Hangzhou 310027, ChinaIn this study, the natural frequencies and roots (Eigenvalues) of the transcendental equation in a cantilever steel beam for transverse vibration with clamped free (CF) boundary conditions are estimated using a long short-term memory-recurrent neural network (LSTM-RNN) approach. The finite element method (FEM) package ANSYS is used for dynamic analysis and, with the aid of simulated results, the Euler–Bernoulli beam theory is adopted for the generation of sample datasets. Then, a deep neural network (DNN)-based LSTM-RNN technique is implemented to approximate the roots of the transcendental equation. Datasets are mainly based on the cantilever beam geometry characteristics used for training and testing the proposed LSTM-RNN network. Furthermore, an algorithm using MATLAB platform for numerical solutions is used to cross-validate the dataset results. The network performance is evaluated using the mean square error (MSE) and mean absolute error (MAE). Finally, the numerical and simulated results are compared using the LSTM-RNN methodology to demonstrate the network validity.https://www.mdpi.com/2076-3417/13/5/2887clamped freefinite element methodtranscendental equationroots (Eigen values)long short-term memoryrecurrent neural network |
| spellingShingle | Madiha Bukhsh Muhammad Saqib Ali Abdullah Alourani Khlood Shinan Muhammad Usman Ashraf Abdul Jabbar Weiqiu Chen Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever Beam Applied Sciences clamped free finite element method transcendental equation roots (Eigen values) long short-term memory recurrent neural network |
| title | Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever Beam |
| title_full | Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever Beam |
| title_fullStr | Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever Beam |
| title_full_unstemmed | Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever Beam |
| title_short | Long Short-Term Memory Recurrent Neural Network Approach for Approximating Roots (Eigen Values) of Transcendental Equation of Cantilever Beam |
| title_sort | long short term memory recurrent neural network approach for approximating roots eigen values of transcendental equation of cantilever beam |
| topic | clamped free finite element method transcendental equation roots (Eigen values) long short-term memory recurrent neural network |
| url | https://www.mdpi.com/2076-3417/13/5/2887 |
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