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 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.