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 transcendental equation in a cantilever steel beam for transverse vibration with clamped free (CF) boundary conditions are estimated using long short-term memory-recurrent neural network (LSTM-RNN) approach. The finite element method (FEM) package ANSYS is used dynamic analysis and, aid simulated results, Euler–Bernoulli theory adopted generation sample datasets. Then, deep (DNN)-based LSTM-RNN technique implemented to approximate equation. Datasets mainly based on geometry characteristics training testing proposed network. Furthermore, an algorithm MATLAB platform numerical solutions cross-validate dataset results. performance evaluated mean square error (MSE) absolute (MAE). Finally, results compared methodology demonstrate validity.