The vibration of a simply-supported beam with rotary springs at either ends is studied. The governing equations of motion are investigated considering the nonlinear effect of stretching. These equations are made non-dimensional and solved to the first-order approximation using the two known methods, namely, the multiple scales and the mode summation. The first five natural frequencies of the beam for different pairs of the boundary condition parameters are evaluated. A multilayer feed-forward back-propagation artificial neural network is trained using these natural frequencies. The artificial neural network used in this study shows high degree of accuracy for the natural frequency of the beam with general pairs of the boundary condition parameters.

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