Integrated analysis of free vibrations in hyperelastic beams: numerical methods, experimental validation, and neural network predictions

This study explores the free vibrations of hyperelastic beams using a combined numerical and experimental approach. The hyperelastic beam equations, developed using Neo-Hookean strain energy functions and Timoshenko’s beam theory, are solved using the meshless collocation method (MCM). Validation is performed through experimental modal tests and the finite element method (FEM). Hyperelastic materials are employed with a focus on a square-section rubber beam. The mechanical properties of the natural rubber are determined through a uniaxial tensile test following ASTM D412 standards. A comprehensive parametric study investigates the influence of material properties, geometrical characteristics, and incompressibility coefficients on the structure’s behavior. The MCM results exhibit a notable level of accuracy compared with the FEM method. Moreover, the MCM results demonstrate less than a 12.39% error in comparison with the experimental modal test. Eventually, a multilayer perceptron (MLP) neural network (NN), as a complementary tool, is provided to predict the vibrational behavior of the studied structure. It is illustrated that the proposed MLP NN has the capability to approximate the system’s vibrational frequencies accurately.