Vibrations analysis and neural network prediction of the locust-leg-inspired tubes

This study investigates the vibration characteristics and data-driven prediction of a VST bio-inspired by the locust leg. Based on the morphological features of the locust leg, mathematical functions are introduced to characterize the axial curvature and radial variations of the tube. The governing equations are derived using Euler–Bernoulli beam theory and Hamilton’s principle. The DQM is employed to obtain natural frequencies and critical buckling loads under multiple boundary conditions. Parametric studies reveal that the bio-inspired tube exhibits frequency veering, modal interchange, and buckling across all four boundary conditions considered. Notably, mode-coalescence flutter is observed specifically under SS and CF constraints. Compared to a UST, the VST shows markedly enhanced sensitivity to the curvature parameter A₀. Boundary conditions significantly influence the frequency values: CS boundaries yield the highest natural frequencies, whereas CF boundaries result in the lowest. The quantification of boundary conditions and cross-sectional properties is achieved via one-hot encoding and one-dimensional vector labels. BP, SVM, and MLP models are developed for data-driven prediction, with the MLP exhibiting superior performance. Furthermore, through SHAP interpretation of the MLP model, machine learning identifies the amplitude A₀ and length L as the primary determinants of the natural frequency.