Nonlinear Vibration of Mechanical Systems

Nonlinear vibration phenomena are central in modern engineering, from large civil structures to micro- and nanosystems. Contributions in this Special Issue Reprint in Vibration showcase the richness of nonlinear dynamics and advances in analytical, numerical, experimental, and data-driven approaches. Contact-induced nonlinear oscillations remain fundamental. Analytical approximations for Hertzian-type restoring forces offer efficient alternatives to numerical solutions while retaining dominant nonlinear scaling. Nonlinearities are key in vibration isolation. Reduced finite element models for wire rope isolators capture geometric effects and hysteretic damping. High static-low dynamic stiffness and quasi-zero stiffness mechanisms enable broadband mitigation under harmonic or seismic loads while maintaining load capacity. In smart structures, nonlinear electromechanical coupling and hysteresis shape dynamic response. Piezoelectric composite beam models highlight memory-dependent effects, while motor gearbox studies show bidirectional coupling is critical for stability prediction.At the nanoscale, hybrid physics-based and machine learning models improve predictions of carbon nanotube dynamics. Nonlinear vibrations also govern flow-induced dynamics, frictional systems, and asymmetric devices. Applications in pipelines and energy systems confirm nonlinear analysis is vital for resilience and structural health monitoring. This Reprint reflects the multidisciplinary, multiscale evolution of vibration research, integrating nonlinear mechanics with efficient modeling and data-driven methods for complex systems.