March 13, 2024 | Jianhua Yang, S. Rajasekar, Miguel A. F. Sanjuán
The article provides a comprehensive review of vibrational resonance, a phenomenon where a nonlinear system responds to a weak, slowly varying input signal in the presence of a fast-varying auxiliary signal. The review covers the historical development, key concepts, and recent advancements in the field. It highlights the importance of characteristic signals, such as harmonic, anharmonic, aperiodic, and frequency-modulated signals, and their impact on vibrational resonance. The article also discusses various nonlinear models, including ordinary differential systems, mapping systems, fractional differential systems, delayed differential systems, and stochastic differential systems, where vibrational resonance has been observed. Additionally, it explores the theoretical formulation of vibrational resonance, including the method of direct separation of motions, linear and nonlinear vibrational resonance, re-scaled vibrational resonance, and ultrasensitive vibrational resonance. The role of noise in vibrational resonance is also examined, along with practical applications in image processing and fault diagnosis. The review concludes with a discussion on future research directions and the potential of vibrational resonance in engineering and scientific applications.The article provides a comprehensive review of vibrational resonance, a phenomenon where a nonlinear system responds to a weak, slowly varying input signal in the presence of a fast-varying auxiliary signal. The review covers the historical development, key concepts, and recent advancements in the field. It highlights the importance of characteristic signals, such as harmonic, anharmonic, aperiodic, and frequency-modulated signals, and their impact on vibrational resonance. The article also discusses various nonlinear models, including ordinary differential systems, mapping systems, fractional differential systems, delayed differential systems, and stochastic differential systems, where vibrational resonance has been observed. Additionally, it explores the theoretical formulation of vibrational resonance, including the method of direct separation of motions, linear and nonlinear vibrational resonance, re-scaled vibrational resonance, and ultrasensitive vibrational resonance. The role of noise in vibrational resonance is also examined, along with practical applications in image processing and fault diagnosis. The review concludes with a discussion on future research directions and the potential of vibrational resonance in engineering and scientific applications.