Vibrational resonance: A review

Over the past two decades, vibrational resonance has garnered significant interest and evolved into a prominent research field. Classical vibrational resonance examines the response of a nonlinear system excited by two signals: a weak, slowly varying characteristic signal, and a fast-varying auxiliary signal. The characteristic signal operates on a much longer time scale than the auxiliary signal. Through the cooperation of the nonlinear system and these two excitations, the faint input can be substantially amplified, showcasing the constructive role of the fast-varying signal. Since its inception, vibrational resonance has been extensively studied across various disciplines, including physics, mathematics, biology, neuroscience, laser science, chemistry, and engineering. Here, we delve into a detailed discussion of vibrational resonance and the most recent advances, beginning with an introduction to characteristic signals commonly used in its study. Furthermore, we compile numerous nonlinear models where vibrational resonance has been observed to enhance readers' understanding and provide a basis for comparison. Subsequently, we present the metrics used to quantify vibrational resonance, as well as offer a theoretical formulation. This encompasses the method of direct separation of motions, linear and nonlinear vibrational resonance, re-scaled vibrational resonance, ultrasensitive vibrational resonance, and the role of noise in vibrational resonance. Later, we showcase two practical applications of vibrational resonance: one in image processing and the other in fault diagnosis. This presentation offers a comprehensive and versatile overview of vibrational resonance, exploring various facets and highlighting promising avenues for future research in both theory and engineering applications.