Stochastic optimization and dynamic analysis of various systems attached to a VINES under unpredictable initial conditions

Abstract

The study thoroughly considers the Vibro Impact Nonlinear Energy Sink (VI-NES) system, highlighting its capacity to absorb and dissipate energy under various initial conditions. This system consists of a Linear Oscillator (LO) or a nonLinear Oscillator (nonLO), featuring a damper, spring, and a ball within a cavity. The analysis incorporates stochastic and deterministic optimization methods. Different initial velocities were applied to assess the system's efficiency. Designers can identify the optimal parameters, including the mass of the impact element, the coefficient of restitution, and the cavity length, that perform effectively over a wide spectrum of initial velocities. This article offers insights into uncovering logical relationships among the optimal values of these parameters, providing guidance for their efficient design. Optimization is employed when the system is excited by an initial velocity. However, when an external force is applied, defining an objective becomes challenging, and the system's behavior must be analyzed instead. Moreover, bifurcation analysis is utilized to explore the system's dynamic behavior in relation to cavity length and the restitution coefficient. The bifurcation diagrams reveal that chaotic strong modulated response (CSMR) occurs at specific values of cavity lengths and restitution coefficients. Additionally, a system with two degrees of freedom and vibro-impact nonlinearity is considered, with optimal parameters for vibro-impact designed to minimize the system's energy. These findings underscore the potential application of VI-NES in engineering contexts, particularly in the design of vibration reduction and energy dissipation mechanisms for complex dynamic systems like mechanical systems and structural engineering. © 2025 Elsevier Ltd