Methodological Description of Obtaining and Stabilizing Solitons in Macromechanical Damped Resonators Subjected to a Base Acceleration

This study focuses on the phenomenon of Intrinsic Localized Modes (ILMs) and solitons in nonlinear systems. Unlike linear systems, nonlinear ones can exhibit solitons even when the periodicity hypothesis is considered. The Nonlinear Schrödinger equation (NLSE) is used to describe the phenomenon in the damped Duffing oscillator chain analyzed in this article. The study presents a general methodology for finding and stabilizing solitonic solutions in macromechanical resonators under base acceleration where a mathematical treatment is presented for an equivalent discrete model and the solution is obtained using the method of multiple scales. The stability of the nonlinear wave is assessed by analyzing physical parameters (stiffness, acceleration, and damping) in order to demonstrate numerically the methodology’s ability to reproduce stationary waves in the coupled oscillators even considering the presence of damping.