The effect of different parametrizations including the perturbation of parameters on the energy transfer in a binary tree-structured mass-spring-damper system with nonlinear energy sinks

Rochlitz, Róbert Zoltán and Bak, Bendegúz Dezső (2026) The effect of different parametrizations including the perturbation of parameters on the energy transfer in a binary tree-structured mass-spring-damper system with nonlinear energy sinks. NONLINEAR DYNAMICS, 114 (15). No. 1017. ISSN 0924-090X

Text R_Rochlitz_B_D_Bak_NODY_cikk.pdf - Published Version Available under License Creative Commons Attribution. Download (7MB)

Abstract

The behavior of a multi-degree-of-freedom nonlinear oscillator arranged in a self-similar binary tree structure is studied for different parametrizations of its block masses and spring stiffnesses. The block masses of the oscillator are connected by linear springs across the levels of the tree, with the exception of the leaves of the tree, which are conventional nonlinear energy sinks. The main goal of the analysis is to investigate the potential of the oscillator to dissipate its energy content rapidly. The energy is fed to the oscillator via impulsive excitations. While nonlinear energy sinks perform well over a broad range of vibrational frequencies, they are sensitive to the input energy magnitude. We study how this sensitivity can be reduced by modifying the parametrization of the oscillator. Parametrizations with a small perturbation of the block masses are also considered. It is shown that the dissipation of the baseline parametrization can be improved by significantly decreasing the masses of the attached nonlinear energy sinks. However, this modification limits the effectiveness to a narrow range of smaller input energies. In contrast, for softer connections and lighter block masses across all levels of the tree, the nonlinear energy sinks provide consistently high dissipation over a much broader range of input energy, facilitated by efficient initial nonlinear beats followed by fundamental targeted energy transfer. The small perturbations of the block masses also improve the dissipation rate in general, but their effectiveness diminishes as the energy content increases. The difference between the unperturbed and perturbed cases is attributed to the separation of nonlinear normal modes with a multiplicity greater than one. These separated modes are involved in complex chaotic interactions, this is confirmed by the calculation of the largest Lyapunov exponent for each case.

Actions (login required)

View Item