Experimental results on the vibratory energy exchanges between a linear system and a chain of nonlinear oscillators

Abstract

Experimental results on a nonlinear chain coupled to a main system are presented. The chain is composed of eight moving masses, each one possesses local nonlinear restoring forcing function and global linear springs for coupling to other masses. The main system is coupled to the first mass of the chain via a linear spring. The main system is under external sinusoidal excitation with sweeping frequency around its targeted mode. Experimental results show that according to the amplitude of the excitation, the system can reach periodic or modulated regimes. The goal of using the nonlinear chain is to examine experimentally the possibility of localization of the vibratory energy of the main system into the chain for the aim of passive control.

Inverted resonance capture cascade: modal interactions of a nonlinear energy sink with softening stiffness

“…To verify this assumption, the stability of B h in τ 0 is determined by linearizing the last set of equations of ( 18) around the fixed points on the SIM obtained from (20), and determining the eigenvalues of the Jacobian matrix. This procedure is common to determine the stability of SIMs [29,36]. We obtain from the linearization…”

“…Physical mechanisms utilized for generating nonlinear restoring force generally exploit geometrical nonlinearities, which usually can be reduced to hardening nonlinearities, in first approximation cubic. These involve transversely loaded strings [27,21], springs [28,29] or beams [30], magnets [31,32,33] or leafs springs [34]. Impact NES are one of the few types of NES whose restoring force is not reducible to a cubic term, but it is still of hardening type [4].…”

Neimark Sacker bifurcations and non-linear energy exchange in chains of non-linear oscillators

“…Such a phenomenon is called a soliton in the case of a propagating wave and of a breather for a stationary wave [6,7]. Therefore, nonlinear chains appear as promising candidates on which to build a vibratory or acoustic control [8,9]. The vibratory energy can be localized in order to be dissipated or on the contrary scattered to be transferred to another frequency domain.…”

A Critical Review of Nonlinear Damping Identification in Structural Dynamics: Methods, Applications, and Challenges

“…Several hypotheses can be used for linear and nonlinear damping of low-damping systems [ 26 , 27 , 28 ]. High-damping systems usually involve structural damage [ 29 ]; however, nonlinear effects on vibrating systems cannot be neglected because of their significant impact on dynamic behaviors [ 30 , 31 ].…”