Relation between Cubic Stiffness and Initial Conditions of Maximum Energy Dissipation in a Nonlinear Vibration Absorber

Abstract

A novel technical finding is proposed based on the analytical study of the underlying conservative system of a small mass nonlinear vibration absorber coupled with a main structure. For the system with linear damping under impulsive excitation, a result is obtained that the initial energy for inducing maximum dissipation of energy in the nonlinear attachment is inversely proportional to the cubic stiffness. The technical point coincides with massive numerical simulations precisely. This relationship between the cubic stiffness and the initial conditions facilitates the tuning of a nonlinear vibration absorber for realizing optimal targeted energy transfer.

Study on Dynamic Behavior and Vibration Reduction Performance of BPNES

“…, and a hyperbolic saddle point, 12 ( , ) (0,0) yy = . The Hamiltonian function and potential function of the system can be expressed as:…”

“…In terms of dynamics and vibration reduction performance, Starosvetsky et al [6] studied the periodic and quasi periodic motions in the system by using the complex variable averaging (CX-A) method, and the local bifurcation phenomenon in the periodic motions was revealed. Kong et al [12] applied the CNES to the vibration control of a 2DOF system. The motion equations were solved through the incremental harmonic balance method.…”