Periodic Motion and Frequency Energy Plots of Dynamical Systems Coupled with Piecewise Nonlinear Energy Sink

The frequency-energy plots (FEPs) of two-degree-of-freedom linear structures attached to a piecewise nonlinear energy sink (PNES) are generated here and thoroughly investigated. This study provides the FEP analysis of such systems for further understanding to nonlinear targeted energy transfer (TET) by the PNES. The attached PNES to the considered linear dynamical systems incorporates a symmetrical clearance zone of zero stiffness content where the boundaries of the zone are coupled with the linear structure by linear stiffness elements. In addition, linear viscous damping is selected to be continuous during the PNES mass oscillation. The underlying nonlinear dynamical behaviour of the considered structure-PNES systems is investigated by generating the fundamental backbone curves of the FEP and the bifurcated subharmonic resonance branches using numerical continuation methods. Accordingly, interesting dynamical behaviour of the nonlinear normal modes (NNMs) of the structure-PNES system on different backbones and subharmonic resonance branches has been observed. In addition, the imposed wavelet transform frequency spectrums on the FEPs have revealed that the TET takes place in multiple resonance captures where it is dominated by the nonlinear action of the PNES.

Vibration suppression and dynamic behavior analysis of an axially loaded beam with NES and nonlinear elastic supports

Recently, dynamic analysis of a beam structure with nonlinear energy sink (NES) and various supports is attracting great attention. Most of the existing studies are about the beam structure with NES or nonlinear boundary supports with zero rotational restraint, respectively. However, there is little research accounting for such two types of complex factors simultaneously. In this work, the dynamic behavior of an axially loaded beam with both NES and general boundary supports is modeled and studied. The Galerkin truncated method (GTM) is employed to make the prediction of dynamic behavior of such a beam system, in which the mode functions of axially loaded Euler–Bernoulli beam with linear elastic boundary conditions are selected as the trail and weight functions. Then, the Galerkin condition is used to discretize the nonlinear governing equation of the beam system and establish the residual equations. The Runge–Kutta method is used to solve the residual matrix which consists of residual equations directly, and the harmonic balance method is also used to verify the results from the GTM. The influence of NES on vibration suppression and dynamic behavior of the beam structure is investigated and discussed. Results show that the vibration states of the beam structure can be transformed effectively through the change of NES parameters. On the other hand, the NES with suitable parameters has a beneficial effect on the vibration suppression at both ends of the beam structure.

Experimental analysis of zero-natural-frequency damper for transmission line large cross project based on NES

The operation experience of transmission line large cross project shows that the traditional anti-aeolian-vibration devices had poor adaptability to complex terrain and micro meteorological conditions, and they were difficult to meet the application requirements of super large cross project at this stage. A zero-natural-frequency damper was designed by introducing nonlinear energy sink in this paper, and the solid prototypes were processed. According to the actual design parameters of conductor using in a large cross project, the anti-vibration effect was tested by using the indoor simulation test span. The test results showed that the anti-vibration effect of the scheme based on the zero-natural-frequency damper could meet the needs of practical engineering. The installation of this damper could improve conductors’ and fittings’ adaptability to complex terrain and enhance the wind and anti-vibration ability of transmission line.