Dynamic analysis of track nonlinear energy sinks subjected to simple and stochastice excitations

Abstract

Track nonlinear energy sinks (track NESs) have been shown to be an effective and applicable strategy to mitigate structural response in recent years. However, previous studies on track NESs has mainly focused on demonstrating the benefits of track NESs through numerical simulations and experiments, with relatively little attention paid to the analytical understanding of the unique dynamics of track NESs. This study analyzes the responses of a track NES when subjected to impulsive and harmonic excitations by the harmonic balance method. Special attention is given to the cause and effect of the peaking behavior that is a prominent characteristic of the track NES's restoring forcedisplacement relationship. Analytical results reveal that the special energy-frequency characteristics of track NESs can be, at times, utilized to enhance the energy robustness that is absent in the conventional cubic NESs. Based on the analytical response expression, an equivalent linearization method (ELM) for the track NESs is developed for stochastic analysis. This ELM is numerically validated on the systems with strong nonlinearities. Stochastic optimization built on the ELM is performed to obtain design parameters of the track NES that can lead to minimum response variances of the primary structure. In particular, the proposed optimization procedure can be applied to seismic optimum design in which the seismic excitations are modeled as filtered whitenoise ground motions. The analytical techniques provided in this study lay the groundwork for the practical implementation of track NESs as a robust and effective control strategy for engineering structures. K E Y W O R D Sharmonic balance method, harmonic excitation, impulsive excitation, peaking behavior, stochastic optimization, track nonlinear energy sink

A vertical‐vibro‐impact‐enhanced track bistable nonlinear energy sink for robust and comprehensive control of structures

“… where x N is the horizontal displacement of the auxiliary mass relative to the track's center, h is the track shape and also the vertical displacement of the auxiliary mass relative to the track's center, and a 1 and a 3 are positive coefficients for the second‐power and fourth‐power terms in the track shape function, respectively. In the horizontal direction, the restoring force provided by the track and the relative displacement of the auxiliary mass are in a relationship that is approximately an order smaller than the polynomial power of the track shape function 15 . The resulting force–displacement relationship therefore includes a negative linear displacement term and a positive cubic displacement term, which resembles the force–displacement relationship of a BNES.…”

“…Therefore, track NESs can keep an almost constant vibrational frequency with energy going upward and sufficiently resonate with the primary structure for a much wider energy range than cubic NESs. 15 An alternative way to maximize the control efficiency is to generate unconventional energy absorption mechanisms through nonsmooth rather than smooth nonlinearity as in cubic NESs, BNESs, and track NESs. The nonsmooth nonlinearity can be readily realized using vibro impacts [38][39][40] and vibro-impact NESs (VI NESs) have therefore been developed by adding impact surfaces to TMDs at both sides of the moving direction.…”

Effectiveness and robustness of an asymmetric nonlinear energy sink‐inerter for dynamic response mitigation

“…The higher modal vibrations observed in the structure facilitate faster energy dissipation and result in smaller structural responses in comparison with the vibrations in the fundamental mode. To date, various types of NESs have been developed which include but are not limited to cubic NESs, 20,21 vibro‐impact NESs, 22,23 rotary NESs, 24,25 MDOF NESs, 26 bistable NESs, 27,28 and track NESs 29,30 . The most studied type is the cubic NES whose restoring force is proportional to the cube of the displacement.…”

Analysis and optimization of a nonlinear dual‐mode floor isolation system subjected to earthquake excitations

“…Recently, nonlinear TMDs with stiffening behavior have gained attention as energy pumping devices or NESs. [35][36][37] Another disadvantage of (linear) TMDs is that they require a relatively large mass. Some researchers have proposed using isolated floors, [38][39][40] stories, [41,42] or other massive components [43] as TMDs, leveraging the mass that is already present in the structure and requiring no additional weight (dead load).…”

“…Some researchers have proposed using isolated floors, [38][39][40] stories, [41,42] or other massive components [43] as TMDs, leveraging the mass that is already present in the structure and requiring no additional weight (dead load). Whereas TMDs are more established for reducing windinduced vibrations, TMDs with large mass [44] and/or engineered nonlinearities [37] hold promise for seismic mitigation as well.…”