The force transmissibility of MDOF structures with a non-linear viscous damping device

Semi-actively Implemented Non-linear Damping for Building Isolation Under Seismic Loadings

“…However, the active control techniques require large power supply and high maintenance cost (Sims et al, 1999), and the stability of the actively controlled building isolation system would also be a concern (Taniguchi et al, 2016). Recently, it has been shown that these problems can be circumvented by using a non-linear damping based isolator that can reduce transmitted vibrations over both resonant and non-resonant frequencies (Peng et al, 2010(Peng et al, , 2011Guo et al, 2012;Lang et al, 2013). For example, Peng et al (2010Peng et al ( , 2011 has shown that non-linear damping can reduce the force transmissibilities over all frequency ranges of concern for both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems subject to sinusoidal loadings.…”

Design of Nonlinear Systems in the Frequency Domain: An Output Frequency Response Function-Based Approach

“…For example, Peng and Lang [21] have derived a recursive algorithm to determine the structure of the OFRF for the system described by a nonlinear differential equation model. More recently, the OFRF based approach has been applied in the analysis and design of nonlinear vibration isolators [22][23][24]. For example, by using the OFRF, Lang et al [22] and Peng et al [23] have rigorously proved significant beneficial effects of nonlinear damping on vibration isolation systems.…”

“…More recently, the OFRF based approach has been applied in the analysis and design of nonlinear vibration isolators [22][23][24]. For example, by using the OFRF, Lang et al [22] and Peng et al [23] have rigorously proved significant beneficial effects of nonlinear damping on vibration isolation systems. Recently, Lv and Yao [24] have applied the OFRF to study the influence of damping coefficients on both the force and displacement transmissibility, showing that the nonlinear isolators can perform better than linear isolators over certain frequency ranges.…”

Enhancing the isolation performance by a nonlinear secondary spring in the Zener model

“…Recent rigorous theoretical works [2][3][4][5] also pointed out that the cubic nonlinear damping (denoted as the first type of nonlinear damping in this paper), i.e., f I d ∝ṙ 3 ( f I d is the damping force andṙ denotes the relative velocity), can suppress the resonance amplitude while keep the force transmissibility almost unchanged at low or high frequencies for a singledegree-of-freedom (SDOF) isolator. This concept was also extended to the study of multi-degree-of-freedom (MDOF) isolation problems by Peng [6] and Lang [7]. Another type of nonlinear damping of similar beneficial effects is also cubic, whose force is a function of both displacement and velocity [8,9] (referred as the second type of nonlinear damping in the following sections), i.e., f II d ∝ r 2ṙ ( f II d is the damping force, r andṙ denotes the displacement and velocity, respectively) or a more general form of velocity-displacement-dependent nonlinear damping force described in Ref.…”

“…As been discussed above, in order to simultaneously meet the requirements of low resonance amplitude and good isolation performance at high-frequency range, these scholars [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] studied the lightly damped or even no damped linear isolators (already have good isolation efficiency at high frequencies) and added nonlinear damping elements to improve their poor resonance performances. While in this paper, we develop another novel way by presenting a sufficient damped isolator (naturally owns low resonance amplitude) and employ a nonlinear spring to reduce its vibration transmissibility at high frequencies without deteriorating its resonance performance.…”