Power Flow in a Two‐Stage Nonlinear Vibration Isolation System with High‐Static‐Low‐Dynamic Stiffness

Abstract

The manuscript concerns the power flow characterization in a two-stage nonlinear vibration isolator comprising three springs, which are configured so that each stage of the system has a high-static-low-dynamic stiffness. To demonstrate the distinction of evaluation for vibration isolation using power flow, force transmissibility is used for comparison. The dynamic behavior of the isolator subject to harmonic excitation, however, is of interest here. The harmonic balance method (HBM) could be used to analyze the frequency response curve (FRC) of the strong nonlinear vibration system. A suggested stability analysis to distinguish the stable and the unstable HBM solutions is described. Increasing both upper and lower nonlinear stiffness could bend the first resonant peak to the left. The isolation range in the power and the force transmissibility plot could be extended to the lower frequencies when the nonlinear stiffness is increased, but the rate of roll-off for the power transmissibility is twice the rate for the force transmissibility at each horizontal stiffness setting. An explanation for this phenomenon is given in the paper.

The Elliptic Harmonic Balance Method for the Performance Analysis of a Two‐Stage Vibration Isolation System with Geometric Nonlinearity

“…It can be seen that the solution of the EHBM can be compared well with the numerical results. More detailed analyses of the force transmissibility are given in [11][12][13][14][15].…”

“…Many of them have the configuration of geometrically nonlinear springs [3][4][5] and dampers [6][7][8] whose arrangement can obtain low dynamic stiffness, thereby reducing the natural frequency without inducing large static deflection [9,10]. Furthermore, two-degree-of-freedom (2-DOF) vibration isolation systems with quasi-zero-stiffness (QZS) and geometrically nonlinear damping have been studied [11][12][13][14]. Lu et al showed that both the force and displacement transmissibilities are mitigated in the isolation range as the horizontal stiffnesses in both stages are increased [11].…”

Numerically Exploring the Potential of Abating the Energy Flow Peaks through Tough, Single Network Hydrogel Vibration Isolators with Chemical and Physical Cross-Links

“…They also include studies of the energy (power) flow through vibration isolators during an earthquake [ 116 ], through vibration isolators into a floating panel [ 117 ], through magneto-sensitive vibration isolators [ 71 , 85 , 118 , 119 , 120 ], through non-linear vibration isolators [ 121 , 122 ] and through steel springs with distributed mass [ 123 ]. Furthermore, they include studies of the energy (power) flow from a centrifugal turbo blower into a chassis frame [ 124 ], in a two-stage non-linear vibration isolation system [ 125 ] and in a two-stage inerter-based vibration isolation system [ 126 ]. Finally, they include calculations and in situ measurements of the energy (power) flow transmitted through vibration isolators to a seating structure [ 127 , 128 ], in situ measurements of the energy (power) flow through elastomeric powertrain vibration isolators in a passenger car [ 129 ] and investigations of the energy (power) flow transmissibility as a measure to evaluate the capacity of an isolation system [ 130 ].…”

Effect of Parameters on the Design of a Suspension System with Four Oblique Springs

“…New solutions and innovative designs have been investigated recently to this purpose, especially in the field of nonlinear dynamics and vibration control [3,4]. Mathematical approaches have been adopted to investigate the dynamic behaviour of nonlinear oscillators, with specific emphasis to prescribed nonlinear functions of stiffness [5,6] and damping [7,8].…”

“…Practical applications of the benefits that nonlinearity can introduce into a mechanical system are reported in the field of energy harvesting from vibrations [9], vibration absorbers [10], shock isolators [11], vibration isolators [12], and elastic systems for potential energy increase [13]. In some cases, a nonlinear stiffness element with a quasi-zero stiffness (QZS) characteristic [2,6,8,12,13] has been proposed to cope with the competing requirements of achieving a high-static stiffness to limit the static deflection and a low-dynamic stiffness to improve the dynamic performance. A cubic stiffness characteristic with hardening behaviour has been commonly reported, and a practical mechanical realization consists of a pair of linear springs located perpendicularly to the direction of motion, which incline as the oscillator moves [2].…”