Dynamic analysis and performance evaluation of nonlinear inerter-based vibration isolators

Jian Yang,Jason Zheng Jiang,Simon A Neild

doi:10.1007/s11071-019-05391-x

Jian Yang, Jason Zheng Jiang + Show 1 more

Open Access

https://doi.org/10.1007/s11071-019-05391-x

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Abstract

This paper investigates a nonlinear inertance mechanism (NIM) for vibration mitigation and evaluates the performance of nonlinear vibration isolators employing such mechanism. The NIM comprises a pair of oblique inerters with one common hinged terminal and the other terminals fixed. The addition of the NIM to a linear spring-damper isolator and to nonlinear quasi-zero-stiffness (QZS) isolators is considered. The harmonic balance method is used to derive the steady-state frequency response relationship and force transmissibility of the isolators subjected to harmonic force excitations. Different performance indices associated with the dynamic displacement response and force transmissibility are employed to evaluate the performance of the resulting isolators. It is found that the frequency response curve of the inerter-based nonlinear isolation system with the NIM and a linear stiffness bends towards the low-frequency range, similar to the characteristics of the Duffing oscillator with softening stiffness. It is shown that the addition of NIM to a QZS isolator enhances vibration isolation performance by providing a wider frequency band of low amplitude response and force transmissibility. These findings provide a better understanding of the functionality of the NIM and assist in better designs of nonlinear passive vibration mitigation systems with inerters.

Highlights

There has been a growing demand for high performance vibration control devices that change the vibration transmission within a dynamic system to meet specific design requirements
The following performance indices may be used [2, 3, 15, 16]: (a) Peak dynamic displacement; (b) Peak transmissibility; (c) Unity isolation frequency band, in which the value of transmissibility is less than unity
This asymptotic behaviour of force transmissibility T R of inerter-based linear isolator has been shown analytically [20]. This deficiency is overcome by having the inerters in the lateral configuration, i.e., adding a nonlinear inertance mechanism (NIM), as the NIM isolator provides much better attenuation of force transmission at high excitation frequencies with force transmissibility reducing with the excitation frequency Ω

Summary

Introduction

There has been a growing demand for high performance vibration control devices that change the vibration transmission within a dynamic system to meet specific design requirements. There is [18, 19], including linear inerter-based vibration isolamuch less work reported on the use of the inertia in tors [20, 21] This approach has been developed to reveal nonlinear passive devices to improve vibration isolation dynamics of nonlinear systems from energy flor viewperformance. Formance [2, 15, 16] These investigations provide insights into the possibility of incorporating inerters alongside 2 Mathematical modelling the horizontal springs of QZS isolators to achieve better suppression of vibration transmission. Vibration iso- 2.1 The NIM lator with geometrically nonlinear inerter subjected to base motion excitation was investigated and it was shown Fig. 1 provides a schematic representation of the proto have performance benefits at high frequencies as com- posed NIM created by using a pair of inerters positioned pared to classical isolators [17].

Inerter-based nonlinear vibration isolators

Backbone curves

Force transmissibility

The NIM isolator

The NIM QZS mount

Discussion of vibration power flow behaviour