Abstract
In order to reveal the bifurcation mechanism and optimize the system design for high-static-low-dynamic-stiffness (HSLDS) vibration isolation system (VIS) with elastic base, the local bifurcation analyses both in unfolding parameter space and physical parameter space were carried out theoretically and numerically. Firstly, the restoring force of the HSLDS-VIS was approximated to linear and cubic stiffness by applying the Maclaurin series expansion and the motion equations of HSLDS-VIS with elastic base were established. Subsequently, the motion equations of HSLDS-VIS with elastic base were formulated to transform the system into a standard form and the averaging method was applied to obtain the single-variable bifurcation equation for the HSLDS-VIS with elastic base in case of primary resonance and 1:2 internal resonance. Furthermore, the transition sets and bifurcation diagrams in the unfolding parameter space were studied by means of singularity theory. Finally, for the engineering application, the transition sets were transferred back to the physical parameter space, thus to obtain the bifurcation diagrams of the amplitude with respect to the external force. The numerical simulation results show that the local bifurcations of HSLDS-VIS with elastic base in case of 1:2 internal resonance are considerable complex and need to be analyzed in six two-parameters spaces, meanwhile, the necessary condition of multiple solutions lies in some physical parameters, which can provide a theoretical basis and reference for design and application of the HSLDS-VIS with elastic base.
Highlights
Undesirable vibration can affect human comfort and even the structural safety, which has become an urgent problem to be solved in engineering
Carrella et al and Wu et al investigated vibration isolators with HSLDS property via the combination of a mechanical spring and magnets [2, 3], Li et al presented a device using a magnetic spring combined with rubber membranes to suppress vibration [4], Zhou et al develop a tunable isolator with HSLDS property by using a pair of electromagnets and a permanent magnet and can act passively or semi-actively[5], Meng et al concerned the quasi-zero-stiffness by combining a negative disk spring with a linear positive spring [6]
If the unfolding parameters lying in the transition sets, a small perturbation is likely to cause a qualitative change in the bifurcation diagrams, which means that are degraded
Summary
Undesirable vibration can affect human comfort and even the structural safety, which has become an urgent problem to be solved in engineering. It is evident that the bandwidth of vibration isolation is often limited by the mount stiffness element required to support a static load To overcome this limitation, the high-static-low-dynamic-stiffness (HSLDS) mechanism is put forward, what results in low natural frequency with a small static displacement. The high-static-low-dynamic-stiffness (HSLDS) mechanism is put forward, what results in low natural frequency with a small static displacement Whilst it maintains locally low stiffness near equilibrium and static load bearing, which reduces the natural frequency and extends the frequency isolation region [1]. BIFURCATION AND SINGULARITY ANALYSIS OF HSLDS VIBRATION ISOLATION SYSTEM WITH ELASTIC BASE. The local bifurcation and singularity analysis of a HSLDS-VIS with elastic base have been presented, which is organized as follows.
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