# Enhancing Vibration Isolation Performance by Exploiting Novel Spring-Bar Mechanism
## 1 Introduction  
Scientists and engineers are often confronted with the tasks of preventing the transmission of excessive vibrations from a vibrating source to its surrounding environment [1]. To deal with them, a common approach is to insert a vibration isolator between the source and the receiving structure. For the effective attenuations of the transmitted force (or displacement), the linear vibration isolation theory suggests that the natural frequency of a linear isolator \(\Omega_{n}\) has to be much lower than the excitation frequency \(\Omega\)[2]. As a result, problems can arise when linear isolators are used in harsh environments, such as in cars, ships, aircrafts, and earthquake vibration isolation units, which are subject to shock, impact, or ground motion excitations containing low-frequency components. In these circumstances, successful vibration isolation requires an ultra-low supporting stiffness for a low natural frequency. This, in turn, results in a large static deflection. However, in many practical devices, the maximum allowable deflection is confined, and the use of low static stiffness becomes infeasible. In view of this, many methods have been proposed to improve vibration isolation performance in the low-frequency range without compromising static deflection. One possible approach is to create anti-resonances in the frequency-response curves so that successful isolation is achieved in a relatively narrow band of excitation frequencies [3]. Alternatively, active control units may be introduced to modify the dynamiccharacteristics of the isolation system in the low-frequency range, but this approach leads to extra energy costs [4]. Recently, there has been a great deal of interest in configuring passive elements with a linear isolator to achieve low-frequency vibration isolations. These elements, usually referred to as Quasi-Zero-Stiffness (QZS) mechanisms [5] or Negative Stiffness Mechanisms (NSM) [6], can generate a negative restoring force or negative stiffness so that low dynamic stiffness of the overall system is achieved while keeping its static stiffness high and the static deflection small. Such mechanisms are often created by springs [7; 8; 9; 10], magnets [11; 12], bars [13; 14], circular rings [15], or composite plates [16]. By transforming a linear system into a nonlinear system with NSMs, it has been shown that the natural frequency of the linearized system can be reduced. Based on linear vibration theories, the functioning frequency range of these isolation systems will be enlarged, and hence better vibration performance can be expected. Apart from the nonlinear stiffness application in the isolation systems, some researchers have also studied the nonlinear isolation by using electromagnetic shunt damping [17; 18]. In recent years, NSMs have also been studied in practical engineering applications and in experimental tests, including drilling systems [19], robots [20], Stewart platforms [21], and vehicle seats [22]. Many previous investigations focused on the displacement response of isolation systems, while the vibration power flow and energy transmission characteristics were often ignored. The vibrational power flow analysis (PFA) combines the effects of both force and velocity responses with a single quantity and can better reflect the transmission of vibration energy within a dynamical system [23]. The power flow analysis approach has been developed into a widely accepted tool to assess vibration transmission in linear/nonlinear dynamical systems [24; 25; 26; 27]. [PERSON] et al. [28] used power flow analysis to investigate the interactional dynamic performance of a system with a vibrating equipment, a nonlinear isolator, and a flexible ship excited by sea waves. [PERSON] et al. studied the power flow behaviour and energy transmission characteristics of the Duffing oscillator [29], a nonlinear absorber [30], and a nonlinear isolator [31].