On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

Abstract

Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

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

“…For high frequency excitation, the displacement transmissibility equals the force transmissibility as shown in [23]. So, (26) becomes…”

“…Note that this is not a severe restriction as the displacements of a practical system are unlikely to be 20% of the length of the horizontal spring. It is also assumed that the maximum value of the excitation force is such that analytical results are valid [12,23]. Using Taylor expansion, (1a) and (1b) and (2) can be approximated by…”

“…In this case, the maximum roll-off rate of the transmissibility doubled. Lu et al [22,23] investigated a twostage nonlinear isolator to promote the HSLDS mechanism. HSLDS in each stage has a profound positive effect on isolation performance.…”

A New Approach to Achieve Variable Negative Stiffness by Using an Electromagnetic Asymmetric Tooth Structure

“…However, most of them are passive mechanism whose negative stiffness cannot be adjusted. For example, a common way to obtain negative stiffness in the research papers [5,6] is using two oblique mechanical coil springs. With these two precompressed coil springs, a negative stiffness can be got in vertical direction but cannot be adjusted as there is no adjustment mechanism.…”

“…Thus, the isolator with magnets is not suitable for vibration isolation at high temperature. Unlike the way of using the electromagnets, Xu and Sun [21] proposed a theoretical model with adjustable negative stiffness by applying actuators to the traditional negative stiffness mechanism shown in [5,6] to change the prestressed length of oblique springs. However, this regulating mode of the negative stiffness may be not very suitable for the practical application due to the empty trip phenomenon.…”