Reply to “On ‘Applications of approximate expressions for complete elliptic integrals’”

Abstract

Quasi-zero-stiffness (QZS) vibration isolators avoid excessive deformation due to gravity, a critical issue in vertical vibration isolation, by providing restoring force with high initial stiffness and low tangent stiffness around the static equilibrium position. Effective use of geometric nonlinearity often plays a central role in QZS mechanisms. Design of such QZS mechanisms, however, tends to be complex, and it is difficult to realize large loading capacity as well as large stroke length at the same time. This paper attempts to resolve these issues by applying newly developed superelastic Cu–Al–Mn shape memory alloy (SMA) bars, characterized by excellent recoverable strain upon unloading along with small hysteresis and nearly flat stress plateau. These features are realized by material design tailored for obtaining mechanical properties required in QZS mechanisms. The use of such tailored superelastic Cu–Al–Mn SMA bars allows us to easily achieve large loading capacity as well as large stroke length while keeping the QZS mechanism simple and compact. In this paper, we derive design equations, produce a prototype, and conduct shaking table tests and numerical simulations to demonstrate the feasibility of QZS vibration isolator with superelastic Cu–Al–Mn SMA bars.