Transient Response Analysis of Foldable Structures with Nonlinear Spring Characteristics

Abstract

In this study, we investigated vibration isolation performance of the foldable cylindrical structure with torsional buckling pattern. The foldable structure is numerically modeled by 12 independent side walls and two top/bottom surfaces connecting by rotational hinges all together. Under static compression, air sealed in the structure is simultaneously compressed to work as air spring. It was revealed that the foldable structure with air could be a high-static-low-dynamicstiffness spring by adjusting a beam radius that was virtually modeled on the hinges to supplement bending stiffness of the fold lines of the actual foldable cylindrical structure. Next, we performed transient response analysis to obtain frequency characteristics of the vibration system consisting of the foldable structure with air. In cases that displacement amplitudes of input signals were small, the resonance frequency was close to zero and transmissibility of the system was less than 1.0 in a whole frequency range. While, for large amplitudes, the resonance frequency went high and the resonance peak was observed. This trend results from nonlinear spring stiffness of the vibration system and is consistent with a theoretical resonance frequency of a nonlinear spring system given as a solution to the Duffing equation.