Nonlinear stiffness and dynamical response characteristics of an asymmetric X-shaped structure

Nonlinearity is more and more shown to be very beneficial to various engineering practice, including vibration control, vibration energy harvesting and structural health monitoring, etc. An X-shaped structure has been investigated recently for its special and beneficial nonlinear stiffness and damping characteristics in passive vibration isolation and suppression. In this study, a novel n-layer vertically-asymmetric X-shaped structure is systematically studied for its generic modelling, nonlinear stiffness/damping features and dynamic response in vibration isolation. It is shown that, (a) micro-gravity environment can reduce the linear natural frequency and it can improve the vibration isolation performance in the vertical direction (good for micro-gravity environment vibration control), and an optimal assembly angle α1 and rod-length ratio s1 can be designed to achieve the minimum natural frequency when the gravity acceleration is not equal to zero for the best vibration isolation performance; (b) the asymmetric structure can produce lower natural frequency than that of symmetric counterparts (i.e. s1 = 1/s2 = 1) by properly adjusting rod-length ratio s1 (or s2), and the developed generic model can be used freely to study the structure response under different asymmetric settings; (c) the transmissibility of the asymmetric X-shaped structure can be tuned to have much lower transmissibility than that of the symmetric counterpart, which is very beneficial for vibration isolation; (d) the structure in the horizontal direction demonstrates very special dynamic response characteristics which can well explain a linear damper in the horizontal direction much better for vibration energy absorption for a much wider frequency range compared with the vertical direction. It should be noticed that instead of direct modeling of the vibration system in vertically direction, the dynamical equation is established with an intermediate variable, due to vertical asymmetry of the structure. The results provide new understanding on the X-shaped structures including its modelling, gravity effect, asymmetric ratio and nonlinear response in both vertical and horizontal directions, which can help practical applications of this class of structures.