Abstract
For complex micro-active machines or micro-robotics, it is crucial to clarify the coupling and collective motion of their multiple self-oscillators. In this article, we construct two joint liquid crystal elastomer (LCE) spring oscillators connected by a spring and theoretically investigate their collective motion based on a well-established dynamic LCE model. The numerical calculations show that the coupled system has three steady synchronization modes: in-phase mode, anti-phase mode, and non-phase-locked mode, and the in-phase mode is more easily achieved than the anti-phase mode and the non-phase-locked mode. Meanwhile, the self-excited oscillation mechanism is elucidated by the competition between network that is achieved by the driving force and the damping dissipation. Furthermore, the phase diagram of three steady synchronization modes under different coupling stiffness and different initial states is given. The effects of several key physical quantities on the amplitude and frequency of the three synchronization modes are studied in detail, and the equivalent systems of in-phase mode and anti-phase mode are proposed. The study of the coupled LCE spring oscillators will deepen people’s understanding of collective motion and has potential applications in the fields of micro-active machines and micro-robots with multiple coupled self-oscillators.
Highlights
Self-excited oscillation is a kind of periodic motion that is maintained by constant external excitations [1–4]
Considering that the thermal excitation from trans to cis is often negligible compared to the light-driven excitation, we define the number fraction of cis isomers in liquid crystal elastomer (LCE) fibers and use the following governing equations to describe the evolution of the number fraction of the cis isomers [66]
This is because the light-driven contraction of the LCE fiber increases as the light intensity increases, and the light energy absorbed by the LCE fiber from the environment increases
Summary
Self-excited oscillation is a kind of periodic motion that is maintained by constant external excitations [1–4]. Based on optically responsive LCE, Ghislaine et al experimentally studied the synchronized oscillations of thin plastic actuators fueled by light and found two kinds of in-phase and anti-phase synchronous oscillation phenomena in the steady-state [30,31] Their numerical simulations qualitatively explained the origin of synchronized motion and found that motion can be regulated by the mechanical properties of coupling. Based on LCE materials, several self-exciting motion modes have been constructed, such as rolling [20], vibration [17], swinging [10,55], stretching and shrinking [56], rotation [57], eversion or inversion [9,58], torsion [59], jumping [60], and buckling [61] modes These self-exciting motion modes provide good ideas for studying the coupling of multiple systems and their collective motion.
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