Liquid crystal elastomer self-oscillator with embedded light source

Light sources that switch periodically over time have a wide range of application value in life and engineering, and generally require additional controller to periodically switch circuits to achieve periodic lighting. In this paper, a self-oscillating spring oscillator based on optically responsive liquid crystal elastomer (LCE) fiber is constructed, which consists of a embedded light source and a LCE fiber. The spring oscillator can oscillate autonomously to achieve periodic switching of the light source. On the basis of the well-established dynamic LCE model, a nonlinear dynamic model is proposed and its dynamic behavior is studied. Numerical calculations demonstrate that the spring oscillator presents two motion regimes, namely the self-oscillation regime and the static regime. The self-oscillation of spring oscillator is maintained by the energy competition between light energy and damping dissipation. Furthermore, the critical conditions for triggering self-oscillation are also investigated in detail, as well as the key system parameters that affect its frequency and amplitude. Different from the existing abundant self-oscillating systems, this self-oscillating structure with simple structure and convenient fabrication does not require complex controller to obtain periodic lighting, and it is expected to provide more diversified design ideas for soft robots and sensors.

Figure 1

Schematic diagram of spring oscillator containing optically responsive LCE fiber, inextensible fiber, shading sleeve, and light source: (a) reference state, (b) initial state, and (c) current state. In self-oscillating state, coupling between light-driven contraction of LCE fiber and its motion can trigger self-oscillation of light source.

Figure 2

Two motion regimes of light source suspended by LCE fiber: (a), (b) Self-oscillation regime ($\tilde{c}=0.05$); (c), (d) static regime ($\tilde{c}=0.15$). The other dimensionless parameters are $\tilde{E}=4, \tilde{I}=0.1, \tilde{g}=0.1, C_0=0.1, \tilde{b}=0.5, {\tilde{L}}_{\mathrm{shading}}=0$. Video 1 present two motion regimes. See Supplemental Material for videos associated some of the figures [65].

Figure 3

Mechanism of self-oscillation of suspended light source. (a) Variation of volume fraction of cis-isomers in with time; (b) dependence between displacement of self-oscillating suspended light source and time; (c) dependence between tension and time; and (d) dependence between tension and displacement. Parameters are set as $\tilde{E}=4, \tilde{I}=0.1, \tilde{g}=0.1, C_0=0.1, \tilde{b}=0.5, {\tilde{L}}_{\mathrm{shading}}=0$, and $\tilde{c}=0.05$.

Figure 4

Snapshots of self-oscillating suspended light source in one cycle shown in Figs. 2 and 2. Suspended light source exhibits continuous periodic self-oscillating due to periodic change in light-driven contraction of LCE fiber.

Figure 5

Effect of elastic modulus on self-oscillating light source, for $C_0=0.1, \tilde{I}=0.1, \tilde{c}=0.05, \tilde{b}=0.5, {\tilde{L}}_{\mathrm{shading}}=0$, and $\tilde{g}=0.1$. (a) Limit cycles. (b) Frequency and amplitude. Critical elastic modulus for triggering self-oscillation is about $\tilde{E}=2.6$. With increase of elastic modulus, amplitude and frequency show upward trend.

Figure 6

Effect of light intensity on self-oscillating light source, for $C_0=0.1, \tilde{E}=4, \tilde{c}=0.05, \tilde{b}=0.5, {\tilde{L}}_{\mathrm{shading}}=0$, and $\tilde{g}=0.1$. (a) Limit cycles. (b) Frequency and amplitude. Critical light intensity that triggers self-oscillation is approximately $\tilde{I}=0.054$. With increase of light intensity, amplitude tends to increase, while frequency remains almost constant.

Figure 7

Effect of gravitational acceleration on self-oscillating light source, for $\tilde{E}=4, \tilde{I}=0.1, \tilde{c}=0.05, \tilde{b}=0.5, {\tilde{L}}_{\mathrm{shading}}=0$, and $C_0=0.1$. (a) Limit cycles. (b) Frequency and amplitude. There exists critical gravitational acceleration, approximately $\tilde{g}=0.174$, to trigger self-oscillation. As gravitational acceleration increases, amplitude shows decreasing trend, while frequency does not change.

Figure 8

Effect of damping coefficient on self-oscillating light source, for $\tilde{E}=4, \tilde{I}=0.1, \tilde{b}=0.5, {\tilde{L}}_{\mathrm{shading}}=0, C_0=0.1$, and $\tilde{g}=0.1$. (a) Limit cycles. (b) Frequency and amplitude. Damping coefficient for triggering self-oscillation has critical value of approximately $\tilde{c}=0.118$. With increase of damping coefficient, amplitude presents decreasing trend, while frequency does not change.

Figure 9

Effect of contraction coefficient on self-oscillating light source, for $\tilde{E}=4, \tilde{I}=0.1, \tilde{c}=0.05, \tilde{b}=0.5, {\tilde{L}}_{\mathrm{shading}}=0$, and $\tilde{g}=0.1$. (a) Limit cycles. (b) Frequency and amplitude. Critical value of contraction coefficient to trigger self-oscillation is approximately $C_0=0.057$. When contraction coefficient is increased, there is clear upward trend in amplitude, while frequency does not change.

Figure 10

Effect of illumination length on self-oscillating light source, for $\tilde{E}=4, \tilde{I}=0.1, C_0=0.1, c=0.2, {\tilde{L}}_{\mathrm{shading}}=0$, and $\tilde{g}=0.1$. (a) Limit cycles. (b) Frequency and amplitude. Presence of critical illumination length that triggers self-oscillation is approximately $\tilde{b}=0.03$. As illumination length increases, both amplitude and frequency remain constant.

Figure 11

Effect of shading length on self-oscillating light source, for $\tilde{E}=4, \tilde{I}=0.1, \tilde{c}=0.05, \tilde{b}=0.5, C_0=0.1$, and $\tilde{g}=0.1$. (a) Limit cycles. (b) Frequency and amplitude. There are two critical shading lengths for triggering self-oscillation, which are approximately ${\tilde{L}}_{\mathrm{shading}}=-0.005$ and ${\tilde{L}}_{\mathrm{shading}}=0.05$. With increase of shading length, amplitude shows trend of rise first and then decrease, while frequency is almost constant.