Self-Sustained Euler Buckling of an Optically Responsive Rod with Different Boundary Constraints

A light-powered self-rotating liquid crystal elastomer drill

Self-oscillating systems can directly convert ambient energy to mechanical work, and new type self-oscillating systems are worth designing for applications in energy harvesters, engines, and actuators. Taking inspiration from the hand drill, we have developed a novel self-rotating drill system, which is consist of a turnplate and a liquid crystal elastomer (LCE) fiber under steady illumination. To investigate the self-rotating behaviors of the LCE drill, we have proposed a nonlinear theoretical model of the LCE drill under steady illumination based on the well-established dynamic LCE model. Numerical calculation reveals that the LCE drill can undergo a supercritical Hopf bifurcation between the static regime and the self-rotation regime. The self-rotation of drill originates from the contraction of winding portion of LCE fiber in illumination at winding state, and its continuous periodic motion is sustained by the interrelation between light energy and damping dissipation. The Hopf bifurcation conditions are also investigated in detail, as well as the vital system parameters affecting its frequency and amplitude. In contrast to the abundant existing self-oscillating systems, this self-rotating drill stands out due to its simple and lightweight structure, customizable dimensions, and high speed, and thus facilitates the design of compact and integrated systems, enhancing their applicability in microdevices and systems. This bears great significance in fields like micro-robotics, micro-sensors, and medical instruments, enabling the realization of smaller and higher-performance devices.

Modeling the light-powered self-rotation of a liquid crystal elastomer fiber-based engine

Self-oscillating systems possess the ability to convert ambient energy directly into mechanical work, and new types of self-oscillating systems are worth designing for practical applications in energy harvesters, engines and actuators. Taking inspiration from the four-stroke engine. A concept for a self-rotating engine is presented on the basis of photothermally responsive materials, consisting of a liquid crystal elastomer (LCE) fiber, a hinge and a turnplate, which can self-rotate under steady illumination. Based on the photo-thermal-mechanical model, a nonlinear theoretical model of the LCE-based engine under steady illumination is proposed to investigate its self-rotating behaviors. Numerical calculations reveal that the LCE-based engine experiences a supercritical Hopf bifurcation between the static regime and the self-rotation regime. The self-rotation of the LCE-based engine originates from the photothermally driven strain of the LCE fiber in illumination, and its continuous periodic motion is sustained by the correlation between photothermal energy and damping dissipation. The Hopf bifurcation conditions are also explored in detail, as well as the vital system parameters affecting self-rotation frequency. Compared to the abundant existing self-oscillating systems, this conceptual self-rotating LCE-based engine stands out due to its simple and lightweight structure, customizable dimensions and high speed, and it is expected to offer a broader range of design concepts applicable to soft robotics, energy harvesters, medical instruments, and so on.

Synchronous behaviors of three coupled liquid crystal elastomer-based spring oscillators under linear temperature fields

Self-oscillating coupled systems possess the ability to actively absorb external environmental energy to sustain their motion. This quality endows them with autonomy and sustainability, making them have application value in the fields of synchronization and clustering, thereby furthering research and exploration in these domains. Building upon the foundation of thermal responsive liquid crystal elastomer-based (LCE-based) spring oscillators, a synchronous system comprising three LCE-based spring oscillators interconnected by springs is established. In this paper, the synchronization phenomenon is described, and the self-oscillation mechanism is revealed. The results indicate that by varying system parameters and initial conditions, three synchronization patterns emerge, namely, full synchronous mode, partial synchronous mode, and asynchronous mode. For strongly interacting systems, full synchronous mode always prevails, while for weak interactions, the adjustment of initial velocities in magnitude and direction yields the three synchronization patterns. Additionally, this study explores the impact of several system parameters, including LCE elasticity coefficient and spring elasticity coefficient, on the amplitude, frequency, and synchronous mode of the system. The findings in this paper can enhance our understanding of the synchronization behavior of multiple mutually coupled LCE-based spring oscillators, with promising applications in energy harvesting, soft robotics, signal monitoring, and various other fields.

Self-Sustained Chaotic Jumping of Liquid Crystal Elastomer Balloon under Steady Illumination

Self-sustained chaotic jumping systems composed of active materials are characterized by their ability to maintain motion through drawing energy from the steady external environment, holding significant promise in actuators, medical devices, biomimetic robots, and other fields. In this paper, an innovative light-powered self-sustained chaotic jumping system is proposed, which comprises a liquid crystal elastomer (LCE) balloon and an elastic substrate. The corresponding theoretical model is developed by combining the dynamic constitutive model of an LCE with Hertz contact theory. Under steady illumination, the stationary LCE balloon experiences contraction and expansion, and through the work of contact expansion between LCE balloon and elastic substrate, it ultimately jumps up from the elastic substrate, achieving self-sustained jumping. Numerical calculations reveal that the LCE balloon exhibits periodic jumping and chaotic jumping under steady illumination. Moreover, we reveal the mechanism underlying self-sustained periodic jumping of the balloon in which the damping dissipation is compensated through balloon contact with the elastic substrate, as well as the mechanism involved behind self-sustained chaotic jumping. Furthermore, we provide insights into the effects of system parameters on the self-sustained jumping behaviors. The emphasis in this study is on the self-sustained chaotic jumping system, and the variation of the balloon jumping modes with parameters is illustrated through bifurcation diagrams. This work deepens the understanding of chaotic motion, contributes to the research of motion behavior control of smart materials, and provides ideas for the bionic design of chaotic vibrators and chaotic jumping robots.

Self-Rotation of Electrothermally Responsive Liquid Crystal Elastomer-Based Turntable in Steady-State Circuits

Self-excited motions, characterized by their ability to harness energy from a consistent environment and self-regulate, exhibit significant potential in micro-devices, autonomous robotics, sensor technology, and energy generation. This study introduces an innovative turntable system based on an electrothermally responsive liquid crystal elastomer (LCE). This system facilitates self-rotation within a steady-state circuit. Employing an electrothermal LCE model, we have modeled and numerically analyzed the nonlinear dynamics of an LCE-rope within steady-state circuits, utilizing the four-order Runge-Kutta method for calculations. The numerical results reveal the emergence of two distinct motion patterns in the turntable system under steady-state conditions: a self-rotation pattern and a static pattern. The self-rotation is initiated when the system's absorbed energy surpasses the energy lost due to damping effects. Furthermore, this paper delves into the critical conditions necessary for initiating self-rotation and examines the influence of various key dimensionless parameters on the system's rotation amplitude and frequency. These parameters include gravitational acceleration, the initial position of the mass ball, elastic stiffness of the LCE and spring, limiting temperature, heating zone angle, thermal shrinkage coefficient, and damping factor. Our computational findings establish that these parameters exert a modulatory impact on the rotation amplitude and period. This research enhances the understanding of self-excited motions and offers promising avenues for applications in energy harvesting, monitoring, soft robotics, medical devices, and micro- and nano-devices.

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.

A Light-Powered Liquid Crystal Elastomer Roller

Achieving and controlling the desired movements of active machines is generally accomplished through precise control of artificial muscles in a distributed and serialized manner, which is a significant challenge. The emerging motion control strategy based on self-oscillation in active machines has unique advantages, including directly harvesting energy from constant ambient light, and it has no need for complex controllers. Inspired by the roller, we have innovatively developed a self-rolling roller that consists of a roller and a liquid crystal elastomer (LCE) fiber. By utilizing a well-established dynamic LCE model and subjecting it to constant illumination, we have investigated the dynamic behavior of the self-rolling roller. Based on numerical calculations, it has been discovered that the roller, when subjected to steady illumination, exhibits two distinct motion regimes: the static regime and the self-rolling regime. The self-rolling regime, characterized by continuous periodic rolling, is sustained by the interaction between light energy and damping dissipation. The continuous periodic rolling observed in the self-rolling regime is maintained through the interplay between the dissipation of damping and the absorption of light energy. In the static state, the rolling angle of the roller begins to decrease rapidly and then converges to zero. Detailed investigations have been conducted to determine the critical conditions required to initiate self-rolling, as well as the essential system parameters that influence its frequency and amplitude. The proposed self-rolling roller has superiorities in its simple structure, light weight, alternative to manual labor, and speediness. This advancement is expected to inspire greater design diversity in micromachines, soft robotics, energy harvesters, and similar areas.

Self-Vibration of Liquid Crystal Elastomer Strings under Steady Illumination

Self-vibrating systems based on active materials have been widely developed, but most of the existing self-oscillating systems are complex and difficult to control. To fulfill the requirements of different functions and applications, it is necessary to construct more self-vibrating systems that are easy to control, simple in material preparation and fast in response. This paper proposes a liquid crystal elastomer (LCE) string-mass structure capable of continuous vibration under steady illumination. Based on the linear elastic model and the dynamic LCE model, the dynamic governing equations of the LCE string-mass system are established. Through numerical calculation, two regimes of the LCE string-mass system, namely the static regime and the self-vibration regime, are obtained. In addition, the light intensity, contraction coefficient and elastic coefficient of the LCE can increase the amplitude and frequency of the self-vibration, while the damping coefficient suppresses the self-oscillation. The LCE string--mass system proposed in this paper has the advantages of simple structure, easy control and customizable size, which has a wide application prospect in the fields of energy harvesting, autonomous robots, bionic instruments and medical equipment.

Self-Vibration of a Liquid Crystal Elastomer Fiber-Cantilever System under Steady Illumination

A new type of self-oscillating system has been developed with the potential to expand its applications in fields such as biomedical engineering, advanced robotics, rescue operations, and military industries. This system is capable of sustaining its own motion by absorbing energy from the stable external environment without the need for an additional controller. The existing self-sustained oscillatory systems are relatively complex in structure and difficult to fabricate and control, thus limited in their implementation in practical and complex scenarios. In this paper, we creatively propose a novel light-powered liquid crystal elastomer (LCE) fiber-cantilever system that can perform self-sustained oscillation under steady illumination. Considering the well-established LCE dynamic model, beam theory, and deflection formula, the control equations for the self-oscillating system are derived to theoretically study the dynamics of self-vibration. The LCE fiber-cantilever system under steady illumination is found to exhibit two motion regimes, namely, the static and self-vibration regimes. The positive work done by the tension of the light-powered LCE fiber provides some compensation against the structural resistance from cantilever and the air damping. In addition, the influences of system parameters on self-vibration amplitude and frequency are also studied. The newly constructed light-powered LCE fiber-cantilever system in this paper has a simple structure, easy assembly/disassembly, easy preparation, and strong expandability as a one-dimensional fiber-based system. It is expected to meet the application requirements of practical complex scenarios and has important application value in fields such as autonomous robots, energy harvesters, autonomous separators, sensors, mechanical logic devices, and biomimetic design.

Heat-Driven Synchronization in Coupled Liquid Crystal Elastomer Spring Self-Oscillators

Self-oscillating coupled machines are capable of absorbing energy from the external environment to maintain their own motion and have the advantages of autonomy and portability, which also contribute to the exploration of the field of synchronization and clustering. Based on a thermally responsive liquid crystal elastomer (LCE) spring self-oscillator in a linear temperature field, this paper constructs a coupling and synchronization model of two self-oscillators connected by springs. Based on the existing dynamic LCE model, this paper theoretically reveals the self-oscillation mechanism and synchronization mechanism of two self-oscillators. The results show that adjusting the initial conditions and system parameters causes the coupled system to exhibit two synchronization modes: in-phase mode and anti-phase mode. The work conducted by the driving force compensates for the damping dissipation of the system, thus maintaining self-oscillation. The phase diagrams of different system parameters are drawn to illuminate the self-oscillation and synchronization mechanism. For weak interaction, changing the initial conditions may obtain the modes of in-phase and anti-phase. Under conditions of strong interactions, the system consistently exhibits an in-phase mode. Furthermore, an investigation is conducted on the influence of system parameters, such as the LCE elastic coefficient and spring elastic coefficient, on the amplitudes and frequencies of the two synchronization modes. This study aims to enhance the understanding of self-oscillator synchronization and its potential applications in areas such as energy harvesting, power generation, detection, soft robotics, medical devices and micro/nanodevices.

Self-Oscillating Liquid Crystal Elastomer Helical Spring Oscillator with Combined Tension and Torsion

Self-oscillation is the autonomous maintenance of continuous periodic motion through energy absorption from non-periodic external stimuli, making it particularly attractive for fabricating soft robots, energy-absorbing devices, mass transport devices, and so on. Inspired by the self-oscillating system that presents high degrees of freedom and diverse complex oscillatory motions, we created a self-oscillating helical spring oscillator with combined tension and torsion under steady illumination, among which a mass block and a liquid crystal elastomer (LCE) helical spring made with LCE wire are included. Considering the well-established helical spring model and the dynamic LCE model, a nonlinear dynamic model of the LCE helical spring oscillator under steady illumination is proposed. From numerical calculation, the helical spring oscillator upon exposure to steady illumination possesses two motion regimes, which are the static regime and the self-tension-torsion regime. Contraction of the LCE wire under illumination is necessary to generate the self-tension-torsion of the helical spring oscillator, with its continuous periodic motion being maintained by the mutual balance between light energy input and damping dissipation. Additionally, the critical conditions for triggering the self-tension-torsion, as well as the vital system parameters affecting its frequencies and amplitudes of the translation and the rotation, were investigated in detail. This self-tension-torsion helical spring oscillator is unique in its customizable mechanical properties via its structural design, small material strain but large structural displacement, and ease of manufacture. We envision a future of novel designs for soft robotics, energy harvesters, active machinery, and so on.

Light-Fueled Synchronization of Two Coupled Liquid Crystal Elastomer Self-Oscillators

The synchronization and group behaviors of self-excited coupled oscillators are common in nature and deserve to be explored, for self-excited motions have the advantages of actively collecting energy from the environment, being autonomous, making equipment portable, and so on. Based on light-powered self-excited oscillators composed of liquid crystal elastomer (LCE) bars, the synchronization of two self-excited coupled oscillators is theoretically studied. Numerical calculations show that self-excited oscillations of the system have two synchronization modes, in-phase mode and anti-phase mode, which are mainly determined by their interaction. The time histories of various quantities are calculated to elucidate the mechanism of self-excited oscillation and synchronization. For strong interactions, the system always develops into in-phase synchronization mode, while for weak interaction, the system will evolve into anti-phase synchronization mode. Furthermore, the effects of initial conditions, contraction coefficient, light intensity, and damping coefficient on the two synchronization modes of the self-excited oscillation are investigated extensively. The initial condition generally does not affect the synchronization mode and its amplitude. The amplitude of self-oscillation always increases with increasing contraction coefficient, gravitational acceleration, and light intensity, while it decreases with the increasing damping coefficient. This work will deepen people's understanding of the synchronization behaviors of self-excited coupled oscillators, and the theoretical framework could be extended to scenarios involving large-scale synchronization of the systems with numerous interacting oscillators.

Self-Sustained Oscillation of Electrothermally Responsive Liquid Crystal Elastomer Film in Steady-State Circuits

Self-excited oscillations have the advantages of absorbing energy from a stable environment and Self-control; therefore, Self-excited motion patterns have broader applications in micro devices, autonomous robots, sensors and energy-generating devices. In this paper, a Self-sustained curling liquid crystal elastomer (LCE) film-mass system is proposed on the basis of electrothermally responsive materials, which can realize Self-oscillation under a steady-state current. Based on the contact model and dynamic LCE model, a nonlinear dynamics model of LCE film in steady-state circuits is developed and numerical calculations are carried out using the Runge-Kutta method. Through numerical calculations, it is demonstrated that LCE film-mass systems have two motion patterns in steady-state circuits: namely, a Self-oscillation pattern and a stationary pattern. Self-sustained curling of LCE film originates from the fact that the energy absorbed by the system exceeds the energy dissipated due to the damping effect. In addition, the critical conditions for triggering Self-oscillation and the effects of several key dimensionless system parameters on the amplitude and period of Self-oscillation are investigated in detail. Calculation results show that the height of electrolyte solution, gravitational acceleration, elastic modulus of LCE film, limit temperature, curvature coefficient, thermal shrinkage coefficient and damping factor all have a modulating effect on the amplitude and period of Self-oscillation. This research may deepen the understanding of Self-excited oscillation, with promising applications in energy harvesting, power generation, monitoring, soft robotics, medical devices, and micro and nano devices.