Bistable Buckled Beam Research Articles

A Triboelectric-Piezoelectric-Electromagnetic hybrid wind energy harvester based on a snap-through bistable mechanism

Real-time monitoring is essential for safeguarding infrastructure in extreme environments, particularly in remote areas with abundant wind resources where sustained strong winds are common. A triboelectric-piezoelectric-electromagnetic hybrid wind energy harvester based on a snap-through bistable mechanism (ST-HWEH) is proposed, which can be used as a sustainable power source and a self-powered wind speed sensor. The piezoelectric energy harvester (PEH), triboelectric nanogenerator (TENG), and electromagnetic energy harvester (EMH) are placed at the maximum strain location, maximum contact area, and maximum displacement position of the bistable buckled beam, respectively, fully utilizing its characteristics in the structural space. The bistable buckled beam undergoes convex and concave snap-through transformations under the magnetic excitation, working synergistically with the buckled boundary to simultaneously achieve the three electromechanical energy conversions, thereby enhancing the electrical output performance of the system. Moreover, both the starting wind speed and resistance torque of the system are effectively reduced through the arrangement of symmetrical excited magnets with antimagnetic poles on the buckled beam. A prototype is prepared and subsequently experimentally verified. The results show that the overall output power density in a composite power generation unit for the ST-HWEH is 83.97 W/m3 at a wind speed of 11 m/s, which is 6.88 times higher than that of the ST-HWEH that only contains TENG. The prototype can easily light up 1000 LED lights at a mild wind speed of 5 m/s and demonstrate self-powered environmental monitoring (taking temperature and wind speed as examples), providing a potential solution for self-powered environmental monitoring and status monitoring of the infrastructure.

Numerical and experimental study of impact dynamics of bistable buckled beams

Bistable systems have been of great research interest due to their rich dynamics arising from a variety of excitations. This study presents an investigation into the nonlinear dynamics of a continuous bistable beam subjected to a form of vibro-impact forcing. A fixed–fixed Euler–Bernoulli beam, precompressed to achieve bistability, is considered, while a shaker with sinusoidally-prescribed velocity applies transverse impact forcing. By varying excitation parameters such as frequency and amplitude, the system response can be tuned. The study begins by employing a Galerkin expansion to the continuous equation of motion, using the buckling modes to remove buckling level dependence and ensure equilibrium symmetry. A Hertzian contact law is chosen to model the collision between the shaker and the buckled beam. The rich dynamics of this system are then explored through numerical and experimental analyses. The focus lies on investigating the emergence of intrawell and interwell dynamics that arise with varying excitation frequency, amplitude, and location. Moreover, we evaluate the significance of including higher-order modes in the modeling of bistable beam dynamics, particularly near snapthrough. This research provides valuable insights into the behavior of continuous bistable structures under vibro-impact forcing, contributing to the understanding and control of such systems in engineering applications.

Finding transition state and minimum energy path of bistable elastic continua through energy landscape explorations

Mechanical bistable structures have two stable equilibria and can transit between them under external stimuli. Due to their unique behaviors such as snap-through and substantial shape changes, bistable structures exhibit unprecedented properties compared to conventional structures and thus have found applications in various fields such as soft robots, morphing wings and logic units. To quantitatively predict the performance of bistable structures in these applications, it is desirable to acquire information about the minimum energy barrier and an energy-efficient transition path between the two stable states. However, there is still a general lack of efficient methodologies to obtain this information, particularly for elastic continua with complicated, unintuitive transition paths. To overcome this challenge, here we integrate energy landscape exploration algorithms into finite element method (FEM). We first utilize the binary image transition state search (BITSS) method to identify the saddle point and then perform nudged elastic band (NEB) calculations with an initial guess based on the BITSS results to find the minimum energy path (MEP). This integrated strategy greatly helps the convergence of MEP calculations, which are highly nonlinear. Two representative cases are studied, including bistable buckled beams and a bistable unit of mechanical metamaterials, and the numerical results agree well with the previous works. Importantly, we numerically predict the complicated MEP of an asymmetric bistable unit of mechanical metamaterials and use experiments to demonstrate that following this MEP leads to successful transition between stable states while intuitive uniaxial compression fails to do so. Our work provides an effective numerical platform for identifying the minimum energy barrier and energy-efficient transition path of a bistable continuum, which can offer valuable guidance to the design of actuators, damping structures, energy harvesters, and mechanical metamaterials.

Complibot: A compliant external pipe climbing robot

The article presents the design of Complibot, a robot with a novel gripper for pipe climbing. The mechanism of the gripper involves the use of a bistable buckled beam, which is a type of bistable compliant mechanism. The bistable buckled beam in the gripper is alternately actuated between its gripped and ungripped states using a camshaft and lever mechanism, which is powered by a single DC motor. The design parameters associated with the gripper are obtained both experimentally and numerically. A proper selection of design parameters helps in the efficient functioning of the gripper. After the design of the gripper, two such grippers are fabricated and attached to each other by two stepper motor-driven lead screws to make a pipe climbing robot with inchworm locomotion. The mobility of the robot is controlled by an Arduino Uno microcontroller after the electronic components have been integrated. Finally, Complibot is subjected to a series of tests to establish its maximum load-carrying capacity when climbing a polyvinyl chloride (PVC) pipe. Complibot is found to perform satisfactorily without slipping while climbing a PVC pipe with a diameter of 105–115 mm, a velocity of 0.2 m/min, a power consumption of 18.58 W, a maximum load-carrying capacity of 114.64 N, and a payload to weight ratio of 0.52.

Nonlinear dynamics and snap-through regimes of a bistable buckled beam excited by an electromagnetic Laplace force

We study the nonlinear forced dynamics of a bistable buckled beam. Depending on the forcing frequency and amplitude, we observe three different regimes: (i) small intra-well oscillations in the neighborhood of one of the equilibria, (ii) transient snap-through ending into intra-well oscillations, (iii) persistent dynamic snap-through. We build experimentally and numerically phase-diagrams determining the forcing amplitude and frequency leading to each of the three regimes. The experiments leverage an original setup based on the use of the electromagnetic Laplace forces. The controlled flow of an electric current through a metallic beam immersed in an electromagnetic field is at the origin of the electromechanical coupling. This non-invasive excitation system allows us to easily tune the forcing frequency and amplitude. The results of our numerical model, based on a weakly nonlinear geometrical approximation and a three-mode Galërkin expansion for the space discretization, are in excellent agreement with the experimental findings. We show that higher-order modes, often neglected in the modal models of the literature, have a major influence on the nonlinear dynamics.

Analytical modeling and experimental validation of rotationally actuated pinned–pinned and fixed–pinned buckled beam bistable mechanisms

Buckled beams have become key building blocks in compliant mechanisms to achieve nonlinear behaviors, such as bistability, constant-force and stiffness tuning. However, designing and modeling such components is challenging due to their highly nonlinear characteristics and existing models typically lack accuracy or rely on numerical computations. This paper aims at giving closed-form formulas to efficiently characterize the snap-through behavior and facilitate the design process of rotationally actuated pinned–pinned and fixed–pinned bistable buckled beams. A new generic analytical model for precompressed beams based on Euler–Bernoulli beam theory is first established and then applied to these two configurations. Finite element and experimental validations are performed, showing excellent agreement with the model. The results show that the angular input at the pinned beam extremity is significantly decoupled from the angular or moment output at the other extremity, until snap-through. Additionally, we show that the stable output values can be controlled by adjusting the precompression displacement of the buckled beam. Finally, we demonstrate the practicality of the studied building blocks and their modeling on a novel bistable gripper design.

Case Study of a MEMS Snap-Through Actuator: Modeling and Fabrication Considerations

MEMS actuators rely on the deformation of silicon structures. Using dimensions smaller than dozens of micrometers reveals that the micro-electro-mechanical systems (MEMS) actuators are affected by fabrication inaccuracies, leading to hardly predictable forces and/or actuation results. In this paper, MEMS bistable buckled beam actuators are presented. A series of structures based on pre-shaped buckled beams of lengths ranging from 2 to 4 mm, constant width of 5 μm and actuation stroke ranging from 20 to 100 μm was fabricated. Experimental data show a significant difference with predictions from a conventional analytical model. The model commonly used for buckled beams design assumes a rectangular beam section, but it is not the case of the fabricated beams. Furthermore, only symmetric buckling modes (mode 1, mode 3…) are supposed to exist during snap-through. In this paper, new analytical models have been developed on the basis of the models of the literature to consider the effective beam shape. The first improved analytical model enabled prediction of the MEMS buckled beams mechanical behavior in a 30% margin on the whole range of operation. A second model has been introduced to consider both the effective shape of the beam and centro-symmetric buckling modes. This refined model exhibits the partial suppression of buckling mode 2 by a central shuttle. Therefore, mode 2 and mode 3 coexist at the beginning and the end of snap-through, while mode 3 quickly vanishes due to increasing rotation of the central shuttle to leave exclusive presence of mode 2 near the mid-stroke. With this refined model, the effective force-displacement curve can be predicted in a margin reduced to a few percentages in the center zone of the response curve, allowing the accurate prediction of the position switch force. In addition, the proposed model allows accurate results to be reached with very small calculation time.

Analysis of snap-through behavior of bistable buckled beam under end-moment static actuation

Bistable buckled beams are one of the most prevalent types of bistable mechanisms due to their simple structural forms, which have attracted significant research attention and wide applications in switches, actuators, and energy harvesters, etc. In general, a mid-span or off-center force is often applied as the external input to actuate the snap-through behavior of bistable buckled beams. Apart from the force actuation, the method of moment actuation for bistable buckled beams is rarely used and studied. Compared with force actuation, moment actuation has certain advantages when the driving motion is out-of-plane rotation. In this work, the first purpose is to analyze the snap-through behavior of the simply supported bistable buckled beam subjected to a concentrated moment applied at one end of the beam. An analytical model based on the energy method is developed to analyze the snap-through behavior of bistable buckled beams, in particular for predicting the moment–angle curves. Moreover, an experimental setup that consists of a torque sensor and a motor is established to analyze the moment–angle responses for bistable beams and verify the analytical model. The finite element model is also established to obtain numerical results to approve the analytical model, which can provide accurate prediction for bistable buckled beams under force actuation. However, compared with FEA results, the analytical model leads to a certain amount of difference in predicting the moment–angle curves of bistable beams under the moment actuation. Therefore, the reasons causing this difference are investigated, and the analytical model is further improved by introducing polynomials into the shape function to obtain more accurate results, which are then well-matched with FEA and experimental results. At last, a parametric analysis is carried out to further study the influence of geometric parameters and pre-compression on the moment–angle curves of snap-through behavior of bistable beams under this end-moment actuation method.

Analytical and experimental study of a clamped-clamped, bistable buckled beam low-frequency PVDF vibration energy harvester

Vibration-based energy harvesting devices have drawn interest as a potential low-maintenance power source for a variety of applications, such as for systems involving distributed networks of remote sensors. In this work, an energy harvesting system is considered that is based on bistable, buckled beams and the flexible piezoelectric polymer polyvinylidene fluoride (PVDF). The stability and dynamic response of the structure under vibration loading is modeled, and the resulting output voltage is analytically predicted. Modeling outputs are compared with experimental results for driving frequencies below 30 Hz, the range for many common vibration energy harvesting environments. The modeling approach used in this work is based on coupled electrical-mechanical equations of motion for a geometrically nonlinear Euler-Bernoulli piezoelectric beam that were developed via Hamilton's principle. A component sectioning procedure was used in conjunction with implementation of matching conditions at the boundaries to solve for the nonlinear static and linearized dynamic structural equations. These gave both the buckling and dynamic shape functions, which were used as a basis for finding the device nonlinear dynamic response. Several parameters including vibrational motion, output voltage, and frequency response were analyzed both theoretically and experimentally under different driving conditions. Good agreement was found between the developed model and the experiments, particularly with respect to predicted regimes of behavior and power output. The results suggest that the proposed modeling approach could be successfully implemented in the design and analysis of other multi-component piezoelectric-based energy harvesting systems.

Bi-stable buckled beam nonlinear energy sink applied to rotor system

In this paper, a bi-stable nonlinear energy sink (BNES) with buckled beam is developed to suppress the vibration of unbalanced rotor system. The structure of the BNES is developed. The specific structures and working principles of the buckled beam are introduced. Based on these, the dynamic equations of the rotor-BNES system are established. Then, the transient and steady state responses of the rotor-BNES system are numerically studied and compared with the linear visco-elastic damper. In addition, the vibration suppression ability and frequency suppression range of the BNES are analyzed. Finally, experiments are carried out and compared with the simulations to confirm the vibration suppression effectiveness of the BNES. The numerical and experimental results show that the designed BNES has a strong vibration suppression effect on the rotor system and can withstand a wide range of energy.

Analytical modeling for rapid design of bistable buckled beams

Double-clamped bistable buckled beams demonstrate great versatility in various fields such as robotics, energy harvesting, and microelectromechanical system (MEMS). However, their design often requires time-consuming and expensive computations. In this work, we present a method to easily and rapidly design bistable buckled beams subjected to a transverse point force. Based on the Euler–Bernoulli beam theory, we establish a theoretical model of bistable buckled beams to characterize their snapthrough properties. This model is verified against the results from a finite element analysis (FEA) model, with maximum discrepancy less than 7%. By analyzing and simplifying our theoretical model, we derive explicit analytical expressions for critical behavioral values on the force-displacement curve of the beam. These behavioral values include critical force, critical displacement, and travel, which are generally sufficient for characterizing the snap-through properties of a bistable buckled beam. Based on these analytical formulas, we investigate the influence of a bistable buckled beam's key design parameters, including its actuation position and precompression, on its critical behavioral values, with our results validated by FEA simulations. Our analytical method enables fast and computationally inexpensive design of bistable buckled beams and can guide the design of complicated systems that incorporate bistable mechanisms.

Buckled MEMS Beams for Energy Harvesting from Low Frequency Vibrations.

Vibration energy harvesters based on the resonance of the beam structure work effectively only when the operating frequency window of the beam resonance matches with the available vibration source. None of the resonating MEMS structures can operate with low frequency, low amplitude, and unpredictable ambient vibrations since the resonant frequency goes up very high as the structure gets smaller. Bistable buckled beam energy harvester is therefore developed for lowering the operating frequency window below 100Hz for the first time at the MEMS scale. This design does not rely on the resonance of the MEMS structure but operates with the large snapping motion of the beam at very low frequencies when input energy overcomes an energy threshold. A fully functional piezoelectric MEMS energy harvester is designed, monolithically fabricated, and tested. An electromechanical lumped parameter model is developed to analyze the nonlinear dynamics and to guide the design of the nonlinear oscillator based energy harvester. Multilayer beam structure with residual stress induced buckling is achieved through the progressive residual stress control of the deposition processes along the fabrication steps. Surface profile of the released device shows bistable buckling of 200μm which matches well with the amount of buckling designed. Dynamic testing demonstrates the energy harvester operates with 50% bandwidth under 70Hz at 0.5g input, operating conditions that have not been demonstrated by MEMS vibration energy harvesters before.

Bidirectional actuation of buckled bistable beam using twisted string actuator

A new actuation mechanism using the twisted string concept to trigger the snap-through of a bistable buckled beam to produce an effective on/off bistable actuator is proposed. The twisted string concept combined with a pin utilizes actuation moment to actuate a bistable beam. The required actuation loads are analytically formulated using the Euler–Bernoulli beam model and solved with the proposed solution algorithm. The actuation mechanism is fabricated to meet the 24.3 N mm actuation requirements. A prototype of the actuator was built, and its performance was evaluated. In a unidirectional actuation, an actuator response time of 104 ms was achieved. The overall response time of the actuator is affected by the length of the string. The twisted string mechanism was also placed in an antagonistic configuration to enable bidirectional actuation. The shape of the input voltage signal also affected the bidirectional performance of the actuator. The actuator produced an actuation bandwidth of 2 and 5 Hz with sine and square input voltages, respectively, while generating 10 mm output displacement.

A piezoelectric energy harvester for broadband rotational excitation using buckled beam

This paper proposes a rotational energy harvester using a piezoelectric bistable buckled beam to harvest low-speed rotational energy. The proposed harvester consists of a piezoelectric buckled beam with a center magnet, and a rotary magnet pair with opposite magnetic poles mounted on a revolving host. The magnetic plucking is used to harvest the angular kinetic energy of the host. The nonlinear snap-through mechanism is utilized to improve the vibration displacement and output voltage of the piezoelectric layer over a wide rotation frequency range. Theoretical simulation and experimental results show that the proposed energy harvester can yield a stable average output power ranging between 6.91-48.01 μW over a rotation frequency range of 1-14 Hz across a resistance load of 110 kΩ. Furthermore, dual attraction magnets were employed to overcome the suppression phenomenon at higher frequencies, which yields a broadband and flat frequency response over 6-14 Hz with the output power reaching 42.19-65.44 μW, demonstrating the great potential of the bistable buckled beam for wideband rotation motion energy harvesting.

Design and Control of a Novel Compliant Constant-Force Gripper Based on Buckled Fixed-Guided Beams

This paper presents the design and control of a novel gripper device with a passive type of compliant constant-force mechanism. The function of constant-force output is achieved by using the combination of a positive-stiffness and a negative-stiffness mechanism. The negative stiffness is generated by a bistable buckled fixed-guided beam. Conventionally, when gripping a target-object using a high-stiffness gripper, both the displacement control and force control are required to prevent the damage of the object. The uniqueness of the developed constant-force gripper is that it can eliminate the dependence on force control while keeping the force constant via its mechanical structure. The gripper performance is evaluated by the established analytical model and nonlinear finite-element analysis, and validated through experimental study on a fabricated prototype. To achieve a precise position output of the gripper jaw, a discrete-time variable structure control strategy based on a nonswitching type of reaching law is realized. The effectiveness of the gripper system is verified by conducting experimental studies on grasp-hold-release operations of a micro copper wire.

Low-Frequency, Low-G MEMS Piezoelectric Energy Harvester

This paper reports the design, modeling and fabrication of a novel MEMS device for low-frequency, low-g vibration energy harvesting. The new design is based on bi-stable buckled beam structure. To implement the design at MEMS scale, we further proposed to employ residual stress in micro-fabricated thin films. With an electromechanical lumped model, the multi-layer beam could be designed to achieve bi-stability with desired frequency range and excitation amplitude. A macro-scale prototype has been built and tested to verifies the prediction of the performance enhancement of the bi-stable beam at low frequencies. A MEMS scale prototype has been fabricated and tested to verify the frequency range at low excitation amplitude. The MEMS device shows wide operating frequency range from 50Hz to 150Hz at 0.2g without external proof mass. The same device with external proof mass has lower frequency range (< 10Hz) with boosted deflection amplitude.

Modeling and Experimental Validation of Actuating a Bistable Buckled Beam Via Moment Input

Bistable mechanisms have two stable equilibrium positions separated by a higher energy unstable equilibrium position. They are well suited for microswitches, microrelays, and many other macro- and micro-applications. This paper discusses a bistable buckled beam actuated by a moment input. A theoretical model is developed for predicting the necessary input moment. A novel experimental test setup was created for experimental verification of the model. The results show that the theoretical model is able to predict the maximum necessary input moment within 2.53%. This theoretical model provides a guideline to design bistable compliant mechanisms and actuators. It is also a computational tool to size the dimensions of buckled beams for actuating a specific mechanism.

Analysis of a Compressed Bistable Buckled Beam on a Flexible Support

The bistable snap-through behavior of a compressed beam is modeled and measured experimentally as its supporting surface is bent through positive and negative curvatures. When the supporting angle of the beam exceeds a critical angle, bistability is lost and only one stable state is supported. The critical angle is controlled only by the initial compressive stress in the beam, and we report a nondimensionalized calculation method for this angle. This large-deflection nonlinear model provides design rules for low-power sensors and actuators that can measure and control surface curvature from the micro- to macroscale.

A bistable buckled beam based approach for vibrational energy harvesting

This paper presents a low cost solution for vibrational energy harvesting based on a bistable clamped-clamped polyethylene terephthalate (PET) beam and two piezoelectric transducers. Beam switching (between two stable steady states) is activated by environmental vibrations. The mechanical-to-electrical energy conversion is performed by two piezoelectric transducers laterally installed to experience beam impacts each time the device switches from one stable state to the other one. The main advantage of our approach lies in the wide frequency bandwidth of the device; in turn, this leads to improved efficiency at very low cost.

Bistable buckled beam and force actuation: Experimental validations

This paper presents recent experimental results on the switching of a simply supported buckled beam. Moreover, the present work is focussed on the experimental validation of a switching mechanism of a bistable beam presented in details in Camescasse et al. (2013). An actuating force is applied perpendicularly to the beam axis. Particular attention is paid to the influence of the force position on the beam on the switching scenario. The experimental set-up is described and special care is devoted to the procedure of experimental tests highlighting the main difficulties and how these difficulties have been overcome. Two situations are examined: (i) a beam subject to mid-span actuation and (ii) off-center actuation. The bistable beam responses to the loading are experimentally determined for the buckling force and actuating force as a function of the vertical position of the applied force (displacement control). A series of photos demonstrates the scenarios for both situations and the bifurcation between buckling modes are clearly shown, as well. The influence of the application point of the force on the bifurcation force is experimentally studied which leads to a minimum for the bifurcation actuating force. All the results extracted from experimental tests are compared to those coming from the modeling investigation presented in a previous work (Camescasse et al., 2013) which ascertains the proposed model for a bistable beam.