Bistable Laminates Research Articles

Structural multistability for multi-speed wind energy harvesting from vortex-induced vibrations

Abstract Piezoelectric energy harvesters utilizing vortex-induced vibrations (VIV) have been extensively studied for converting wind energy into usable power for microelectronics. In this work, we explore the use of structural bistability to increase the range of flow speeds over which energy can be harvested without the need for complicated assemblies. We propose a harvester system featuring a piezoelectric transducer bonded to a cantilevered bistable composite laminate, which has two distinct equilibrium shapes at room temperature. To enhance the VIV, we attach a cylindrical bluff body to the free edge of the harvester. The structure’s inherent bistability allows for high power generation at two different flow speeds, contrasting with the single synchronization region typical of linear piezoelectric harvesters. We develop a reduced-order model to predict power output across varying flow speeds and validate these predictions through wind tunnel experiments, showing good agreement. Furthermore, we conduct a parametric study to optimize the model parameters for maximum power output. Our results demonstrate that the bistable harvester can generate up to 4.5 mW of power over a wind speed range of 9.3 m s−1–11.7 m s−1, outperforming the limited speed range of traditional linear VIV-based harvesters. This work underscores the potential to design VIV-based energy harvesters capable of operating efficiently across multiple flow speed ranges using a single structure with its dual stable configurations.

Active vibration control and optimal position of MFC actuator for the bistable laminates with four points simply support

Active vibration control and optimal position of MFC actuator for the bistable laminates with four points simply support

Study on stable configurations and snap through of the rectangular VS bi-stable laminates with curvilinear fiber alignment

With advances in fiber placement technology, variable stiffness bistable laminates (VSBL) composited by curvilinear fiber format become a subject of intense interest for morphing structures due to their lower weight, adjustable stiffness and a richer range of stable configurations compared to straight fiber bistable laminate. Merely conducting research on square laminates is not enough allowing for practical application scenarios. This article investigates the influence of geometrical parameters of VSBL on the stable state configuration and static snap through actuated by MFC systematically. A quadratic variable curvature polynomial is used to fit the transverse displacement according to classical laminate theory. By means of von-Karman geometrical relationship and the Rayleigh-Ritz method, stable configurations of the VS bistable laminate are solved. By comparing with finite element results, the reliability and precision of the current results are verified. It shows that changing fiber orientation leads to significant effects on the steady state configuration and critical bifurcation points. Theoretical analysis of VS bistable laminates containing the smart piezoelectric material MFC is followed by analytical modeling. The voltage threshold required for actuating snap through of two stable states is acquired by smart material layer MFC. The specific reasons for the differences in the configurations of VS bistable laminates are illustrated by analyzing distribution of the stiffness of VSBL in the plane.

Nonlinear effect on stable state and snap-through bistability of square composite laminate

Bistable structures with the elastic instability caused by buckling are confirmed to perform significantly in micro-electromechanical systems, metamaterials, energy harvester, vibration isolation and morphing structures. The target of this paper is to explore the dynamic responses of cross-ply bistable composite laminate, focusing on the nonlinear effect of the single- and double-well vibration. Both theoretical and finite element (FE) methods are employed to simulate the nonlinear vibration and dynamic snap-through of bistable composite laminate under the foundation excitation at the center. In the theoretical model, the governing equations are established via Lagrange's equation based on the first-order shear deformation theory, von Karman nonlinear strain-displacement relation and Rayleigh-Ritz method. The fourth-order Runge-Kutta method is adopted to solve the governing equations, and the numerical results are validated by FE model. Subsequently, the details of the dynamic responses are analyzed to identify the nonlinear effects in the form of bifurcation diagram, phase portrait, time history, Poincare maps and amplitude spectrum. The dynamic responses are examined for a series of excitation parameters in both time and frequency domain. Through fixed frequency and frequency sweep tests, the nonlinear phenomenon of the single- and double-well vibrations are analyzed including superharmonic resonance, stiffness softening, hysteresis phenomenon, various periodic and chaotic vibration. The diverse responses to external inputs contribute significantly to efficiently predicting mechanical behaviors in real-world conditions, thereby offering indispensable theoretical support for structural design applications.

Inverse design of bistable composite laminates with switching tunneling method for global optimization

Bistability enables adaptive designs with tunable deflections for applications including morphing wings, robotic grippers, and consumer products. Composite laminates may be designed to exhibit bistability due to pre-strains that develop during the processing of the polymer matrix, enabling fast reconfiguration between two stable shapes. Unfortunately, designing bistable laminates is challenging because of their highly nonlinear behavior. Here, we propose the Switching Tunneling Method to address this challenge by alternating between gradient-based local minimization and tunneling search phases, with the enhancement of objective expression switching to improve numerical conditioning. Results demonstrate high effectiveness compared to existing optimizers; the Switching Tunneling Method achieves a 99% success rate in finding all energy minima across general composite layups. Additionally, our method facilitates the inverse design of variable pre-strain fields, enabling bioinspired, positive Gaussian curvatures, which are not possible with conventional pre-strain laminates. Validations through both finite element analysis and 3D printed samples confirm the optimal designs.

Pattern reconfigurable antenna with specified main lobe deflection and stable bandwidth by using bistable composite laminates

Pattern reconfiguration of antennas has become a very important measure to improve the signal gain and working bandwidth by manipulating beam direction. Developing rational methods to find the reconfigurable structure is a key problem. In this paper, a collaborative optimization method is proposed to comprehensively consider both the geometric parameters of the bistable substrate and the size of the radiation patch. This method enables the design of a pattern reconfigurable antenna with specified main lobe deflection and stable bandwidth. Specifically, by using a two-step process, the log-periodic dipole antenna (LPDA) is conformally mapped from the planar substrate to the bistable substrate. Further investigation reveals that the main lobe deflection angle and bandwidth stability are influenced by the geometric parameters of the bistable substrate and the size of radiation dipoles, respectively. Thus, these parameters are selected as design variables for solving the proposed collaborative optimization model. The transformation between two stable configurations enables the proposed LPDA to deflect the main lobe of the H-plane pattern by 30° while maintaining consistency in the E-plane patterns. Importantly, the resonant frequencies remain unaffected and the bandwidth does not decrease during the pattern reconfiguration. Notably, the pattern reconfigurable mechanism is rooted in that the transformation between the two stable configurations alters the number and position of the dipoles in the radiation region and their current path, thereby changing the radiation direction of electromagnetic waves. The proposed collaborative optimization method has a potential application for other types of antennas and offers opportunities for various applications in the field of wireless communication.

On maintaining bistability of prestressed laminates after clamping

Bistable composite laminates exhibit a high degree of shape change and stiffness variation between their stable configurations, making them suitable for applications in morphing structures and energy harvesting. However, integration of these laminates into larger systems often imposes different boundary conditions, which can eliminate one of their stable states. Moreover, clamping one or more edges of a rectangular bistable laminate causes a drastic change in its strain energy landscape, indicating a strong interplay between the laminate geometry, boundary conditions, and prestress. In this work, we investigate the effect of clamping on the bistability of rectangular prestressed laminates. An analytical approach is proposed to examine the deflection decay imposed by the boundary condition along the laminate’s length. Different prestress values, laminate dimensions, and material properties are analyzed to establish their effect on the curvature change due to the localized clamp effect. A length criterion is determined to guarantee bistability after clamping the bistable laminate, suggesting the need to utilize complementary techniques to retain the bistable behavior for orthotropic prestressed laminates. Different strategies to counter the clamped edge effect and thereby retain the bistability of these types of laminates are then examined. The proposed analytical model is expanded to consider multi-section composite laminates, showing the role of the symmetric regions in bistability retention. Finally, the results from the model are validated against experiments.

Numerical analysis of an innovative solar collector utilizing bistable composite laminates and macro fiber composite actuators

Innovative designs for solar collectors have attracted substantial academic and industrial interests owing to the high efficiency of solar panels in the recent past. This paper proposes the analysis and numerical design of a novel solar collector model composed of bistable laminates bonded with Macro Fiber Composite (MFC) actuators and solar cells. The bistable cross-ply laminate serves as the steering mechanism in this design by providing multiple stable shapes for the innovative solar collector design. Bistable morphing structures have received growing interest in aerospace structures and wind turbines due to their rapid shape-changing ability in response to changes in operating conditions, and this paper aims to integrate them more into the solar energy sector. The snap-through and snap-back motion of bistable laminates can be controlled by the voltage inputs of MFC actuators. The change of bistable laminate shape holds the solar cell in a position approximately at the latitude angle of the place to capture maximum solar energy. A systematic finite element parametric study has been performed to identify the optimum size and location of MFC actuators to achieve an energy-efficient snap-through and snap-back transition. As a result, a numerical design of a solar collector with six bistable elements has been proposed. In order to check the feasibility of the proposed designs, a numerical study has been performed to evaluate the total energy output and to optimize the solar panel tilt angle. ASHRAE’s solar irradiation model proposed in the literature has been used to identify the optimum solar panel tilt angle for maximum annual solar irradiation. This innovative solar collector model has demonstrated promising results, holds the potential for widespread application across various engineering domains, and paves the way for increased adoption of intelligent structures in everyday life.

Dynamics of bistable composite plates

Nonlinear asymmetric bi-stable composite laminates, characterized by multistable nature and rich dynamics, have seen increased application potential recently. This has necessitated a detailed dynamical analysis of bistable laminates. In this manuscript, the nonlinear behaviour of asymmetric [0n/90n] bistable laminates with free–free boundary conditions is investigated through simulations and experimental observations. A refined 17 degrees of freedom (dofs) analytical model is developed, fusing Raleigh–Ritz with Hamilton’s principle to obtain the governing nonlinear equations of motion. A nonlinear finite element (FE) model is also developed using ABAQUS®. Experiments are conducted by clamping the midpoint of the plate with a shaker and then exciting it. The composite laminate shows many intricate dynamics, such as sub-harmonic and super-harmonic oscillations, intra-well oscillation (periodic and chaotic), and inter-well snap-through (periodic and chaotic snap-through) prominently. The primary focus of this paper is to highlight the potential of bistable laminates by elucidating the existence of large-amplitude vibrations over a broad frequency range under different input and system parameters. Further, it has been observed that attached mass plays a significant role in modifying the response bandwidth for cross-well oscillation for a given excitation frequency and amplitude. Hence fine-tuning of masses can excite different nonlinear dynamic characteristics of the laminate, making it applicable in different engineering fields.

Experimental study and numerical simulation of morphing characteristics of bistable laminates embedded with 3D printed shape memory polymers

Bistable laminates have potential applications in areas such as buffer and soft robotics due to their two stable states and ability to deform through both snap-through and snap-back processes. However, conventional orthotropic bistable laminates with two stable state configurations and snap loads are similar in magnitude. There is a problem that the deformation cannot be easily driven when the laminate stiffness is high. To solve this problem, a clever design is needed to reduce the snap-back load and increase the snap-through load so that the driven deformation can be realized more easily. In this paper, we propose a design method to suppress and control the deformation of bistable laminates by utilizing the shape memory of 3D-printed shape memory polymers (SMP), which enables the laminates to increase the stiffness while reducing the driving force. First, a numerical model of viscoelasticity of the laminate is established to study its deformation characteristics, and the numerical results are compared with experimental results with good agreement. The effect of SMPs on the snap load and principal curvature of bistable laminates is also investigated. Finally, the interlayer interface bonding of the bistable laminates is examined in microscopic perspective. The results demonstrate that 3D printed SMPs can effectively enhance the snap-through load and reduce the snap-back load of bistable laminates, achieving deformation suppression and control while maintaining good interlaminar bonding with carbon fiber composites. This study provides new insights and practical significance for the deformation suppression and active control of bistable structures.

Quantification of the out-of-plane loading fatigue response of bistable CFRP laminates using a machine learning approach

This study proposes data-driven machine learning models to predict the nonlinear load-displacement response in constant amplitude high-cycle fatigue loading of unsymmetric, cross-ply bistable carbon fiber reinforced polymer composites. Four selected ML models are trained on experimental fatigue data with eleven unique frequency, temperature, and boundary conditions combinations. Stiffness and damage index values, which serve as additional evaluation metrics, are calculated using the predicted load data. The models capture the nonlinear load response with acceptable error for in-domain experimental conditions. Model expandability demonstrates the sensitivity of machine learning models to training features but suggests an economical alternative to extensive fatigue experiments.

Large-ratio stiffness switching via harnessing the in-plane buckling and bi-stability of high-load capacity composite laminates

Stiffness tuning is crucial in developing many advanced engineering systems such as morphing aircraft, soft robotics, etc. Achieving a significant stiffness change while maintaining a high load-bearing capacity in compression is a challenging task. This study addressed this challenge by exploiting the in-plane buckling and bistability of asymmetric carbon fiber composite laminates. Due to the inverted curvatures of these laminates at their two stable states, they showed two distinct in-plane compression behaviors—stiff response where the laminate behaved like a thin curved column (with a stiffness coefficient near 68 N mm−1), and compliant response where the laminate acted like a soft non-linear spring (with stiffness near 0.7 N mm−1). As a result, a simple snap-though between these two stable states offered a significant stiffness change, with a high/low stiffness ratio of ≈97. By using extensive finite element simulations, experimentation, and a semi-empirical curved plate buckling model, this study examined the mechanics underpinning the laminate’s 3-step buckling and the influences of asymmetric boundary contacts with friction. Additionally, three strategies to enhance the laminate’s performance—adjusting the aspect ratio, applying lateral loads, and parallel stacking were examined. It also demonstrated cellular structure concepts using these bistable laminates. Remarkably, by simply adding a small lateral in-plane force (e.g., a rubber band), one could substantially increase the stiffness ratio of the composite laminates to ≈200 and load-bearing capacity at the stiff configuration, outperforming the state-of-art variable stiffness methods.

Segmented layered bistable piezoelectric laminates for enhanced energy harvesting from wind‐induced vibration

AbstractIn this study, a segmented layered bistable piezoelectric energy harvester (SBPEH) has been developed and thoroughly investigated for its wind energy harvesting capabilities. The SBPEH's performance was comprehensively evaluated through the creation of a detailed 3D finite element model using Abaqus and XFlow software, and further validated via rigorous wind tunnel experiments. The results of this research demonstrate the SBPEH's remarkable potential for wind energy harvesting. With a wide operational wind speed range, it achieved a maximum measured power output of 5.476 mW, coupled with an outstanding power density of 68.45 mW/cm3, both of which were realized at a wind speed of 13 m/s. It is worth noting that as the wind speed surpasses a specific threshold, the energy harvesting efficiency of the SBPEH experiences a decline, emphasizing the importance of identifying the optimal operational wind speed range for maximizing energy output. These findings offer valuable insights for the enhancement and application of SBPEHs, contributing to the advancement of renewable energy technologies and providing an eco‐friendly solution for power generation.Highlights The study introduces a new segmented layered bistable piezoelectric energy harvester (SBPEH) design for wind energy harvesting, addressing the limitations of traditional harvesters. Performance is evaluated through 3D finite element modeling, ABAQUS, Xflow simulations, and wind tunnel experiments. The SBPEH operates efficiently across a broad wind speed range (6–14 m/s), showcasing optimal output power of 5.476 mW at 13 m/s.

Investigations on the dynamic snap-through of MFC bonded self-resetting bistable laminates

Unsymmetric composite laminates having two stable equilibrium configurations have been studied extensively in the recent past due to their potential applications in morphing structures. Surface bonded Macro Fiber Composites (MFC) actuators have been considered as a viable solution to trigger the snap-through transition in bistable laminates. Although MFC bonded bistable laminates are widely used in morphing applications, they might require considerably high voltage inputs to achieve the required levels of actuation control during the shape transition. As a solution, other possible energy sources can be combined with active MFC patches to reduce the snap-through energy required from the single source of MFC actuation. In this work, we examine the dynamic behavior of bistable composite plates actuated using MFC actuators, where external vibration energy has been used to assist with the MFC-controlled actuation between stable states. A refined semi-analytical model based on the Rayleigh–Ritz formulation has been proposed, where the membrane energy and the bending energy are separately evaluated. Bending components are directly evaluated using the approximated transverse displacement functions, whereas the membrane components are evaluated separately by combining compatibility conditions and equilibrium equations. Results from the proposed semi-analytical framework are compared with a full geometrically nonlinear finite element framework and necessary experimental observations. The results show a significant reduction in the snap-through energy demand on MFC layers where external dynamic excitation assists the snap-through process. Additionally, a parametric study is performed using variable stiffness (VS) fiber orientation parameters, achieving bistable laminate-MFC configurations that lower snap-through requirements through the proposed morphing strategy. Thus, the study offers to aid a multi-efficient snap-through strategy for the morphing of multistable composite structures.

A comprehensive formulation for determining static characteristics of mosaic multi-stable composite laminates under large deformation and large rotation

Multi-stable composite laminates are composite materials that exhibit multi-stable states, making them highly suitable for use in morphing structures. These materials are capable of maintaining each stable state without expending any energy. As a result, they are used extensively in numerous applications and garnered the interest of scholars and aerospace organizations. In the context of practical applications, such as morphing structures, it is insufficient for designers to rely solely on common bi-stable composite laminates that exhibit large deformations and medium rotations to achieve their desired objectives. Consequently, based on the objectives of the design, there are two potential resolutions to address this limitation. A designer may utilize mosaic multi-stable composite laminates to achieve a morphing structure that exhibits high flexibility, significant deformation, and substantial rotation. The utilization of a series connection between a bi-stable composite laminate and a symmetric composite laminate results in the formation of a mosaic bi-stable composite laminate with variable stiffness. Furthermore, the amalgamation of two asymmetric composite laminates with inverted orientations engenders a mosaic tri-stable composite laminate. The present research examines the static characteristics of mosaic bi-stable and tri-stable composite laminates. It also seeks to analyze the factors affecting the behavior of these types of laminates. A geometrically exact model was formulated for this objective. Apart from the geometrically exact model, a widely used and uncomplicated model relying on the conventional Classical Laminated-Plate Theory (CLPT) and Von-Karman nonlinear strains was employed. The proposed models were validated through finite element simulations. The system's static equations were derived using the virtual work principle and the Rayleigh-Ritz method. The present study examines and explores quasi-static snap-through behavior between stable states through the application of concentrated forces. The findings indicate a high level of concurrence between the outcomes derived from the geometrically exact model and the finite element analyses, particularly in composite laminates exhibiting significant deformations and rotations.

Cross-well dynamics for vibration energy harvesting of base-excited antisymmetric bi-stable laminate with a point being fixed

The cross-well dynamic of the bi-stable laminates triggered by ambient vibration is a typical nonlinear dynamic, the larger deformation makes the bi-stable laminates attract much attention in vibration energy harvesting. To obtain the performance of cross-well dynamics and vibration energy harvesting of the bi-stable laminate theoretically, a 4-layer harmonic base-excited antisymmetric cross-ply bi-stable laminates with d31 type Marco fiber composite (MFC) for vibration energy harvesting is proposed. The bi-stable laminate is fixed at a chosen point where a base excitation is applied as displacement excitation. The first order shear deformation laminated plate theory (FSDT), geometric nonlinear, and the energy principle are employed to obtain the governing equation of the system in terms of the polynomial coefficients of configuration functions. Two stable configurations are calculated by the principle of minimum potential energy, which is used as the initial state for the energy harvesting analysis. The stable configurations are predicted, and evaluated by comparing them with ABAQUS. The cross-well nonlinear dynamic behaviors and the performance of energy harvesting are analyzed. The effects of excitation level, excitation frequency, and the position of the fixed point on the cross-well dynamics and energy harvest characteristics of the antisymmetric bi-stable laminates are investigated in-depth, and some new aspects are revealed. It demonstrates that the base displacement harmonic excitation can induce chaotic cross-well vibration in a high-frequency band when the fixed point is far away from the center point, the various cross-well vibration of the system is more likely to occur in the dominate-frequency resonant band.

Analysis and experiments of bi-stable laminate configuration control based on MFC piezoelectric actuation

This paper studies the configuration change control and the snap-through phenomenon of bi-stable laminate with the MFC piezoelectric plate. The kinetic and potential energy expressions of the piezoelectric bi-stable laminate were obtained based on the von-Karman hypothesis. The constitutive equations of the system were given using a six-parameter displacement model, and the potential function of the system was derived using Hamilton’s principle. The configuration changes of the piezoelectric bi-stable laminate under different geometrical conditions were analyzed. The influence of voltage on the bi-stable laminate configuration was studied by applying different driving voltages. The snap-through energy variation of the piezoelectric bi-stable laminate under different geometrical conditions was investigated. In the experimental part, the changes in bi-stable laminate configuration with different geometrical conditions and after attaching the piezoelectric plate were compared. Different driving voltages were applied to measure the difference in piezoelectric bi-stable laminate configuration, and the critical snap-through voltages were recorded. The measured changes in bi-stable laminate configuration and snap-through voltage at different voltages prove the correctness of the theoretical presentation.

Kinetic Shades: Designing a Shape-Morphing Device with Bistable Laminates and Shape Memory Actuators

Kinetic Shades: Designing a Shape-Morphing Device with Bistable Laminates and Shape Memory Actuators

Enhancing the Design Space of Bistable Laminates by Tailoring the Attachment Boundary Conditions

Abstract Bistable and multistable laminates are structural elements with more than one stable equilibrium configuration. The bistability makes them very interesting for the design of compliant mechanisms. However, these laminates are extremely sensitive to boundary conditions and attachment methods. It has been shown prior in the literature that restrictive boundary conditions can lead to the loss of bistability or unwanted deformation modes. This article develops attachment concepts that leverage the structural behavior changes caused by boundary conditions to expand the design space of bistable elements for structural applications. A systematic means of using the boundary conditions to improve the stability margins and load introduction of bistable tape springs is demonstrated. The stability margins and the achievable angles have been quantified using an analytical model previously developed by Guest and Pellegrino. Subsequently, high-fidelity finite element (FE) simulations are done in abaqus™ to determine the limits of the proposed method in terms of localization effects. Based on the analytical model and simulation outcomes, layup, size, and attachment points are determined, and two prototypes are fabricated, illustrating the effectiveness of the proposed method in expanding the design space of traditional bistable tape springs.

Dynamic response of piezoelectrically actuated bistable cross-ply laminates under oscillating impulse voltages

Multistable composite laminates are ideal candidates for morphing applications due to their ability to switch between multiple stable states with proper actuation mechanisms. Surface-bonded macro fiber composite (MFC) actuators to trigger snap-through between one stable shape to another by applying external voltages have attracted considerable attention recently. In this work, dynamic snap-through of bistable unsymmetric cross-ply laminate using MFC actuators under oscillating impulse voltages has been investigated. Both unimorph and bimorph laminate-MFC configurations are considered for the analysis. The stable equilibrium configurations of the MFC-actuated bistable laminate, considering the effects of MFC bondage, are discussed using the proposed finite element (FE) framework. Under the action of oscillating impulse voltages, the single-well and cross-well oscillations of the active bistable plate are analyzed in detail through time responses and phase portraits. The FE results show the advantage of actuating MFC layers through the oscillating impulse voltages as it leads to a reduction in the maximum snap-through voltage requirements.