Bistable Composite 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.

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.

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.

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.

Characterization and modeling of bistable laminates for kinetic shading screens

There is an critical need in kinetic envelope design to propose sustainable solutions that can adjust to changing outdoor conditions. Bistable composite laminates are compliant systems appealing for kinetic building envelopes because they present two stable equilibrium states and transition between them with little input energy. This study characterizes the behavior of bistable laminates for kinetic screens by developing an FEA model and conducting experimental testing to validate the model and compare both data sets. The FEA model predicts the laminates’ cured states, snap-through movement, and required actuation force. The FEA model can accurately predict the cured states of the laminates. Regarding the movement of the laminate and actuation force, the simulation results mostly correlate quantitatively with the experimental data and differ qualitatively. However, the FEA model can accurately predict the critical force required to snap through the laminates, which ranges between 2.5 and 4 N.

Fatigue performance evaluation of bistable composites at different combinations of loading and environmental conditions

Bistable composite laminates have large-scale applications in morphing and energy-harvesting structures, but their fatigue performance remains largely unexplored. This study investigates the stiffness and damage progression and evaluates bistable performance to develop protocols for long-term applications. We analyze the effects of displacement-controlled fully reversible high cycle fatigue-loading on stiffness, damage, curvature, and snap-through load in the out-of-plane loading direction at eight different combinations of parameters with frequency from 1 to 10 Hz, two boundary conditions, and temperature from 22°C to 150°C up to 3 to 10 million cycles. Stiffness and damage evolution analysis demonstrate the first two stages in out-of-plane fatigue loading. The study proposes a damage definition in terms of load adapting with two fatigue damage models: (1) Shiri Model and (2) Wu Model, while both models exhibit reasonable accuracy in predicting damage for the first two stages despite deviating at the final cycle due to assuming this cycle as the final failure cycle. Of the two models, the Shiri model provided a smaller range of model parameter values, 0.22 and 0.43, for parameters p and q, respectively, which reflects adjustability to different test conditions by maintaining a moderate range. Specimens encountered no final failure by fiber breakage and did not lose bistability for any combination. Curvature and snap-through load measurements have not substantially changed due to fatigue loading. These findings confirm application protocols with a broad range of parameters for which the laminates can operate without significant fatigue damage and maintain their bistable performance for an infinite lifetime.

A bistable pure carbon fiber composite symmetric laminate and its preparation, modeling, and experimental verification

A novel bistable symmetric laminate of pure carbon fiber composite is presented in this article. First, an analytical model was established based on the results of finite element analysis (FEA) using the segmented continuous displacement function. Then, the bistable pure carbon fiber composite symmetric laminate was prepared in the experiment. Both the analytical and FEA results are in considerable agreement with the experimental results. Finally, the effects of various laminate lengths, widths, ratios, thicknesses and materials were investigated. The results showed that the bistable pure carbon fiber composite symmetric laminate has larger deformation and lower snap-through load.

Explainable Artificial Intelligence to Investigate the Contribution of Design Variables to the Static Characteristics of Bistable Composite Laminates.

Material properties, geometrical dimensions, and environmental conditions can greatly influence the characteristics of bistable composite laminates. In the current work, to understand how each input feature contributes to the curvatures of the stable equilibrium shapes of bistable laminates and the snap-through force to change these configurations, the correlation between these inputs and outputs is studied using a novel explainable artificial intelligence (XAI) approach called SHapley Additive exPlanations (SHAP). SHAP is employed to explain the contribution and importance of the features influencing the curvatures and the snap-through force since XAI models change the data into a form that is more convenient for users to understand and interpret. The principle of minimum energy and the Rayleigh-Ritz method is applied to obtain the responses of the bistable laminates used as the input datasets in SHAP. SHAP effectively evaluates the importance of the input variables to the parameters. The results show that the transverse thermal expansion coefficient and moisture variation have the most impact on the model's output for the transverse curvatures and snap-through force. The eXtreme Gradient Boosting (XGBoost) and Finite Element (FM) methods are also employed to identify the feature importance and validate the theoretical approach, respectively.

Integrated a nonlinear energy sink and a piezoelectric energy harvester using simply-supported bi-stable piezoelectric composite laminate

A nonlinear device is presented for simultaneous vibration absorption and energy harvesting. This device is composed of a nonlinear energy sink and a piezoelectric energy harvester (NES-EH), and its core component is the simply-supported bi-stable piezoelectric composite laminate (BPCL). Its outstanding advantages are light weight, simple and reliable structure. The theoretical model is developed to model a harmonically excited linear oscillator coupled with NES-EH. The Runge–Kutta method and the harmonic balance method (HBM) are used to solve the theoretical model numerically and analytically. The vibration suppression efficiency is utilized to quantify the vibration absorption performance, while the energy harvesting performance is assessed by bandwidth for energy harvesting and maximum voltage within the bandwidth. The effects of the excitation amplitude, the concentrated mass of NES-EH, the length and width of BPCL, and the load resistance are considered on the performances of NES-EH. The vibration absorption and energy harvesting performances of NES-EH can be improved by adjusting these parameters. In addition, the proposed NES-EH can achieve the goal of higher power density and normalized power density under low-amplitude excitation and simultaneously have a good vibration absorption effect. Finally, approximate analytical solutions are obtained by using HBM to exhibit various bifurcations and singularities.

Bistable characteristics of unsymmetric cross-ply composite laminates considering different boundary shapes

The aim of this paper is to study the bistable characteristics of unsymmetric cross-ply composite laminates induced by thermal stress during the curing process when considering different boundary shapes. The changes in geometry for five types of planform shapes, have been focused, which are named rectangular planform (RP), elliptical planform (EP), trapezoidal planform (TP), diamond planform (DP) and cruciform planform (CP) respectively. The parameters that characterize the bistable performance of the laminates, including the principal curvature and snap load, were measured. The principal curvatures in different stable configurations were determined with analytical, numerical, and experimental methods, and the load-displacement curves in the snapping process were successfully obtained. Moreover, the boundary effect caused by the difference in planform shapes, which cause the local curvature of the bistable composite laminate to change, were also discussed. Predictions from an analytical shell model are verified through comparisons with nonlinear finite element simulations and experimental test results.

The dynamic regimes and the energy harvesting of the energy harvester based on the bistable piezoelectric composite laminate

The dynamic regimes and the energy harvesting of the bistable energy harvester based on the bistable piezoelectric composite laminate are elaborated here. To identify the all-around dynamic regimes and assess the bistable energy harvesting performance, the forward frequency sweep, the reverse frequency sweep and the resistance sweep are conducted. The peak-to-peak frequency–amplitude response curves on the displacement and the voltage output are graphically presented. The single-well vibration, the limit cycle oscillations, the intermittency between the limit cycle oscillations and the chaotic snapthrough, the intermittency between the multiple periods snapthrough and the chaotic snapthrough, the multiple periods snapthrough and the chaotic snapthrough are elaborated by the Time history diagram, the Phase diagram and the Poincare map. The dynamic regimes are graphically presented delivering the stability zone for the dynamic responses and the optimal region for the energy harvesting. The RMS power output and the Max voltage output are checked to be the value judgements. Due to the softening nonlinear effect and the hysteresis, the conspicuous biases between the forward and reverse frequency sweeps are found to exist illustrating that the limit cycle oscillations expand the bandwidth of the double-well regimes during the reverse frequency sweep. From the perspective of the energy harvesting capacity, the limit cycle oscillations are demonstrated to be optimal, the double-well responses generally outperform the single-well responses concerning the off-resonance and the single-well responses concerning the primary resonance around the reduced modal frequency may outperform the double-well responses except the limit cycle oscillations. The load resistance is crucial to the power generation performance and needs optimizing with the change of the external excitation. The load resistance, the external excitation amplitude and frequency are interrelated and can be optimized simultaneously for the maximum power generation efficiency.

A bi-stable device for simultaneous vibration absorption and energy harvesting using bi-stable piezoelectric composite laminate

A bi-stable device is presented for simultaneous vibration absorption and energy harvesting by introducing the piezoelectric element into the bi-stable nonlinear energy sink (BNES), which is called the bi-stable piezoelectric absorber (BPZA). BPZA only consists of the cantilever bi-stable piezoelectric composite laminate (BPCL) and tip masses. This BPZA is a lightweight, simple and reliable structure since it does not need any external devices to maintain bistability. A finite element model (FEM) and an equivalent theoretical model are developed to model a harmonically excited linear oscillator coupled with BPZA. The Runge-Kutta method is used to solve the theoretical model numerically. The effects of the excitation amplitude, the tip mass of BPZA and the load resistance are considered on the vibration suppression efficiency and energy harvesting of BPZA. The results show adjusting these parameters can improve the vibration suppression efficiency and energy harvesting of BPZA. In addition, the experimental prototype is prepared and verifies the rightness of the finite element model and theoretical model. The BPZA achieves the goal of higher power density at lower acceleration and simultaneously has a good vibration absorption effect. Maximum power of 15.8mW is generated at an excitation frequency of 22 Hz and acceleration of 0.5 g.

Effect of snap-through force location on morphing of bistable variable stiffness laminates

Unsymmetric composite laminates exhibit two or more stable states due to the presence of residual thermal stresses induced during the curing process. The paper aims to exploit the possibility of assessing the morphing behaviour of bistable composite laminates using semi-analytical and numerical models. A Rayleigh-Ritz based semi-analytical model is used to investigate the variable stiffness (VS) bistable laminates generated using curvilinear fibre alignments. The obtained results are verified using a fully non-linear numerical model developed in a commercially available finite element package. In order to identify the influence of loading location on the snap-through behaviour, a parametric study is proposed in the present research. Snap-through is achieved through transverse point loads. The novelty of this work resides on the investigation of load application location on the snap-through action where the transverse load is applied at various locations on the lamina surface. Earlier research on the morphing of bistable square composites is mainly on the application of concentrated load at the centre of the laminate geometry, which is considered as an ideal location for snap-through action. The designer may also have to choose other locations for the application of snap-through loads since the lamina centre may not be appropriate always in structural applications. Four different loading locations are selected for the present analysis, and snap-through loads are calculated to check the effect of loading location. Parametric studies are performed using the proposed semi-analytical and numerical models to investigate the effect of selected loading point positions on the snap-through process. The analysis is extended to a selected VS laminate family to understand the influence of loading point positions on the curvilinear fibre alignments.

Wind-induced vibration behavior of bistable hybrid symmetric laminate

Bistable composite laminates have the potential advantage in the fields of wind energy harvesting and deformable wings, which involve many fluid–structure interaction issues. This paper presents the fluid–structure interaction analysis of a cantilevered bistable hybrid symmetrical laminate (BHSL) in the uniform wind. In this work, a finite element model based on the Lattice Boltzmann Method (LBM) is used to analyze the wind-induced response of the BHSL and its variations with respect to wind speed and laminate length. Then, the wind-induced vibration behavior of BHSL is verified by wind tunnel tests. The finite element analysis (FEA) results are in good agreement with the experimental results. The results show that as the wind speed increases, the BHSL transitions from a single-well vibration response to a cross-well vibration response. The wind-induced vibration analysis of BHSL will provide analytical methods for its application in deformable wings and energy harvesting for wind-induced vibration.

Developing Equations for Free Vibration Parameters of Bistable Composite Plates Using Multi-Objective Genetic Programming.

For the last three decades, bistable composite laminates have gained publicity because of their outstanding features, including having two stable shapes and the ability to change these states. A common challenge regarding the analysis of these structures is the high computational cost of existing analytical methods to estimate their natural frequencies. In the current paper, a new methodology combining the Finite Element Method (FEM) and Multi-Objective Genetic Programming (MOGP) is proposed for the analysis of bistable composite structures, leading to some analytical relations derived to obtain the modal parameters of the shells. To achieve this aim, the data extracted from FEM, consisting of the ratio of the length to width (a/b) and the thickness (t) of the laminate, is split into Train and Validation, and Test, subsets. The former is used in MOGP, and four formulas are proposed for the prediction of the free vibration parameters of bistable laminates. The formulas are checked against the Test subset, and the statistical indices are calculated. An excellent performance is observed for all GP formulas, which indicates the reliability and accuracy of the predictions of these models. Parametric studies and sensitivity analyses are conducted to interpret the trend of input parameters in the GP models and the level of sensitivity of each natural frequency formula to the input parameters. These explicit mathematical expressions can be extended to the other bistable laminates to obtain their natural frequencies on the basis of their geometrical dimensions. The results are validated against the experimental data and verified against FEM outcomes.

Elastic Guided Waves in Bistable Composite Structures - Experimental and Numerical Investigation

Background: Bistable composite laminates are emerging as smart structures in automotive and aerospace applications. However, the behavior of the wave propagation within such laminates has not been investigated, which hinders their implementation in Structural Health Monitoring (SHM) and Non-Destructive Evaluation (NDE). Objective: As a result, this manuscript examines the propagation behavior of guided waves in bistable composite structures. By understanding the effect of pre-stressing in bistable composite laminates on the characteristics of propagating waves, such as velocity and amplitude, a more knowledgeable decision about their applications in flaw detection and assessment can be made. Methods: The fundamental symmetric (S0) and anti-symmetric (A0) Lamb wave modes were investigated during propagation in two bistable composite laminates, [0/90]T and [02/902]T, and were assessed experimentally and numerically using ABAQUS. For the tested frequencies, which ranged from 60 kHz to 250 kHz, the behavior of the propagating wave was evaluated for both stable configurations and across two different actuators that were lined up with the fiber directions. Signal processing techniques were thus extensively used to enhance the measured signals and identify both the group velocities and the amplitudes’ trend of the S0 and A0 wave modes. Results: Our results showed that there is a minimal variation (typically below 1%) in the amplitude and velocity of the A0 and S0 modes when the composite plates switch between the first stable configuration and the second stable configuration in both composite plates. These results were numerically validated by replicating the bi-stability of the composites. The numerical data were in relatively close agreement (10% average error) with the experimental values and trends. Furthermore, the bistable effect was examined in detail relative to a reference numerical flat (monostable) plate. Although the bistable effect induced a notable amount of internal residual stress, this did not significantly impact the propagating wave modes, with a maximum difference of about 2% when comparing wave velocities. Conclusions: The effect on the wave propagation behavior along different directions of both stable configurations was shown to be minimal. These results, which were validated numerically, clear the ambiguity on the usage of these laminates in experimental health monitoring.

Morphing of bistable variable stiffness composites using distributed MFC actuators

The use of piezoelectrically controlled bistable composite laminates for morphing applications has received increased attention in recent years. So far, most existing investigations have explored the possibility to trigger snap-through using large-sized piezoelectric Macro Fibre Composite (MFC) actuators bonded at the centre of the bistable laminate. However, bonding large-sized MFCs at the centre of the plate leads to flattening of the midsection of the laminate, which can result in the loss of bistability. This study presents an alternative approach of bonding distributed smaller MFCs over the entire surface of the laminate and investigate the resulting stable shapes and the change in snap-through voltages. Self-resetting piezoelectrically controlled active laminates where the MFC patches are distributed over the laminate surface have been investigated. A semi-analytical model using the Rayleigh–Ritz technique is developed to account for the distributed actuation system. Results from the proposed semi-analytical framework are verified using a corresponding finite element model. The bistable shapes, as well as the snap-through and snap-back voltages, are calculated for different distributed MFC configurations and are compared with a single MFC laminate system. Snap-through voltage predictions from the proposed semi-analytical formulation and the finite element model are compared with the experimental results for a single MFC patch available from the literature. Further, the possibility to tailor the snap-through voltages of the proposed laminate-MFC configuration is explored by replacing conventional cross-ply laminates with variable stiffness (VS) laminates generated from curvilinear fibre alignments. A finite element parametric study is performed by tailoring the VS fibre orientation parameters to achieve a bistable laminate-MFC configuration with lower snap-through requirements where the designed laminate is actuated with distributed MFC patches.