Bifurcation, which alters the number and stability of equilibria in multistable systems, is the primary mechanism governing the formation of elastic sequential snap-through instabilities. However, to date, there is no general understanding of the multistable energy landscape organized by bifurcations underlying snap-through. Here, we conduct a theoretical, numerical, and experimental analysis of serial bistable planar curved beams widely proposed in the recent literature, developing numerical algorithms and experimental schemes to explore the bifurcation structures within the energy landscape. Such systems provide sufficient physical transparency, owing to their low dimension and clear interaction, making them ideal for the analysis of bifurcation structures. Two types of elastic sequential snap-through instability are discovered: competition-induced phase transitions, triggered by limit forces (switching fields) between units, and unit phase transitions, triggered by the equivalent stiffness of system variables within each unit. In our method, we propose a general tunable snap-through path design strategy for use in multistable systems, which can be extended to broader systems with interacting units. Importantly, by tuning stiffness properties and the limit force perturbations, custom-designed saddle-node bifurcation pairs and traverse-stable paths can be achieved, providing universal design rules for elastic sequential transitions.

Multistable mechanical systems can store and release elastic energy through snap-through instabilities, but controlling transition pathways between stable states remains challenging when multiple routes are accessible. Here, we introduce a two-mass von Mises truss as a general model for studying pathway selection governed by coupled saddle-node bifurcations. The system consists of two coupled snap-through units with geometric imperfections, giving rise to four stable configurations: a fully inverted state, a fully natural state, and two intermediate mixed states. We show that the coupling stiffness reorganizes the quasi-static bifurcation structure and selects among three transition pathways under release: sequential snapping through one mixed state, direct cooperative snapping, or sequential snapping through the other mixed state. Using pseudo-arclength continuation, we track the relevant saddle-node bifurcations and identify the parameter regimes associated with each quasi-static pathway. We then demonstrate that dynamic bifurcation delay provides an additional rate-dependent mechanism for pathway selection. Even when the quasi-static bifurcation structure favours a unique sequential pathway, finite-rate loading delays snap-through beyond the corresponding static saddle-node points and can reorder the snapping sequence of the two units. A local reduction of the coupled dynamics near each saddle-node yields normal forms with coupling-dependent critical points and coefficients. The resulting theory identifies distinct rate-dependent delay laws in the inertia-dominated and overdamped regimes and predicts the critical rate at which the snapping order reverses. These results establish a general mechanics framework for tuning transition pathways in multistable systems through elastic coupling and loading-rate control.

Geometrical design endows the curved beam with asymmetric bistability without prestress, contributing to its widespread applications in integrated forming and microscale fabrication. However, the gravity bias inherent in these applications is rarely considered, undermining the accurate prediction of its real-world dynamics. To address this, a gravity-biased nonlinear dynamic model is established via Hamilton's principle and reduced to a Duffing-type equation with a constant term using Galerkin's method. Numerical simulations show that both the interwell oscillations and the contained vacillating behavior manifest as V-shaped regions in the excitation amplitude-frequency parameter space. Bifurcation analysis reveals that the left and right boundaries of the vacillating region correspond to saddle-node and period-doubling bifurcations, respectively, both of which can be theoretically predicted. Furthermore, gravity bias is shown to deepen the lower potential well. For an upward-curved beam, it enlarges the excitation range for interwell motion when initiated from the upper equilibrium, while narrowing the range when starting from the lower one. The influence of key geometric parameters is also systematically examined. Base excitation experiments were conducted to equivalently simulate distributed force excitation, and the results validate the theoretical predictions. This work elucidates the effects of practical environmental conditions and structural parameters on the nonlinear dynamics of curved beams, thereby providing a foundation for the design of mechanical metamaterials and related engineered systems.

This review comprehensively synthesizes the progress concerning the aerodynamic and aeroelastic characteristics of morphing aircraft over the past years (circa 2010-2026). The morphing strategies are categorized into three primary dimensions based on established classifications: chordwise morphing (primarily camber morphing), spanwise morphing (primarily spanwise bending), and planform morphing (including sweep and span morphing). For each morphing strategy, the investigations are systematically reviewed, detailing advances in steady and unsteady aerodynamics, aeroelastic modeling and characteristics, and the application of active control strategies (aeroelastic and maneuver control). Distinct research priorities exist for different morphing strategies: chordwise camber morphing focuses primarily on aerodynamics, while spanwise bending centers on aeroelastic modeling and characteristics. Moreover, given the potential application in configuration adjustments across different flight phases, research on sweep and span morphing predominantly focuses on steady and quasi-steady states. The review also summarizes the current methodologies employed in aerodynamic and aeroelastic analysis and highlights the primary approaches for incorporating aerodynamic (primarily computational fluid dynamics) and structural nonlinearities, as well as their interaction frameworks, such as coupling with computational structural dynamics. The implementation of morphing in control systems is also reviewed, where a notable trend is the integration of control law modules (primarily feedforward and feedback control) into fluid–structure interaction frameworks. As a conclusion, the gap between model and practical application for morphing aircraft still exist. The challenges of detailed modelling for actuation system and time-varying aerodynamics should be paid more attention.

A morphing skin must withstand local aerodynamic loads while remaining flexible enough to accommodate the shape changes of the morphing aircraft. The conflicting requirements can be satisfied by tuning the mechanical properties of the variable stiffness composites. In the present study, the variable stiffness composite is investigated by varying the lamina angles through 3D printing of curvilinear continuous fibre. At first, the design requirements and application scenario are introduced. The fabrication method is introduced and tensile tests are also performed to obtain the mechanical properties of the printed composite lamina. Then, the numerical model is established to explore the mechanical properties of the variable stiffness composite. Optimisation is carried out to balance the different mechanical properties. Finally, a composite sample is manufactured, which is tested to validate the proposed concept. The results demonstrate that the variable stiffness composite exhibits significant improvements in mechanical properties compared with the straight fibre composite.

Asymmetric cross-ply laminates exhibit two stable configurations due to thermal residual stresses developed during or after curing and cooling process, which may cause them to bend in both directions. Bistable laminates, such as asymmetric cross-ply laminates, exhibit excellent response speed and load-bearing capacity, and strong nonlinear and negative stiffness characteristics during deformation. These characteristics make bistable laminates highly promising for wide applications in morphing wings, soft actuators, energy harvesting and electronic devices. Especially in the aerospace field, morphing wings composed of bistable laminates can improve flight performance, enhance control, and reduce drag and flutter. To overcome the shortcomings of traditional discrete rigid deformation structures and promote the development of adaptive structures to lightweight, self-driven and high-performance systems, this paper integrates Macro Fiber Composite (MFC) into bistable laminates to replace the traditional exciter for actuation. An analytical model is derived using Hamilton's principle and the Rayleigh-Ritz method, by comparing the calculation results of commonly used fourth-order and sixth-order dynamic analytical models with ABAQUS finite element shell models to determine systematic parameter and stable configurations. Summarizing the advantages of the existing dynamic actuation, this paper proposes resonant actuation which can change the structure to ensure that the inertia forces and stiffness forces cancel each other over the desired actuation period. Based on the strong nonlinear characteristics of bistable laminates, the method for determining the critical actuation load is systematically summarized for the first time. In order to find bistable laminates with low energy actuation and large deformation, taking the size of the composite laminates as a variable to establish a global mathematical model of critical actuation load by Response Surface Methodology (RSM). Taking the actuation voltage required for one unit deflection as the objective function, the non-dominated sorting genetic algorithm-II (NSGA-II) is used to find the Pareto front, determining the best operating specimens for experimental verification. This approach lays a theoretical foundation for exploring low energy consumption paths and global optimization of MFC actuation, paving the way for the large-scale application of morphing wings.

This data article presents modal test data for 30 specimens: 11 uniform and 20 stepped cantilever plates fabricated from FDM-printed PLA and CNC-machined aluminium. The dataset includes modal frequencies and mode shapes measured by scanning laser Doppler vibrometry (SLDV) using chirp excitation (3200 FFT lines). Numerical modal data are provided from finite element models (ABAQUS for uniform plates; Nastran for stepped plates) using beam, shell, solid, beam-beam, beam-plate coupled, and plate-plate formulations. Material parameters are obtained from tensile tests on 21 PLA specimens with seven print orientations to characterise anisotropy. The reusable data comprise raw modal spectra, material stress-strain curves, manufacturing tolerance measurements, FEM input files (inp and bdf), CAD models (stp), and modal animations. This data article supports the companion research article "Comparative modal analysis of beam-plate coupled models for isotropic active camber morphing wings'' and provides a standalone benchmark for validating structural models of rigid-flexible coupled morphing wings.

For structures with rigid-flexible coupling, such as active camber morphing wings, traditional beam and plate models for conventional wings have some limitations, especially to capture both chord-wise flexibility and torsional effects at the same time accurately and efficiently. This paper aims to address this gap and improve the prediction of natural frequencies and vibration modes for such morphing wing structures. The natural frequencies and vibration modes of three isotropic cantilever beams models, i.e., varying aspect ratios (AR), stepped cantilever beams with different ARs and with different morphing segment ratio, are experimentally measured by Scanning Laser Doppler vibrometry (SLDV), and compared with finite element (FEM) model results. For conventional wings, the plate model is more accurate for small AR wings, while the beam model performs better for large AR wing. However, in camber morphing wings with varying geometries, using the beam model for the stiff sections and the plate model for the flexible sections can achieve the highest accuracy and efficiency. The reason is that combined beam-plate model effectively captures the chordwise bending of the flexible trailing edge and the spanwise bending and torsion of the rigid leading edge. The results provide a theoretical foundation for simplified equivalent models of rigid-flexible coupled structures, especially for active camber morphing wings.

As researchers continue to develop morphing aerospace structures capable of changing shape in real time to adapt to varying operating conditions, minimising the actuation effort required for shape change remains a persistent challenge. Excessive actuation mass, structural complexity, and energy consumption may offset the aerodynamic performance benefits provided by morphing capability. One promising approach to tackle these problems is to use dynamic response to actuate the structures at resonance. For example, actuating bending dominated morphing structures with integrated piezoelectric materials near their resonance frequency can produce significant displacements with reduced energy requirements. However, in this case, the actuation frequency is limited to the resonance frequency, as determined by the mass, stiffness, and damping of the structure within its operating environment, which may constrain the application scenarios. If instead, a stiffness tuning mechanism is integrated into the system, then resonance across a broader range of actuation frequencies would be possible by actively tuning the system stiffness. In the current study, a mechanism for achieving tunable stiffness in the context of a bending dominated morphing structure is first proposed. The mechanism can increase or reduce the structure stiffness, which can eventually change the resonance frequency. A theoretical analysis and finite element simulation are then performed to investigate the structural properties of the mechanism. Based on the specific stiffness of a particular camber morphing concept, the stiffness tuning mechanism is then optimised to expand the range of obtainable stiffnesses. At last, an experimental demonstrator is built to validate the mechanism by measuring the trailing edge displacement when the resonance actuation is applied with varying actuation frequencies. The concept is validated on a morphing trailing edge mechanism, illustrating its practical potential in aerospace structures requiring frequency-adaptive actuation.

Bistable composite laminates, capable of maintaining two stable configurations without continuous energy input, are promising candidates for morphing aerospace structures. This study investigates the nonlinear dynamic behavior of cantilevered bistable composite plates and proposes a resonance-based actuation strategy for efficient configuration switching. A nonlinear dynamic model is developed based on Hamilton's principle and the Rayleigh-Ritz method to accurately model nonlinear dynamic behavior of bistable plates. The dynamic characteristics under varying excitation amplitudes are analyzed through bifurcation diagrams, time histories, phase portraits, and Poincare maps, revealing the evolution from periodic oscillations to period-doubling bifurcations, chaotic motion, and eventually snap-through. As the excitation frequency approaches the modal frequency, the vibration amplitude increases significantly. When the excitation amplitude exceeds a critical threshold, snap-through occurs, accompanied by the structure switching from one stable state to another. The theoretical predictions show good agreement with the experimental observations. The proposed resonance-based strategy enables rapid and energy efficient configuration switching, providing practical insights for morphing structure design.

With higher aspect ratios and the trend toward compliant designs in morphing aircraft, such structures are prone to undesired structural responses under fuselage vibration and aerodynamic loading. To address this issue, this paper proposes a preload-adjustable compliant torsional quasi-zero-stiffness (CT-QZS) isolator for low-frequency vibration isolation of flexible beam structures through boundary modification. The CT-QZS isolator integrates a negative-stiffness (NS) component composed of rotated bistable buckled beams and a positive-stiffness (PS) component composed of compliant curved beams. A tunable sliding groove on the rigid outer ring of the PS component allows continuous preload adjustment by changing the relative angle between the PS and NS components without altering the quasi-zero-stiffness (QZS) range. The torque–angle characteristic of the PS component is derived using Euler beam theory and the unit-load method and validated through quasi-static experiments. The threshold condition and parametric tuning rule of the negative stiffness are investigated through bifurcation analysis and parametric finite element simulations. Two CT-QZS isolators obtained from two different design strategies are integrated as non-invasive rotational boundaries at the root of a PLA cantilever beam. Experimental results demonstrate that the proposed preload-adjustable QZS isolators significantly reduce the first natural frequency and the vibration isolation onset frequency, achieving high static stiffness and low dynamic stiffness simultaneously compared to both the baseline fixed support and various linear isolators. The design offers an effective solution for low-frequency vibration isolation of flexible aerospace structures, such as high-aspect-ratio wings, morphing wings, and deployable space mechanisms.

This paper presents a multistable morphing skin structure to achieve low in-plane stiffness, high out-of-plane stiffness, and high strain capacity. It is based on bistable preshaped curved beams, which enable large deformations through stable state transitions rather than linear elastic deformation. The in-plane mechanical properties are analyzed using large deformation beam theory and potential energy landscape approaches. The mechanical response of the theoretical model is in good agreement with both numerical and experimental results. The out-of-plane mechanical property is studied using standard three-point bending tests, which show that the hybrid array form can significantly enhance out-of-plane stiffness. The multistable morphing skin structure offers advantages in reducing actuation energy consumption and overcoming parasitic resistance in flexible structures.

The stress distribution within threaded connections exhibits significant complexity attributable to the intricate interfacial friction between mating surfaces, which critically influences the coupled relationship among tightening torque, rotational angle, and axial preload. This study establishes a comprehensive assembly analytical framework incorporating three critical factors: thread contact deformation, screw body distortion, and frictional distribution evolution during and after assembly processes. Through this model, three distinct deformation patterns and corresponding stress distribution characteristics in bolted joints have been systematically identified. Subsequent numerical simulations quantitatively reveal the generation mechanisms of these stress patterns under varying operational conditions. Particularly, parametric analysis demonstrates that reduced stiffness of clamped components amplifies both rotational displacement and axial deformation of fasteners. The proposed methodology further elucidates the mechanism underlying post-assembly preload relaxation phenomena. Experimental validation through quasi-static testing confirms measurement consistency across torque-preload-angle parameters, with theoretical predictions showing excellent consistency with experimental data. This analytical advancement enhances fundamental understanding of bolted joint mechanics while providing theoretical guidance for engineering applications in precision assembly and structural safety assessment.

Constrained by fixed frame dimensions, conventional drones usually demonstrate insufficient capabilities to accommodate complex environments. However, the reconfigurable drone can address this limitation through its deformable frame equipped with actuators or passive interaction mechanisms. Nevertheless, these additional components may introduce an excessive weight burden, which conflicts with the lightweight objective in aircraft design. In this work, we propose a novel reconfigurable quadrotor inspired by the swimming morphology of jellyfish, with only one actuator placed at the centre of the frame to achieve significant morphological reconfiguration. In the design of the morphing mechanism, three telescopic sleeves are driven by the actuator, enabling arms’ rotation to achieve a maximum projected area reduction of 55%. The nested design of sleeves ensures a sufficient morphing range while maintaining structural compactness in the fully deployed mode. Furthermore, key structural dimensions are optimized, reducing the central motor load by up to 65% across configurations. After deriving parameter variations during morphing, Proportion–Integration–Differentiation (PID) controllers are implemented and flight simulations are conducted in MATLAB. Results confirm the drone’s sustained controllability during and after reconfiguration, with an “8”-shaped trajectory tracking root mean square error (RMSE) of 0.109 m and successful traversal through long narrow slits, reducing mission duration under certain conditions.

Morphing wings can improve the aerodynamic performance of aircraft and expand their flight envelope. Elastic deformation of the morphing structure can enable continuous and smooth shape changes of the morphing aircraft, which is important in morphing technologies. However, airframe structures need to resist aerodynamic loads, and elastic deformation consumes a significant amount of energy during the morphing process, which increases the weight and size of the actuation system, undermining the morphing benefits. To address this problem, an actuation system based on the energy-balancing principle is proposed to reduce the energy requirement of the morphing wing, thereby reducing its weight and size. The energy-balancing principle is achieved using the elastic strain energy of structural deformation during morphing. Because the structural deformation corresponding to morphing is elastic, the strain energy can be recycled, which reduces energy requirements. The recovery and utilization of the elastic strain energy can be achieved by integrating the energy storage elements in the actuation mechanism. Theoretically, if friction is not considered, the actuation energy required to deform the structure can be provided by the energy storage elements without the need for any external energy. This will result in the overall system achieving the energy-balancing state and significantly reduce the energy consumption. In addition, from the perspective of stiffness, the energy-balancing state suggests a quasi-zero overall stiffness of the actuation system, and a negative-stiffness mechanism associated with the structural stiffness is required to create a quasi-zero overall stiffness. In the current study, a negative-stiffness mechanism based on the spiral pulley mechanism was first designed. The stiffness provided by the spiral pulley mechanism can balance the structural stiffness required for structural deformation, which creates a quasi-zero-stiffness system and reduces the actuation force requirement because the overall stiffness of the system is close to zero. A prestretched spring was used as an energy storage element, and a kinematic model was established to analyze the motion process. The moment output and magnitude of the negative stiffness generated during the motion process were derived. The stiffness of the deformed structure was measured, and the negative-stiffness mechanism was optimized using a genetic algorithm. The optimization results show that the negative-stiffness of the system can significantly reduce the energy requirement. However, the stiffness of the morphing wing structure varies from the design point because of manufacturing, assembly, and other factors. Considering the disturbances and uncertainties of the system, a stiffness-tuning mechanism was introduced to enhance the adaptability of the negative-stiffness mechanism. By changing the position of the connection point of the spring, the negative and overall stiffness can be adjusted. Theoretical analysis shows that the range of the overall stiffness expanded, allowing the system to better satisfy energy-balancing requirements under varying structural stiffnesses. Finally, the actuation system is integrated into a fishbone morphing wing, and the experimental platform is established. Actuation experiments were conducted and the currents of the servo actuator were measured using the current sensor. The experimental results show that the energy-balancing system can reduce energy consumption by 44.54%, which indicates that the energy-balancing method has the potential to significantly reduce energy consumption. In addition, it was verified that the stiffness-tuning mechanism can adjust the structural stiffness by tuning the connection point position, which can improve the effectiveness of the energy-balancing system.

Morphing wingtips have the potential to improve aircraft performance. By connecting the wingtips and the wings with a compliant structure, a continuous aerodynamic surface can be achieved for a better aerodynamic performance. However, how to maintain the shape-changing capability while keeping a high stiffness to carry aerodynamic loads is a key problem. In this paper, based on asymmetric stiffness, a type of single-row corrugated panel is designed to satisfy the limited space around the wingtip. A finite element model of the single-row corrugated panels is established, and parameter analysis is performed to investigate the impact of the thickness characteristics of the corrugated panel on the folding angle. The corrugated panel is then optimised to find the maximum folding angle. Based on the optimisation results, corrugated panels with asymmetric and symmetric stiffness are fabricated and tested. The results demonstrate that the asymmetric stiffness corrugated panels have the capability to increase the wingtip folding angle.

The application of spanwise morphing wings makes it possible to transport and launch large-size Mars exploration UAVs. This article proposes a modular variable spanwise morphing wing for high-aspect-ratio aircrafts, and analyses the characteristics of the morphing wing by theoretical analysis, numerical simulation and experimental verification. The novel spanwise morphing wing is based on the Sarrus-inspired deployable structure, which can increase the wing's lift by changing the spanwise length. The pre-strain torsion springs are assembled to provide the initial driving moment of the morphing mechanism. A regular triangle cross section is selected by evaluating the bending and torsional stiffness, and deployable triangular prism mechanisms are identified. Through releasing the pre-strain torsion springs to achieve expansion and implant Sarrus linkages along the straight motion paths. A lockable structure is designed, and the main factors affecting the self-locking property are analysed. A rigid origami skin is proposed, which maintains the airfoil's continuous smoothness after spanwise morphing. The kinematics of the spanwise morphing wing unit is developed using the Lagrange equation, and the theoretical models of morphing wings with different numbers of units are obtained. The unit numbers influence fully expanded time, and the time decreases gradually along the wingtip's direction. Finally, a one-way fluid-structure interaction analysis is performed to investigate the spanwise morphing mechanism and origami skin response under aerodynamic loads. Results show that the skeleton mechanism's maximum stress is below the material's yield strength, and the origami skin's maximum out-of-plane deformation is less than 0.5% of the wing chord, which provides a necessary theoretical basis for applying the spanwise morphing wing.

Bolt fasteners play a crucial role in modern engineering equipment, and understanding the stress distribution in the bolt during the assembly process is essential for enhancing its reliability. However, traditional experimental methods based on the principle of photoelasticity may not accurately reflect the actual assembly process and engineering materials. To address this issue, a novel experimental approach is proposed in this paper, which utilizes optical fibers to measure stress in the bolt during the assembly process. By affixing an optical fiber to the inside of the bolt and employing the optical frequency domain reflectometry (OFDR) technique, the axial stress distribution in the bolt can be obtained. In addition, the concept of an axial force gain factor is introduced to establish the relationship between the maximum axial force and preload. It is found that the calculated maximum axial force of the bolt is approximately 1.4 to 1.5 times the preload. The experimental results show that the stress distribution obtained through the proposed method is consistent with conventional photoelasticity experiments. Furthermore, a comparison with previous studies validates the accuracy of the experimental findings. The experimental approach presented in this paper can realize the real-time measurement of bolt stress distribution, which is of great significance for engineering application.

A novel tension-twist coupling morphing wing is proposed using tension-twist coupling metamaterials as the wing spar. The tension-twist coupling deformation was achieved by stacking of unit cells with tension-shear coupling behaviour. A finite element model was created to study the coupling behaviour of the unit cell, where the effect of cell configuration on the tension-shear coupling properties were numerically explored. The tension-twist coupling of the metamaterials was analysed and validated by a set of static tests using samples fabricated by selective laser sintering (SLS). The metamaterial was then implemented into a morphing wing to achieve adaptive twist. It was found that a valuable wing twist can be achieved by a relatively small actuation force, which can lead to a significant improvement in the overall aerodynamic performance. This novel way of realising the twist deformation of morphing wing reduces the demand for its driving system.

Bolt connection structure is widely utilized in modern large-scale equipment. Understanding the stress distribution along the bolt during assembly process is essential for improving its reliability. In this paper, assembly torque model is established to formulate the relationship between tightening torque and preload force, and a linear proportionality between them is obtained. The stress distribution during assembly process is modeled. Rotation angle and displacement distribution can be obtained from the proposed method. To validate our model, numerical simulation analysis is carried out to obtain the load and deformation distribution under different conditions. Comparison with the previous literature confirms the accuracy of the proposed model.