Self-oscillatory systems sustain continuous motion by harvesting energy from a steady environment through internal feedback, in contrast to conventional oscillators that depend on inertia and demand materials with rapid responsiveness to external stimuli. In this study, we experimentally design a bistable liquid crystal elastomer (LCE) self-excited oscillator operating under steady illumination. The oscillator consists of an LCE fiber, a spring, a rigid rod, a rope, and a hysteretic occluder. A quasi-static analysis under constant light reveals two distinct motion regimes: a steady regime and a self-oscillatory regime. Periodic motion arises from the contraction and relaxation of the LCE fiber, leading to alternating leftward inclination of the rigid rod under illumination and rightward inclination in darkness. Owing to the bistable configuration, asynchronous motion is generated, introducing a hysteresis-related delay in the optical feedback. This hysteretic effect relaxes the requirement for rapid response and enables sustained self-excited oscillations under steady illumination. Furthermore, the dependence of the critical contraction strain and oscillation period on the system parameters is systematically examined. Compared with the existing self-oscillating systems, the proposed design achieves reliable self-excited oscillation with reduced experimental complexity and fewer mechanical components, enabling its potential use in sensing, energy harvesting, and soft robotics.
In this study, a novel offset support design for enhancing the stability of fluid-conveying pipes is proposed. Specifically, by offsetting the simple support, the nonlinear stiffness in both tension and bending of the pipes is effectively increased. On the basis of the absolute nodal coordinate formulation (ANCF), a theoretical model for a pipe with an offset support under various boundary conditions is established and validated through experiments. A systematic investigation is subsequently conducted to explore the effects of the offset position and amplitude on the static deformation, stability, and nonlinear dynamic behaviors. The results indicate that the proposed offset support can significantly increase the stability of the fluid-conveying pipe and reduce its deformation amplitude. In most cases, a larger offset amplitude generally corresponds to a higher critical fluid velocity and a smaller deformation amplitude. With respect to the support position, placing an offset support at one-quarter of the span from the supported end can substantially improve the stability of simply supported pipes. With respect to cantilevered pipes, adding an offset support at the free end can considerably increase the critical flow velocity of the pipe. When the flow velocity is in the subcritical region, a pipe with an offset support maintains in-plane static deformation with a small amplitude. In the supercritical flow velocity region, compared with a pipe without an offset support, a pipe with an offset support has a smaller nonplanar configuration. This study provides new insight into enhancing the stability of fluid-conveying pipes via an offset support design, which features simple implementation and considerable application potential in engineering practice.
Soft manipulators exhibit coupled geometric-material nonlinearities under large deflections, which complicate modeling, shape estimation, and closed-loop force control while incurring high computational costs. In this paper, a control-oriented reduced-order adaptive piecewise Euler-Bernoulli (APEB) beam model for tendon-driven slender soft arms is presented. A nonlocal end-force correction is explicitly embedded in the bending equilibrium to capture the projection and attenuation of distal tendon tension and external loads toward the proximal end. To curb the cost of high-dimensional discretization, we introduce curvature/strain-gradient-guided adaptive segmentation with local cubic-spline interpolation: nodes are refined only in regions of severe deformation, whereas fewer degrees of freedom (DoFs) are maintained elsewhere. Based on this discretization, we derive the complete weak-form residual, assemble the tangent stiffness (Jacobian) matrix, and formulate an iterative Newton update, which yields a solver that efficiently computes static equilibria with numerically stable convergence. The model enables fast skeleton reconstruction (shape estimation without external optical tracking) and direct end-effector Jacobian generation through local-to-global coordinate mapping, thereby mapping tendon inputs to the end-effector pose for closed-loop and force control. Simulations and benchtop experiments on a four-tendon continuum actuator show millimeter-level accuracy in the trunk shape and end-effector position across varying cable tensions, and the proposed approach outperforms conventional kinematic and classical beam-theory models in terms of both accuracy and computational efficiency. The model is intended for quasistatic, bending-dominated configurations in which torsional deformation and out-of-plane loading are negligible.
Multiferroic composites hold great promise in electronic devices because of their exceptional magnetoelectric coupling effects, and multilayer core-shell nanofibers are considered as ideal carriers for achieving high-performance responses. However, existing theories often assume perfectly circular fiber cross-sections while neglecting the interfacial effects. This makes it difficult to accurately characterize the elliptical cross-sections and nanoscale interface properties commonly observed in practical fabrication. To address this issue, this study establishes a theoretical model for multilayer multiferroic nanofiber composites. The model simultaneously accounts for both the fiber shape and interfacial effects. Using the generalized self-consistency method and complex function approach, this work further derives analytical solutions for the effective magneto-electric-elastic (MEE) moduli. Based on this model, the study systematically investigates the influence of the coated fiber shape, fiber size, coated fiber volume fraction, and inner-to-outer coating thickness ratio on the composite’s effective MEE moduli. The findings reveal the synergistic mechanism, by which the elliptical fiber shape and multiple interfacial effects regulate the magnetoelectric anisotropy, thereby providing crucial theoretical guidance for designing the structure of high-performance multiferroic nanocomposites and optimizing their performance.
Through appropriate thermo-mechanical stimulation, shape memory polymers (SMPs) can exhibit autonomous shape-morphing capabilities, which are referred to as entropic elastic (EE) or reversible plastic (RP) intelligent responses. Currently, few studies in the literature address unified constitutive modeling for these two types of intelligent responses, and thermodynamic consistency is lacking. Here, we develop a unified thermodynamically consistent constitutive model that captures hyperelastic-viscoelastic and elasto-viscoplastic couplings, thereby reproducing both the EE and RP intelligent responses. Through verification against experimental data and results from subsequent mechanistic and parametric studies, the constitutive model can not only integrate the theoretical representations of these two phenomena into a mathematical framework, but also reveal the consistencies and differences between the two types of intelligent responses.
Metamaterial-based nonreciprocity has emerged as a promising frontier for novel wave manipulation, yet most realizations rely on external biasing or auxiliary mechanisms, restricting their robustness and applicability. Here, we investigate the inherent nonreciprocity in a nonlinear metamaterial without any external apparatus. Fundamentally, since structural asymmetry governs the internal mode distribution, amplitude-dependent nonlinearity inevitably creates distinct boundary-excitations for forward and backward waves, inherently leading to nonreciprocity. To effectively combine structural asymmetry with nonlinearity, we leverage a diatomic configuration as a robust baseline, and introduce alternating nonlinear stiffnesses. We develop a rigorous analytical framework based on the Rayleigh-Schrödinger perturbation to capture the amplitude-dependent dispersion of the asymmetric unit cell. The numerical simulations validate the analytical predictions, and demonstrate direction-specific bandgap modulation for forward and backward waves. This study advances the understanding of nonlinear dynamics by elucidating how the interplay between structural asymmetry and nonlinearity passively induces non-reciprocal transmission, offering a pathway toward self-adaptive wave control systems.
Thin elastic layers bonded on one or both surfaces to rigid substrates are ubiquitous in coatings, adhesives, and integrated circuits. Their response to applied surface tractions is commonly represented by reduced mattress (or Winkler) models and shear-lag models. Classical reduced relations typically ignore normal-tangential coupling and are often confined to compressible and isotropic solids. In this work, we develop a Hankel-transform formulation for axisymmetric loading of transversely isotropic layers and perform a systematic thin-layer (or long-wavelength) asymptotic expansion to obtain high-order surface traction-displacement relations. The resulting reduced relations provide extended Winkler and shear-lag-type models that retain the coupling between normal and shear responses and accommodate transverse isotropy. These asymptotic models provide a practical basis for predicting deformation fields and stress transfer in layered and bonded systems.
In this study, the frequency and vibration responses of a sandwich micro-beam are derived based on the modified couple stress theory (MCST). The face sheets are made of pure aluminum, and a magneto-rheological (MR) core is used to control vibrations. The displacement fields are assumed based on the classical beam theory (CBT) and modified classical beam theories. Based on Hamilton’s principle, the governing equations of motion are obtained. To solve these temporal equations, the finite difference method (FDM) with an optimal number of nodes is applied. The effects of various parameters, including viscoelastic properties, magnetic fields, aspect ratio, core-to-face-sheet thickness ratio, MR materials, face sheets, and material length-scale parameters, on the frequency and vibrational response are investigated. In the literature, the effects of different parameters on the frequency response function (FRF) or vibration response are considered. The results obtained from the vibration response and FRF using the FDM show that the viscoelastic property of the MR core causes settling time in the vibration response and a decrease in the excitation frequency of the FRF. Increasing the magnetic field has a negligible effect on the excitation frequency in the FRF, but it increases the vibration response and settling time. The piezoelectric face sheets raise the FRF and suppress the vibration response of the MR sandwich micro-beam compared with the aluminum counterpart.
Piezoelectric quasicrystals (PQCs), characterized by unique phonon-phason coupling and piezoelectric effects, exhibit significant potential for use in next-generation smart structural devices. However, their complex electrothermomechanical buckling behavior remains a challenging analytical problem. This paper presents a symplectic electrothermomechanical buckling model for two-dimensional (2D) decagonal PQC cylindrical shells. By using the symplectic mathematics and Donnell’s thin shell theory, the governing buckling equations for axially compressed PQC cylindrical shells are reformulated into a Hamiltonian system. Consequently, the original buckling problem is transformed into a symplectic eigenproblem that can be solved directly, obviating the necessity of trial functions. By use of the symplectic eigenfunction expansion, analytical symplectic buckling equations are obtained, allowing the critical buckling loads and buckling mode shapes to be solved simultaneously. The results indicate that, in addition to the geometry, voltage, and temperature, the phonon-phason-electric coupling inherent in PQC materials significantly influences the critical buckling loads. These analytical results provide a reliable reference for validating other computational approaches.
Radial countersunk screw lap joints are widely employed to connect adjacent cabin sections in small- and medium-diameter missiles. However, the analysis and design of joint stiffness pose challenges because of geometric discontinuities, clearance, and friction nonlinearities. In this paper, a theoretical model for rapid and reliable prediction of nonlinear joint stiffness is developed. The joint is first discretized into multiple subjoints, each of which is defined to carry only a tensile or compressive load under external loading. The evolution of contact states is incorporated to simulate nonlinear tension and compression stiffness. By combining Bernoulli’s hypothesis with the ellipsoidal deformation theory, the joint rotational stiffness is derived. Finally, the effectiveness of the proposed stiffness prediction method is validated via experiments and detailed simulations. Furthermore, an orthogonal experimental design is used to analyze the importance of critical design parameters. The results indicate that the proposed theoretical model provides satisfactory accuracy. The specification and number of screws are the primary factors influencing the joint rotational stiffness, whereas the lap length and cabin thickness exert a secondary effect. This study presents an explicit theoretical mapping between the structural design parameters and joint nonlinear stiffness, thus facilitating improved design and optimization of jointed structures.
The traditional nonlinear energy sink (NES) exhibits high robustness over a wide frequency interval under unidirectional excitation. However, variable excitation directions and intensities are common in engineering applications, and the vibration reduction performance of the conventional NES remains uncertain. In this paper, a dynamic model of a linear oscillator (LO) equipped with an NES is established to investigate the effects of the excitation direction and intensity on the NES performance. Moreover, a three-dimensional model is designed, and a corresponding experimental platform is constructed. The vibration reduction performance of a conventional NES is theoretically investigated under variable excitation directions and intensities. Moreover, the dynamic characteristics are revealed for both free and forced vibrations. Experimental tests are conducted to validate the prediction results. This study demonstrates that the vibration suppression performance of the NES is highly sensitive to both the excitation direction and intensity. Overall, although the performance of the NES decreases with increasing excitation angle, vibration can be effectively suppressed over a wide angle range. This finding indicates that the traditional NES is highly robust to the excitation direction. In addition, the NES exhibits notable damping performance within a wide excitation range, especially at high excitation angles. For relatively low and very high excitation intensities, the performance of the NES is poor. The vibration reduction trend under the coupling effect of the excitation intensity and direction is systematically revealed. A critical excitation intensity is identified, at which the NES exhibits weaker performance at low angles but enhanced performance at high angles. The findings provide a theoretical basis for promoting NES engineering applications.
We derive closed-form solutions to the three-dimensional Eshelby’s problem of a spherical Eshelby inclusion undergoing uniform deviatoric eigenstrains concentrically embedded in an isotropic elastic finite spherical domain with a traction-free or rigidly clamped boundary. The interface between the inclusion and its surrounding domain is assumed to be of Steigmann-Ogden type. Our solutions indicate that the stresses and strains within the spherical inclusion are generally nonuniform because of the effects of the finite spherical domain and the Steigmann-Ogden imperfect interface. The internal elastic field of stresses and strains is uniform within the spherical inclusion when a condition that relates the single interface parameter to the geometric parameter and Poisson’s ratio of the finite domain is satisfied. When the spherical edge is rigidly clamped, a Gurtin-Murdoch interface is found to be sufficient to achieve this interior uniformity property. In contrast, when the spherical edge is traction-free, a Steigmann-Ogden interface with nonzero and positive bending stiffness parameters must be used to achieve the interior uniformity property.
Multilayer structures composed of quasi-zero-stiffness (QZS) units exhibit mechanical characteristics distinct from those of a single unit, and their behaviors are governed by the coupling mechanism between the QZS units. This paper introduces the coupling coefficient to quantitatively describe this mechanism, classifying the system into strongly coupled and weakly coupled states. Through theoretical analysis, numerical simulation, and experimental testing, the static and dynamic responses under different coupling states are comparatively investigated. The results show that in the strongly coupled system, the deformation behavior of each QZS unit shows high consistency, leading to a wider QZS region, weaker nonlinear characteristics, and stronger dynamic response. In the weakly coupled systems, the low degree of deformation coordinations among the units results in different QZS regions, enabling low-frequency vibration isolation under varying loads. The analytical approach of the coupling mechanisms and the static and dynamic response behaviors generated by the two coupling mechanisms provide guidance for the structural design of multifunctional and highly adaptable multi-level QZS metamaterials.
Bilayer films are widely employed as actuators because of their ability to undergo bending deformations in response to environmental stimuli. While the bending curvature induced by uniform stimuli can be accurately described by the classical Stoney formula, predicting the deformation of bilayer films under spatially non-uniform stimuli remains challenging. The difficulty lies mainly in the coupling between the film’s responsive deformation and the local stimulus intensity that it experiences. To address this challenge, in this study, we extend the classical Stoney relation by developing a theoretical framework that links the local curvature of the film to the space-dependent stimulus intensity. This framework enables the precise prediction of the deformed configurations of bilayer films subjected to complex, non-uniform stimulus fields. The theoretical results are validated through finite-element simulations and experimental measurements, demonstrating excellent agreement. Our findings provide a solid theoretical foundation for controlling the responsive deformation of bilayer actuators to spatially varying stimuli, which facilitates the application and development of soft thin-film actuators.
This paper proposes a novel low-energy impact trajectory design framework for near-Earth asteroids (NEAs), exploiting the dynamical properties of invariant manifolds within a Jupiter-perturbed Sun-Earth planar bicircular restricted four-body problem (RFBP). First, we investigate the influence of Jupiter’s perturbation on the instantaneous Jacobi constant C, which governs the evolutionary behavior of the zero-velocity curves. An energy mechanism is then established to link the instantaneous C with the feasible region for asteroid entry into the Earth-Moon sphere of influence (EMSOI). Using this mechanism, a screening procedure is developed to identify potential Earth-impacting asteroids by analyzing their accessible impact regions. Subsequently, low-energy impact trajectories are designed by joining unstable manifolds and the Lambert transfer, which is further optimized via the particle swarm optimization (PSO) algorithm. Finally, the numerical simulations conducted for asteroids 2010 XC15 and 2023 JD6 demonstrate that the proposed method significantly reduces propellant consumption. Overall, this study provides a practical and low-energy strategy for asteroid defense and deep-space mission design.
The dissipative characteristics of deformation recovery in curved nanobeams are crucial for micro/nano-device reliability. In situ experiments reveal the dependence of recovery characteristics on loading direction, but existing theories fail to elaborate this mechanism, and efficient prediction methods are scarce. This study proposes an elastic-viscoelastic core-shell model under Kirchhoff’s small deformation hypothesis, accounting for surface-inner dissipation and geometric differences. Using the time-domain differential method, we convert the integral model into an equivalent differential model and derive an analytical solution for the deformation recovery. Combined with finite element (FE) analysis, we study the load/geometric effects on the viscoelastic recovery of the nanocircular-arc. The results agree well with the experimental results and the FE simulations. They show that laminated structures and surface dissipation endow the recovery process with two intrinsic characteristic time scales and two stages, including an instantaneous jump and long-term evolution, in which the synergy and competition between bending and axial deformation cause the dependence of recovery behavior on the loading direction and symmetry-breaking phenomena. This study clarifies experimental mechanisms and provides a new dissipation control approach.
The analysis of penetration mechanics is critical for the offensive targeting and defensive design of underground facilities. Although computational methods are fundamental to penetration analysis, they are often constrained by a trade-off between accuracy and computational efficiency. Emerging artificial intelligence (AI) methods, with inherent strengths in modeling complex high-dimensional relationships from available data, provide promising alternatives for building intelligent surrogate models. This study proposes a fusion-enhanced radial basis function network (FE-RBFN) for penetration prediction, solving forward and inverse problems with multi-fidelity data. FE-RBFN employs three interconnected subnetworks to extract features and capture nonlinear correlations at varying fidelity levels. To overcome the challenge of data scarcity, FE-RBFN embeds a data fusion strategy to fully leverage multi-fidelity data from multiple sources. The experimental results demonstrate that our network yields rapid and precise predictions, outperforming traditional machine learning methods. Notably, in multi-fidelity scenarios, FE-RBFN exhibits robust prediction accuracy despite the limited availability of high-fidelity data.
Conventional ceramics and glasses exhibit high strength and stiffness; however, their inherent brittleness often leads to catastrophic fracture under mechanical loading. To overcome this limitation, natural materials such as nacre and sutures offer a compelling structural blueprint. Inspired by these natural architectures, a bio-inspired composite system that integrates a brick-and-mortar arrangement with a geometrically interlocked suture interface is developed. Uniaxial tensile experiments demonstrate that this hybrid design effectively combines nacre-like interfacial sliding with geometric interlocking, resulting in synergistic mechanical enhancements. To further elucidate the underlying deformation and failure mechanisms, comprehensive numerical simulations of the tensile behavior in glass-polymer bioinspired composites are carried out. Key micromechanical processes considered in the calculation include the frictional pull-out of glass interlocking structures, plastic deformation of the polymer matrix, and debonding at the composite interface. The failure of the composites is controlled by the competition between the geometric interlocking of the glass, the plastic deformation of the polymer matrix, and the interface debonding of the composite material. Increasing the interlocking angle and interfacial friction coefficient significantly elevates the tensile strength by promoting the frictional resistance during pull-out. A strong interfacial strength and a large failure displacement enhance the effective toughness of the interface, which promotes stable and progressive damage evolution, leading to improved overall mechanical properties. In contrast, the yield strength of the polymer matrix has no significant influence on the peak tensile strength in the present design configuration. It is also found that the interlocking with strong friction interaction and strong interface can activate significant energy-dissipation mechanisms, thereby significantly enhancing the toughness of the composites.
Most existing vibration absorbers are limited by the need for precise tuning, and are difficult to suppress broadband vibration. A nonlinear damping absorber (NDA) is proposed in this paper to control the vibrations of structures in multiple modes, providing nonlinear damping in multiple directions and enabling broadband and multidirectional vibration suppression. A pipe is selected as the research object to analyze its dynamic behaviors and vibration suppression mechanisms. The vibration reduction performance of the NDA on the in-plane vibration and out-of-plane vibration of the pipe is studied through experimentation and theory. First, the configuration of the NDA is designed, and its mechanical model is established. An experimental platform is built for the parameter identification and multi-directional vibration reduction test of the absorber. Second, based on the generalized Hamilton’s principle, the mechanical model describing the in-plane vibration and out-of-plane vibration of the pipe with the NDAs is derived. The approximate solution of the nonlinear response is derived and numerically validated. The multi-directional and multi-modal vibration reduction efficiency of the NDAs for the structures is analyzed. The research results show that the proposed absorber can significantly control the multi-directional vibration. Nonlinear damping effectively broadens the vibration reduction bandwidth, and improves the damping efficiency, with the cubic term playing the dominant role. Finally, a concept of multi-modal weighted optimization is proposed. The absorber parameters are optimized through the particle swarm optimization (PSO) algorithm. This paper provides a new type of absorbers for the vibration control of multiple directions in broadband.
The wavelet multi-resolution interpolation Galerkin method (WMIGM) is combined with a mixed explicit-implicit time-stepping scheme to solve the one-dimensional Burgers’ equation at high Reynolds numbers, where the solutions exhibit evolving steep local gradients. In the proposed framework, a dynamic sequence of node distributions with local multi-resolution refinement is adaptively constructed according to the gradient information identified by a wavelet transform. The approximate solution at previous time levels, required in the time-stepping procedure, is represented by the same wavelet expansion used in its original construction, thereby eliminating the need for interpolation between different node distributions. Several representative numerical examples are presented to assess the accuracy, convergence, and robustness of the proposed adaptive wavelet method. The results demonstrate that the proposed approach possesses a higher accuracy and a faster convergence rate than many existing numerical methods, and can accurately capture complex shock dynamics without spurious oscillations, including boundary layer formation from smooth initial profiles and shock merging processes.
