Table of Content

30 June 2026, Volume 47 Issue 7

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Excitation direction and intensity-dependent damping performance of a nonlinear energy sink: theory and experiments

Xiaofeng GENG, Shican LIU, Li ZHANG, Kexiang WEI, Yingan KANG, Xingjian JING, Hu DING

2026, 47(7):  1433-1446.  doi:10.1007/s10483-026-3401-7

Abstract ( 12 )   PDF (7862KB) ( 9 )  

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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.

Offset support design for enhancing the stability of flexible fluid-conveying pipes

Runqing CAO, Yixiang HE, Jiachun HU, Huliang DAI, Lin WANG

2026, 47(7):  1447-1468.  doi:10.1007/s10483-026-3402-8

Abstract ( 13 )   PDF (2876KB) ( 4 )  

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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.

Adaptive piecewise Euler-Bernoulli beam model for tendon-actuated soft slender manipulator

Jin WANG, Yisong ZHAO, Fei GAO, Yongjian ZHAO

2026, 47(7):  1469-1486.  doi:10.1007/s10483-026-3411-9

Abstract ( 8 )   PDF (1129KB) ( 2 )  

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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.

Inherent nonreciprocity in double-alternatingnonlinear metamaterial

M. H. BAE, J. H. PARK, C. S. PARK, H. LEE, H. M. SEUNG

2026, 47(7):  1487-1510.  doi:10.1007/s10483-026-3404-6

Abstract ( 9 )   PDF (3926KB) ( 1 )  

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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 nonreciprocal transmission, offering a pathway toward self-adaptive wave control systems.

Effective magneto-electro-elastic moduli of elliptical multi-coated multiferroic nanocomposites with surface effects

Tingting SA, Yan LI, Lihong CHANG, Fanfan NAI, Fusheng MIAO, Wenshuai WANG

2026, 47(7):  1511-1532.  doi:10.1007/s10483-026-3408-6

Abstract ( 9 )   PDF (3923KB) ( 1 )  

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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.

Thermodynamic constitutive modeling for analyzing the consistencies and differences of intelligent responses induced by thermo-elastic-viscoplastic couplings

Hao DUAN, W. M. HUANG, Hao ZENG, Jianping GU, Huiyu SUN

2026, 47(7):  1533-1548.  doi:10.1007/s10483-026-3409-7

Abstract ( 9 )   PDF (187KB) ( 1 )  

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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.

Symplectic electrothermomechanical buckling solutions for two-dimensional decagonal piezoelectric quasicrystal cylindrical shells

Xin SU, Yuhang LI, Jufang JIA, Xinsheng XU, Andi LAI, Zhenhuan ZHOU

2026, 47(7):  1549-1568.  doi:10.1007/s10483-026-3410-8

Abstract ( 11 )   PDF (1068KB) ( 3 )  

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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.

A spherical Eshelby inclusion with a Steigmann-Ogden interface in a finite domain

Xu WANG, P. SCHIAVONE

2026, 47(7):  1569-1580.  doi:10.1007/s10483-026-3403-9

Abstract ( 11 )   PDF (1367KB) ( 1 )  

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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.

Frequency and vibration responses of a magneto-rheological sandwich micro-beam based on modified couple stresstheory and finite difference method

M. JAFARI, M. MOHAMMADIMEHR

2026, 47(7):  1581-1602.  doi:10.1007/s10483-026-3405-7

Abstract ( 16 )   PDF (2537KB) ( 6 )  

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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.

Asymptotic models for thin transversely isotropic elastic layers

Guozheng ZHANG, Zhaohe DA

2026, 47(7):  1603-1624.  doi:10.1007/s10483-026-3406-8

Abstract ( 12 )   PDF (359KB) ( 3 )  

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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.

Theoretical modeling of nonlinear rotational stiffness for missile radial countersunk screw lap joints

Shuo ZHANG, Ning GUO, Chao XU

2026, 47(7):  1625-1646.  doi:10.1007/s10483-026-3407-9

Abstract ( 8 )   PDF (3136KB) ( 2 )  

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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.