Table of Content

31 March 2026, Volume 47 Issue 4

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Buckling and parametric excitation stability optimization of fluid-conveying pipes by frequency design

Xiaoye MAO, Kexin CHANG, Jie JING, Tianchang DENG, Hu DING, Liqun CHEN

2026, 47(4):  675-694.  doi:10.1007/s10483-026-3372-6

Abstract ( 69 )   PDF (2959KB) ( 29 )  

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A methodology is proposed to enhance the buckling and parametric excitation stability of fluid-conveying pipes by designing their natural frequencies. As a direct indicator of structural stiffness with respect to deformation, which is intrinsically related to the overall structural stability, the natural frequency is adopted as the primary design criterion for enhancing system stability. Based on the generalized Hamilton’s principle, the governing equation for a multi-restrained pipe system is derived. The analysis reveals that, the natural frequencies can be maximized by appropriately selecting the constraint locations, which induces the best buckling stability. Although increasing the flow velocity generally reduces the natural frequency, the optimal constraint location remains relatively unchanged, eventually approaching the location of the maximal critical flow speed, beyond which the pipe loses its static stability. Furthermore, the proposed method introduces additional nodes into the natural mode shape, indicating that a higher energy threshold is required to trigger the resonance. Consequently, the parametric resonance under pulsating flow conditions becomes more difficult to initiate. Meanwhile, with the frequency design, the pipe can prevent the occurrence of parametric resonance with smaller critical damping. Compared with other approaches aimed at enhancing the stability of fluid-conveying pipe systems, the proposed method offers greater practicality for engineering applications, as it only requires adjusting the constraint locations and the optimal location is insensitive to the flow speed.

Development and application of a lumped parameter model for predicting blast wave effects on middle ear dynamics

Hongge HAN, Liang WANG, Zhanli LIU, Yongtao SUN, Anshuai WANG, Yueting ZHU, Jie WANG, Haoqiang GAO, Qian DING

2026, 47(4):  695-718.  doi:10.1007/s10483-026-3366-8

Abstract ( 54 )   PDF (11719KB) ( 11 )  

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The human ear is one of the most vulnerable organs to blast damage in modern warfare. The accurate prediction of blast wave effects on the ear has become a key challenge in auditory trauma research. A lumped parameter (LP) model, with parameters optimized using a genetic algorithm, is developed to efficiently predict the middle ear’s dynamic response to blast waves. The model accurately predicts tympanic membrane (TM) and stapes responses, particularly the first peak. Frequency-domain displacement and sensitivity analyses show that the middle ear responses are concentrated in a low-frequency range, with the blast wave amplitude significantly influencing the overall responses. TM responses are more sensitive to decay time at higher frequencies, while stapes responses are more sensitive at lower frequencies. This method achieves competitive accuracy and high computational efficiency. Based on this model, a risk index based on stapes displacements is proposed to optimize and evaluate hearing protection systems.

Transcranial electrical stimulation enhancing brain network integration: a dynamic modeling study

Haodong WANG, Ying YU, Qingyun WANG

2026, 47(4):  719-740.  doi:10.1007/s10483-026-3371-9

Abstract ( 38 )   PDF (11609KB) ( 6 )  

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The transcranial electrical stimulation (tES) has the potential to modulate the brain cognitive function. However, the dynamic mechanisms underlying this modulation remain incompletely understood. Based on a whole-brain network dynamic model, this study investigates the regulatory mechanisms of tES on brain integration levels and its restorative effects under conditions of structural lesion. The results demonstrate that in normal networks, both the integration level and synchronization level exhibit an inverted U-shaped relationship with the global coupling strength γ, peaking in the central region of the parameter space. Under unilateral or bilateral tES, the integration level shows a bidirectional regulatory effect related to the stimulation intensity. The moderate stimulation enhances the integration peak while maintaining the inverted U-shaped curve, whereas excessive stimulation leads to a decline in integration. In structural lesion models, both focal node lesions and diffuse connection losses lead to a reduction in the integration level, with more severe connection losses resulting in more significant decline in integration. Further research reveals that the impact of node lesions on integration is modulated by the inhibitory gain β, and the appropriate adjustment to β can mitigate the functional decline caused by lesions. At specific stimulation intensities, tES can partially restore the integration capacity of the lesion network. However, the restorative effect is simultaneously dependent on both β and γ. This study suggests that tES may influence multi-scale information integration by modulating nodal excitability and network dynamic stability. The relevant findings provide a theoretical basis for parameter optimization and target selection in individualized neuromodulation strategies for diseases such as stroke and traumatic brain injury.

Stochastic stability analysis of fluid-conveying pipes under multiplicative Gaussian white noise excitations

Hufei LI, Sha WEI, Hu DING, Liqun CHEN

2026, 47(4):  741-766.  doi:10.1007/s10483-026-3375-9

Abstract ( 45 )   PDF (5797KB) ( 16 )  

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This study investigates the stochastic stability of simply-supported fluid-conveying pipes under multiplicative Gaussian white noise excitations. The high-dimensional coupled stochastic differential equations for the fluid-conveying pipe are established through the generalized Hamilton principle and the Galerkin truncation method. The stochastic averaging method for quasi non-integrable Hamilton systems is used to decouple and reduce the dimension of the high-dimensional coupled pipe system with gyroscopic forces, yielding a one-dimensional Itô stochastic differential equation for the total energy of the pipe. According to the singular boundary classification theory of one-dimensional time-homogeneous diffusion processes, a stochastic stability criterion for the fluid-conveying pipe is proposed. The stability analyses of the time history responses of energy, displacement, and velocity for the pipe system are obtained via the Monte Carlo approach, thereby verifying the effectiveness of the proposed stability criterion in different parameter planes. Furthermore, the effects of system parameters, such as the fluid speed, multiplicative Gaussian white noise intensity, and pipe length, on the stochastic stability domain of the pipe system are discussed. The results indicate that as the fluid speed, the multiplicative Gaussian white noise intensity acting on the first-order mode, or pipe length increases, the stable domain of the system decreases. Conversely, the stable domain of the fluid-conveying pipe system increases as the multiplicative Gaussian white noise intensity acting on the second-order mode, pipe thickness, or Young’s modulus increases. It is worth noting that the appropriate increase in the multiplicative Gaussian white noise intensity acting on the second-order mode contributes to improving the stable domain of system. This method lays a theoretical foundation for the safe and stable operation of fluid-conveying pipes under random vibration.

Wave propagation in functionally graded piezoelectric sandwich doubly-curved nanoplates based on nonlocal strain gradient theory

Jie WANG, Juan LIU, Yinghui LI, Cheng LI, Bo ZHANG, Biao HU, Huoming SHENG

2026, 47(4):  767-790.  doi:10.1007/s10483-026-3369-7

Abstract ( 39 )   PDF (2104KB) ( 18 )  

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This study examines the wave propagation behavior of functionally graded (FG) piezoelectric sandwich doubly-curved nanoplates subjected to thermo-electric loading. The sandwich nanoplates are composed of a piezoelectric layer and an FG interlayer, deposited on a viscoelastic substrate, where the material parameters of the FG interlayer are influenced by temperature variations. By establishing a nonlocal strain gradient constitutive equation that incorporates piezoelectric and thermal effects, the displacement and strain fields of doubly-curved structures are formulated within the framework of first-order shear deformation theory (FSDT). The governing equations are derived using Hamilton’s principle, and then the dispersion relations for the doubly-curved nanoplates are computed through harmonic solution methods. Finally, the systematic analysis is conducted to investigate the effects of curvature parameters, scale parameters, FG indices, and foundation parameters on the wave propagation characteristics. The findings contribute to a deeper understanding of the wave propagation behavior of complex doubly-curved sandwich structures.

Study on indentation formation mechanism and mass loss under impact loading in concrete penetration

Yulong ZHENG, Yao TANG, Duo ZHANG, Xianwen RAN

2026, 47(4):  791-814.  doi:10.1007/s10483-026-3367-9

Abstract ( 36 )   PDF (3525KB) ( 8 )  

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Current erosion models for penetrating projectiles are almost exclusively developed for either rigid-body assumptions or hyper-velocity impacts. At such velocities, projectile deformation is primarily rheologically dominated. These models rarely capture the medium-velocity regime, where the impact speed drives plastic deformation, and the surface indentation governs progressive wear. The gap is addressed in this study by presenting a multi-scale framework that couples indentation mechanics, cavity-expansion theory, and impact-wave dynamics, and quantitatively correlates the indentation depth with the material properties and impact speed for the first time. Dimensional analysis identifies the dimensionless governing group, i.e., the dimensionless projectile elastic-inertial ratio T_p, dimensionless penetration resistance-inertia ratio T_t, dimensionless projectile ductility parameter λ₁, and dimensionless target strength parameter λ₂ as the trigger for erosion initiation. Then, a physically based wear model is derived analytically and calibrated against high-resolution simulations using adaptive mesh refinement to capture the projectile indentation. The resulting empirical formula is validated against independent experimental data, yielding errors of less than 7%. The proposed model provides armor-piercing projectile designers with an accurate and ready-to-use predictive tool for erosion in the medium-velocity regime.

On well-posed local-nonlocal mixed integral model of piezoelectricity for dynamic stability and vibration analysis of piezoelectric Timoshenko nanobeams with general boundary constraints

Pei ZHANG, P. SCHIAVONE, Luke ZHAO, Dongbo LI, Yanming REN, Hai QING

2026, 47(4):  815-838.  doi:10.1007/s10483-026-3370-8

Abstract ( 41 )   PDF (700KB) ( 10 )  

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Existing research has shown that nonlocal piezoelectric differential models often yield inconsistent dynamic responses for nanostructures. To address this issue, the two-phase local-nonlocal integral formulation has been proposed and has garnered increasing scholarly attention as an effective alternative. This study presents the first implementation of this theoretically consistent and paradox-free framework to investigate the size-dependent dynamic stability and free vibration behavior in piezoelectric Timoshenko nanobeams. The generalized boundary conditions are simulated through elastic constraints incorporating both translational and rotational springs at both beam ends. Departing from conventional approaches, the present formulation simultaneously accounts for size effects in both bending deformation and axial deformation caused by external voltages via the derivation of an equivalent differential representation of the well-posed local-nonlocal integral piezoelectric model. This formulation is rigorously complemented by a complete set of constitutive constraint conditions, ensuring mathematical well-posedness throughout the analytical framework. The generalized differential quadrature method (GDQM) is used to discretize the governing differential equations, enabling numerical determination of dynamic instability regions (DIRs) for various boundary configurations. Following comprehensive validation through comparative analyses, we systematically examine the influence of nonlocal parameters, static force factors, and boundary stiffness characteristics on the DIRs of the beams. Furthermore, this investigation underscores the significance of incorporating nonlocal effects into voltage-induced axial loading, addressing a critical gap in the current understanding of electromechanical coupling at nanoscale dimensions.

Analysis and optimization of bandgaps in plate-type metastructures with different configurations

Fenglian LI, Yin ZHU, Junhui YAN

2026, 47(4):  839-858.  doi:10.1007/s10483-026-3374-8

Abstract ( 30 )   PDF (1418KB) ( 12 )  

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Several types of acoustic metamaterial (AM) plates have been developed to achieve low-frequency and wide bandgaps, which are adjusted by their geometric configurations and material properties. This paper combines the classical plate theory and the characteristics of piezoelectric materials, and uses the plane wave expansion method (PWEM) to derive the bandgap theoretical model of plate-type metastructures. The dispersion curves of the structures composed of elastic materials, piezoelectric materials, and functionally graded (FG) materials are compared and studied, and verified with the finite element simulation results. Then, the effects of temperatures, piezoelectric parameters, scatterer shapes, scatterer distributions, scatterer tapers, rubber layers, and spiral groove configurations on the bandgap of plate-type metastructures are discussed, and the material and geometric parameters are optimized with the genetic algorithm (GA). This study provides a reference for the design of low-frequency broadband structures.

Frequency and mass optimization for an axially functionally graded GNP-reinforced conical shell with variable thickness

Zhigang ZHAO, Jun GAO, Feng LI, H. AFSHARI

2026, 47(4):  859-882.  doi:10.1007/s10483-026-3373-7

Abstract ( 50 )   PDF (5540KB) ( 5 )  

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This paper studies the optimization of mass and frequency for a polymeric conical shell reinforced with graphene nanoplatelets (GNPs). The volume fraction of the GNPs and the thickness of the shell change along the meridional direction. The modeling of the conical shell is conducted by the first-order shear deformation theory (FSDT), and the governing equations and boundary conditions are derived by Hamilton’s principle. A semi-analytical solution is presented, including an analytical solution carried out in the circumferential direction and a numerical solution conducted in the meridional direction utilizing the differential quadrature method (DQM). To maximize the fundamental frequency and minimize the mass, the particle swarm optimization (PSO) is utilized, taking into account some constraints on the minimum thickness of the shell and the maximum volume fraction of the GNPs. The optimization process involves finding the optimal profiles of thickness and volume fraction of the GNPs.

Multi-particle mass sensing based on a single-walled carbon nanotube resonator

Jie WANG, Yin ZHANG

2026, 47(4):  883-904.  doi:10.1007/s10483-026-3376-6

Abstract ( 48 )   PDF (2082KB) ( 6 )  

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Based on the Timoshenko beam theory, a model for mass resonator sensor to detect multiple particles is developed. For a beam made of single-walled carbon nanotube (SWCNT), the nonlocal effects are incorporated in the governing equations. The approximate analytical solution for the resonance frequency of the system is derived by assuming that the mass of the adsorbed particles is much smaller than that of the system. The mass and position parameters of the multiple adsorbed particles are decoupled to establish an efficient detection method utilizing resonant frequency shifts. The identification process for the doubly clamped beam is systematically analyzed in numerical simulations. In addition, the axial force arising from temperature changes is incorporated into the beam model. The robustness of the proposed particle detection method against noise is analyzed. The model and analytical framework presented in this study provide a theoretical guideline for the design of nanoscale mass resonator sensors and particle mass detection under thermomechanical coupling conditions.

Structural optimization of stress-bearing structures of nearly incompressible problems under design-dependent pressure loads

T. T. BANH, N. T. Y. NGUYEN, H. P. BAN, D. LEE

2026, 47(4):  905-926.  doi:10.1007/s10483-026-3368-6

Abstract ( 53 )   PDF (12989KB) ( 11 )  

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An efficient and innovative method is presented for the stress-related structural topology optimization (TO) in coupled mechanical-pressure systems by leveraging flexible polygonal meshes. With a polytopal composite finite element approach, the volumetric locking in nearly incompressible materials is reduced. A fluid-flow-based model is built, in which a design-dependent pressure variable is introduced to capture the loading conditions within the system. The P-norm approach consolidates the stress metrics into a global measure, while the clustered regional scaling and adaptive techniques enhance the solutions for stress-limited cases. The primary contributions of this work include a novel framework for addressing the stress challenges in coupled mechanical-pressure systems via flow-based modeling, the adaptability to both compressible and nearly incompressible materials, and the compatibility with diverse mesh types, including triangular, quadrilateral, and polygonal elements. The numerical examples demonstrate, for the first time, optimized topologies for nearly incompressible materials under stress constraints in coupled mechanical-pressure environments, emphasizing the unique strength of this approach.

Convective shielding mechanisms in melting of double circular ice bodies

Minghao GENG, Kaileong CHONG, Yuan MA

2026, 47(4):  927-940.  doi:10.1007/s10483-026-3365-7

Abstract ( 45 )   PDF (1854KB) ( 12 )  

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Global climate change has intensified research on glacier melting. Direct numerical simulations employing the phase-field method are conducted to investigate the influence of arrangement angle α (ranging from 0° to 90°) on the melting dynamics of two-dimensional double circular ice bodies under uniform flow at Re = 400 and Pr = 7, aiming to elucidate the interactions within ice clusters. As α varies, the melting process can be divided into three distinct regimes characterized by different flow structures: individual, collective, and shielding regimes. In the individual regime, the melting rates of the two ice bodies exhibit negligible differences. In the collective regime, the downstream ice body melts faster than the upstream one. In the shielding regime, the shielding effect markedly impedes the melting of the downstream ice body, resulting in its slower melting rate relative to the upstream counterpart. Notably, at α = 90°, the downstream ice body becomes fully enveloped by the low-temperature wake, inducing a profound shift in its melting scaling law from the convection-dominated classical form A(t) = A₀(1 – t/t_f)^4/3 to a conduction-dominated form A(t) = A₀(1 – t/t_f).