Applied Mathematics and Mechanics (English Edition)

Non-planar vibration characteristics and buckling behaviors of two fluid-conveying pipes coupled with an intermediate spring

Dali WANG, Tianli JIANG, Huliang DAI, Lin WANG

2025, 46(10): 1829-1850. doi:10.1007/s10483-025-3306-9

Abstract ( 26 )

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This study investigates the dynamical behavior of two parallel fluid-conveying pipes by developing a non-planar dynamical model of the two pipes coupled with an intermediate spring. A systematic analysis is conducted to evaluate the effects of spring parameters on the non-planar vibration characteristics and buckling behaviors of the coupled system. The nonlinear governing equations are derived with Hamilton’s principle, subsequently discretized through Galerkin’s method, and finally numerically solved by the Runge-Kutta algorithm. Based on the linearized equations, an eigenvalue analysis is performed to obtain the coupled frequencies, modal shapes, and critical flow velocities for buckling instability. Quantitative assessments further elucidate the effects of the spring position and stiffness coefficient on the coupled frequencies and critical flow velocities. Nonlinear dynamic analyses reveal the evolution of buckling patterns and bifurcation behaviors between the lateral displacements of the two pipes and the flow velocity. Numerical results indicate that the intermediate spring increases the susceptibility to buckling instability in the out-of-plane direction compared with the in-plane direction. Furthermore, synchronized lateral displacements emerge in both pipes when the flow velocity of one pipe exceeds the critical threshold. This work is expected to provide a theoretical foundation for the stability assessment and vibration analysis in coupled fluid-conveying pipe systems.

Nonlinear dynamics of intricate constrained fluid-conveying pipelines based on the global modal method

Ye TANG, Yuxiang WANG, Hujie ZHANG, Tianzhi YANG, Fantai MENG

2025, 46(10): 1851-1866. doi:10.1007/s10483-025-3308-7

Abstract ( 21 )

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In recent years, scholars around the world have shown increasing interest in elastic support structures, leading to significant progress in dynamic modeling techniques for pipeline systems. Although multiple analytical approaches exist, engineers increasingly prioritize computationally efficient, precise low-order models for practical implementation. In order to address this need, this study develops an innovative nonlinear dynamic formulation for pipelines accounting for both foundation and boundary nonlinearities. The proposed solution methodology initiates with global mode extraction using the global mode technique, followed by a detailed implementation procedure. Model validation is conducted through a cantilever pipeline case study featuring nonlinear support conditions, where strong agreement between the proposed model’s predictions and finite-element benchmark solutions demonstrates its reliability. Subsequently, a comprehensive parametric study investigates the combined effects of foundation stiffness, boundary constraints, excitation intensity, and nonlinear interaction terms on the vibrational response of the cantilever pipe. This systematic approach yields critical insights for practical engineering designs and applications.

Vibration and response behaviors of composite sandwich cylindrical shells with a carbon nanotube-reinforced damping gel honeycomb core

Peiyao XU, Zhuo XU, Shang GENG, Hui LI, Yan ZHOU, Haijun WANG, Jian XIONG, Zeng LIN, Jun LI

2025, 46(10): 1867-1882. doi:10.1007/s10483-025-3304-7

Abstract ( 27 )

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This study provides a thorough investigation into the vibration behavior and impulse response characteristics of composite honeycomb cylindrical shells filled with damping gel (DG-FHCSs). To address the limitations of existing methods, a dynamic model is developed for both free and forced vibration scenarios. These models incorporate the virtual spring technology to accurately simulate a wide range of boundary conditions. Using the first-order shear deformation theory in conjunction with the Jacobi orthogonal polynomials, an energy expression is formulated, and the natural frequencies and mode shapes are determined via the Ritz method. Based on the Newmark- $β$ method, the pulse response amplitudes and attenuation characteristics under various transient excitation loads are analyzed and evaluated. The accuracy of the theoretical model and the vibration suppression capability of the damping gel are experimentally validated. Furthermore, the effects of key structural parameters on the natural frequency and vibration response are systematically examined.

Dynamic modeling and simulation of irregular faults in axle box bearings of high-speed trains

Xiaohui GU, Yajia WANG, Pengfei LIU, Zechao LIU, Shaopu YANG

2025, 46(10): 1883-1902. doi:10.1007/s10483-025-3303-6

Abstract ( 21 )

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Axle box bearings are critical components of high-speed trains. Localized defects, such as pitting and spalling, on raceways or rollers pose significant threats to the operational safety of railway vehicles. In this work, a novel bearing-flexible axle box-vehicle coupling model is established to explore the vibration characteristics of axle box bearings with irregular localized defects. First, based on the contact and kinematic relationship between rollers and raceways, the three-dimensional (3D) bearing force elements are analyzed and formulated. Second, the established model and a flexible axle box are integrated into the vehicle, and the responses of the normal and faulty bearings under the combined excitations of wheel roughness and track irregularities are simulated. Third, the simulation results are verified through a rolling-vibrating test bench for full-scale wheelsets of high-speed trains. The comparisons of the fault-induced repetitive transients in the time-domain and the fault characteristic frequencies in the envelope spectra demonstrate the efficiency of the proposed model. Finally, based on the flexible axle box model, a sensitivity analysis of the accelerometer placements to the bearing faults is carried out, and the optimal one is identified based on both the time-domain and frequency-domain signal-to-noise ratios (SNRs) for engineering applications.

Nonlinear 1:1 internal resonance in graphene platelet-reinforced fluid-conveying pipes

Guilin SHE, Yujie HE

2025, 46(10): 1903-1920. doi:10.1007/s10483-025-3305-8

Abstract ( 18 )

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This study investigates the nonlinear dynamics of geometrically imperfect graphene platelet-reinforced metal foam (GPLRMF) fluid-conveying pipes under the 1:1 internal resonance condition. With simply supported boundary conditions, the system is subject to the combined external lateral loads and internal pulsating fluid excitations. The nonlinear dynamic model is established with the Euler-Lagrange equations and then systematically discretized via the Galerkin method. The multi-scale analysis reveals how material properties and geometric imperfections influence the internal resonance. Particular emphasis is placed on elucidating, through the modal energy analysis, the energy exchange mechanisms between the first two vibration modes.

Nonlinear traveling wave vibration of rotating ferromagnetic functionally graded cylindrical shells under multi-physics fields

Feng LIAO, Yuda HU, Tao YANG, Xiaoman LIU

2025, 46(10): 1921-1938. doi:10.1007/s10483-025-3302-9

Abstract ( 18 )

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The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded (FG) cylindrical shells under multi-physics fields is investigated. Grounded in the Kirchhoff-Love thin shell theory, the geometric nonlinearity is incorporated into the model, and the constitutive equations are derived. The physical parameters of functionally graded materials (FGMs), which exhibit continuous variation across the thickness gradient, are of particular interest. The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton’s principle. The nonlinear partial differential equations are discretized with the Galerkin method, and the analytical expression of traveling wave frequencies is derived with an approximate method. The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions. Finally, the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies. The results show that the factors including the power-law index, temperature, magnetic field intensity, and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.

Dynamic modeling of a fully flexible rotor-stator system with bolt joint and rubbing-induced nonlinear vibration

Hong GUAN, Hui MA, Tianrui YANG, Yanyan CHEN, Yao ZENG, Qinqin MU, Bangchun WEN

2025, 46(10): 1939-1954. doi:10.1007/s10483-025-3301-8

Abstract ( 18 )

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In addition to blade-to-casing rubbing, drum-to-labyrinth rubbing is another common interaction in aero-engines. In this study, the labyrinth seal is simplified and modeled as an inner ring. First, considering the flexibility of both the drum and inner ring, a novel rubbing force model applicable to drum-inner ring rubbing is proposed, and this model is partially validated with the measured vibration responses. Incorporating both drum-inner ring rubbing faults and bolt joint effects, a dynamic model of the shaft-disk-drum-inner ring-vane-casing system (SDDIRVCS) is established with beam-shell hybrid elements to investigate the nonlinear dynamic responses induced by rubbing at various rotational speeds. The established dynamic model of the SDDIRVCS is validated by the comparison of its modal characteristics with those obtained from the ANSYS simulations. The results indicate that the rotor spectrum is dominated by odd-multiple harmonics, while the stator spectrum exhibits prominent even-multiple harmonics. Moreover, the rubbing location between the drum and the inner ring varies with the dynamic behavior of the rotor system.

Two interacting harmonic non-elliptical compressible liquid inclusions

Xu WANG, P. SCHIAVONE

2025, 46(10): 1955-1966. doi:10.1007/s10483-025-3309-8

Abstract ( 21 )

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We present the design of two interacting harmonic non-elliptical compressible liquid inclusions embedded in an infinite isotropic elastic matrix subjected to uniform remote in-plane stresses. The original constant mean stress (or the first invariant of the stress tensor) in the matrix remains undisturbed in the presence of the two harmonic liquid inclusions. The two non-elliptical liquid-solid interfaces are described by a four-parameter conformal mapping function that maps the doubly connected domain occupied by the matrix onto an annulus in the image plane. The closed-form expressions for the internal uniform hydrostatic stress fields within the two liquid inclusions are obtained. The hoop stresses are uniformly distributed along the two liquid-solid interfaces on the matrix side.

Vibration characteristic analysis of a cracked piezoelectric semiconductor curved beam

Qiaoyun ZHANG, Xiaoyan ZHANG, Jiahao XU, Zhicai SONG, Minghao ZHAO

2025, 46(10): 1967-1982. doi:10.1007/s10483-025-3307-6

Abstract ( 35 )

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The fracture mechanics theory posits that cracks induce strain energy concentration near their tips in structural components, generating localized flexibility that impedes crack propagation. Theoretically, cracks are represented as dimensionless, massless spring models, effectively capturing crack characteristics and cross-sectional properties at the crack location. Leveraging this spring-based representation, this study establishes an open-crack model for a one-dimensional (1D) piezoelectric semiconductor (PSC) curved beam under dynamic loading. This model enables the investigation of vibration characteristics in cracked structures. The analytical solutions for the electromechanical fields of the beam are derived using the differential operator method, and the natural frequencies together with the corresponding generalized mode shapes of the beam are determined analytically. Furthermore, the effects of the crack parameters on the natural vibration characteristics of the PSC curved beam are analyzed.

A new rope-sheave traction contact force model incorporating complex geometric features developed through parameter identification methods

Yunting HAN, Hui HU, Haoran SUN, Xi SHI

2025, 46(10): 1983-2006. doi:10.1007/s10483-025-3300-7

Abstract ( 47 )

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The complex geometrical features of mechanical components significantly influence contact interactions and system dynamics. However, directly modeling contact forces on surfaces with intricate geometries presents considerable challenges. This study focuses on the helically twisted wire rope-sheave contact and proposes a contact force model that incorporates complex geometric features through a parameter identification approach. The model’s impact on contact forces and system dynamics is thoroughly investigated. Leveraging a point contact model and an elliptic integral approximation, a loss function is formulated using the finite element (FE) contact model results as the reference data. Geometric parameters are subsequently determined by optimizing this loss function via a genetic algorithm (GA). The findings reveal that the contact stiffness increases with the wire rope pitch length, the radius of principal curvature, and the elliptic eccentricity of the contact zone. The proposed contact force model is integrated into a rigid-flexible coupled dynamics model, developed by the absolute node coordinate formulation, to examine the effects of contact geometry on system dynamics. The results demonstrate that the variations in wire rope geometry alter the contact stiffness, which in turn affects dynamic rope tension through frictional energy dissipation. The enhanced model’s predictions exhibit superior alignment with the experimental data, thereby validating the methodology. This approach provides new insights for deducing the contact geometry from kinetic parameters and monitoring the performance degradation of mechanical components.

Explicit approximate solutions to two transcendental equations in two-phase stratified flow

Baisheng WU, Yixin ZHOU, Zeyao CHEN, Siukai LAI

2025, 46(10): 2007-2016. doi:10.1007/s10483-025-3299-6

Abstract ( 21 )

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Stratified flow is a common phenomenon in horizontal tubes of two-phase flow systems. However, the existing methods for calculating the wetted angle of the flat interface model and the central angle of the two-circle model rely on solving implicit transcendental equations, which require iterative numerical root-finding methods, thereby introducing computational complexity and inefficiency. This paper proposes the high-precision explicit approximate solutions for the two models, directly correlating the geometric parameters with the flow parameters, thus significantly enhancing the efficiency and accuracy of two-phase flow analysis.

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