首页期刊导航|International journal of non-linear mechanics
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International journal of non-linear mechanics
Pergamon Press
International journal of non-linear mechanics

Pergamon Press

0020-7462

International journal of non-linear mechanics/Journal International journal of non-linear mechanicsSCIISTPEI
正式出版
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    Stochastic dynamics analysis of quasi-partially integrable Hamiltonian based on NN-SAM

    Hu, MenglinZan, WanrongJia, WantaoSun, Jiaojiao...
    1.1-1.20页
    查看更多>>摘要：Stochastic response and reliability analysis of quasi-partially integrable Hamiltonian systems are two important yet difficult problems due to high dimensionality and nonlinearity. Deep neural networks (DNNs) and the stochastic averaging method (SAM) can address the difficulty of system dimensionality in their own ways. This paper proposed a method called NN-SAM by merging physics-informed neural networks (PINNs) and SAM to solve the stochastic response and reliability of multi-dimensional quasi-partially integrable Hamiltonian systems. Firstly, by analyzing the resonance for quasi-partially integrable Hamiltonian systems, the averaged stochastic differential equations (SDEs) with less dimension for resonant and non-resonant cases through SAM are derived, respectively. Based on these averaged SDEs, the averaged Fokker-Planck-Kolmogorov (FPK) equation, the backward Kolmogorov (BK) equation and Pontryagin equation are obtained with mixed boundary conditions, including reflecting boundary, absorbing boundary or periodic boundary. Then, the PINNs are constructed for the response prediction and reliability assessment of the non-resonant case, including solving the averaged FPK equations, the BK equation and Pontryagin equation with or without periodic boundary conditions. For the resonant case, periodic layers are introduced as a hard constraint to the neural network to handle the periodic boundary conditions caused by resonance. Finally, two numerical examples are worked out and verified by the results from the Monte Carlo (MC) simulation. This work provides an effective technique for the stochastic response and reliability problems of quasi-partially integrable systems.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Size-dependent nonlinear dynamics of two-directional functionally graded microbeams in thermal environment under a moving mass

    Vu A.N.T.Nguyen D.K.
    1.1-1.15页
    查看更多>>摘要：© 2024 Elsevier LtdThe size-dependent nonlinear dynamics of two-directional functionally graded (2D-FG) microbeams in a thermal environment under a moving mass is studied for the first time in the framework of the refined higher-order shear deformation theory (HSDT) and modified couple stress theory (MCST). The variation of the temperature-dependent material properties in the axial and thickness directions is estimated by the Mori–Tanaka homogenization scheme. Considering the rotary inertia and shear deformation, the nonlinear differential equations of motion, obtained from Hamilton's principle, are discretized using an enriched beam element. Numerical results determined by the Newmark method in combination with Newton–Raphson iterative procedure confirm the efficiency of the derived beam formulation in predicting the nonlinear dynamics. The enriched beam element, which is derived herein by using hierarchical functions to enrich the conventional shape functions, is capable of furnishing accurate nonlinear dynamic characteristics with fewer elements compared to the conventional one. It is shown that the difference between the dynamic response predicted by the linear analysis and the nonlinear one increases by increasing the temperature, but it decreases by increasing the size scale parameter. The effects of the material gradation, temperature rise and micro-scale parameter on the nonlinear dynamic behavior of the 2D-FG microbeams are studied in detail and highlighted.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Hyperelasticity: Lennard-Jones potentials

    Kuznetsov, S. V.
    1.1-1.6页
    查看更多>>摘要：A set of the modified Lennard-Jones potentials used for modeling 1D hyperelasticity ensuring (i) positive definiteness of the tangent elastic modulus; (ii) a natural state at zero strain; and, (iii) negative stress at negative strain and vice versa. With these conditions the constructed set of the modified Lennard-Jones potentials allow modeling a broad range of elastic stress-strain states at both static and dynamic loadings. It has also been found that the considered potentials when applied to the problem of acoustic wave propagation, lead to the appearance of shock wave fronts, similar to those observed in bi-modular media with discontinuous elastic moduli.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Effect of the suspended block's weight on the nonlinear dynamics of a non-ideal magnetic levitation model connected to an energy harvester

    Kandil A.Francis A.C.Elsaid A.Zahra W.K....
    1.1-1.16页
    查看更多>>摘要：© 2024 Elsevier LtdMagnetic levitation (MAGLEV) technology over the years has attracted significant attention, not just for transportation purposes – as in MAGLEV trains and vehicles, but also for energy harvesting purposes. This paper presents a detailed study of a non-ideal magnetic levitation system, emphasizing the potential for energy harvesting while taking into account the weight of the oscillating suspended block in the middle. Geometry of axis translation is used to account for the new consideration of the middle block's weight. Both numerical simulations using Runge-Kutta method and analytical solution through the method of multiple scales are utilized to study the system's behavior. Numerical results confirm resonance behaviors of the middle block and electrodynamic shaker, supported by phase plane and Poincare maps describing system stability under varying conditions. Through the analytical findings, the study considers the system's response to mechanical-electrical damping variations and center magnet mass changes. Parametric variations reveal subtle effects on system dynamics, showing the relationship between damping, mass, and the oscillation amplitude. Moreover, power output analyses indicate that, at the presence of internal resonance, the power is approximately three times more than the case of absence of internal resonance. Overall, incorporating weight yields better power output, making the way for future research development in system design and application.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Tension/torsion of electroactive solid cylinders

    Rajagopal K.R.Wineman A.
    1.1-1.4页
    查看更多>>摘要：© 2024 Elsevier LtdIn his pioneering work in nonlinear elasticity, Rivlin studied the tension–torsion of a solid isotropic homogeneous elastic cylinder and obtained expressions for the twisting moment as well as the normal force for all bodies belonging to that class in terms of the angle of twist and the stretch. The deformation considered by Rivlin was a universal controllable deformation in that it can be engendered by just the application of the appropriate surface tractions. In this short note we consider the tension–torsion of a solid electroelastic cylinder under the action of an electric field along the axis of the cylinder, and determine expressions for the twisting moment and normal force that depend on the angle of twist, stretch and the applied electric field. We obtain an expression for the torsional rigidity of the electroelastic solid cylinder that depends on the electric field, thereby implying its torsional rigidity can be “tuned” by varying the electrical field. While within the context of classical Cauchy elasticity one observes the compression of the isotropic solid cylinder, namely the POYNTING effect, we show that the cylinder can be made shorter or longer by controlling the electrical field.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Research on nonlinear characteristics of multi-clearance gear system based on fractal theory

    Wang, LeDu, YanpingBai, HuijuanWang, Zhaohua...
    1.1-1.13页
    查看更多>>摘要：The presence of factors such as tooth side clearance, bearing clearance, and time-varying meshing stiffness introduces strong nonlinearity into mechanical system, significantly impacting the reliability and safety of mechanical equipment. When analyzing the dynamic characteristics of gear systems, the clearance factor can not be ignored. Few studies have considered the coupling effect of bearing clearance and tooth side clearance on the nonlinear characteristics of gear system, and the influence mechanism remain unclear. In this paper, a nonlinear dynamic model of a single-stage gear system with six degrees of freedom (6-DOF) was established, incorporating the coupling effects of tooth side clearance and bearing clearance. Using the control variable method, the tooth side clearance and bearing clearance were regarded as constant or dynamic clearance, respectively. The dynamic characteristics of the gear system were analyzed through time history chart, phase diagram, Poincare section diagrams, and fast Fourier transform (FFT) spectrum. When studying dynamic clearance, the influence of surface micromorphology on the clearance was considered based on fractal theory. The results showed that when tooth side clearance and bearing clearance were regarded as constants, the periodicity of the gear system remained essentially unchanged despite variations in clearance values. When tooth side clearance was considering as a fractal clearance and bearing clearance as a constant, the system's periodicity changed with variations in the fractal dimension D. When tooth side clearance and bearing clearance were treated as fractal clearances, the system transitioned from a chaotic state to a periodic state with increasing fractal dimension D. This paper provides a theoretical foundation for the design and manufacturing of gear and bearing surfaces in the future.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Dynamic analysis and vibration isolation characteristics of a compact quasi-zero-stiffness vibration isolator

    Wu, ShaopeiChen, MinHe, BoLi, Guofang...
    1.1-1.15页
    查看更多>>摘要：Aiming at the low-frequency vibration of high-precision instruments, this paper investigates a compact QuasiZero-Stiffness (CQZS) vibration isolator based on elastic materials with high static and low dynamic characteristics. This isolator is designed with a specific structure and parameter selection, making it a quasi-zerostiffness system with high static and low dynamic characteristics, and has the advantages of simple structure, high reliability, no friction, and good isolation performance. The article adopts the analytical idea of static analysis-dynamic analysis-vibration isolation performance analysis to derive the parameter conditions of the system with quasi-zero stiffness, and finite element simulation is used to verify the reliability of the theoretical derivation. The amplitude-frequency response of the system under simple harmonic force is solved based on the harmonic equilibrium method, and the saddle-node bifurcation set of the system is solved by the stability discriminant condition of Mathieu's equation, and the distribution of the periodical motion and the transition law in the parameter domain are investigated by multiparameter co-simulation, and the effects of the system parameters on the saddle-node bifurcation set and the force transmissibility are analyzed, and the performance of vibration isolation is evaluated. The study shows that: the system is induced by pitchfork bifurcation, saddlenode bifurcation, period-doubling bifurcation and boundary excitation to complete the transfer between the basic periodic motions; under the same parameter conditions, compared with the linear vibration isolation system, the resonance frequency ratio, the peak force transmissibility, and the starting vibration isolation frequency ratio of the CQZS vibration isolation system have been reduced by about 27%, 25.8%, and 62.98%, respectively, which broadens the vibration isolation frequency band, and the low-frequency isolation performance.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Study on shear creep test and nonlinear model of granite structural plane under coupled freeze-thaw cycle and chemical corrosion

    Zhang, FengruiYin, WeiZhang, KunJiang, Haopeng...
    1.1-1.15页
    查看更多>>摘要：To investigate the combined effect of freeze-thaw cycles and chemical corrosion on the shear creep characteristics of rock structural planes in cold regions, taking the granite structural planes of Huibai Tunnel in Jilin Province as the research object, microscopic structural observation and shear creep test were carried out on the structural surfaces treated by acidic, neutral and alkaline solution immersion and freeze-thaw cycles, analyzed the damage characteristics and creep mechanism of structural planes. The results show that: (1) With the increase of freeze-thaw and chemical corrosion, the structural plane of the mineral particles significantly reduced, the structural plane shows phenomena such as dissolution and hydrolysis, and the surface is gradually smoothed. (2) Compared with the natural condition, the instantaneous deformation of the samples under 20, 40, and 60 freeze-thaw cycles in H2SO4 solution increased by 47.43%, 64.52%, and 128.57%, the creep deformation increased by 36.58%, 53.68%, and 107.31%, and the instantaneous shear modulus decreased by 25.34%, 40.31%, and 64.35%. The instantaneous deformation, creep deformation and creep rate of the structural plane gradually increase with the increase of freeze-thaw and chemical corrosion, while the instantaneous shear modulus and long-term shear strength show a decreasing trend. (3) Compared with the natural condition, the instantaneous deformation of the samples in H2SO4, NaOH and NaCl solutions increased by 128.57%, 68.29% and 85.36% respectively under 60 freeze-thaw cycles, the creep deformation increased by 107.31%, 62.52% and 76.88% respectively, and the instantaneous shear modulus decreased by 64.35%, 50.31% and 56.54% respectively. The acidic H2SO4 solution has the greatest impact on the damage and creep parameters of the structural planes, followed by NaOH solution, with NaCl solution causing the least damage. Furthermore, in the damage process of structural planes, the freeze-thaw cycle and chemical corrosion promote each other mutually, since the combined influence of two-factor on damage and creep characteristics are greater than the influence of single factor. Based on the experimental results, considering the influence of freeze-thaw and chemical corrosion on model parameters, a nonlinear viscous element was introduced to describe the accelerated creep characteristics, the shear creep damage model of structural plane was established, and the reasonableness of the model was verified through test data. Finally, the three-dimensional roughness JRC3D of the structural plane was selected as the evaluation index, and the influence of the three-dimensional roughness JRC3D on the shear creep mechanical properties of the structural plane was discussed. The research results have guiding significance for the long-term stability evaluation of rock mass engineering in cold regions.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Nonlinear time-delay feedback control of a suspended cable under temperature effect

    Peng J.Xia H.Xie X.Lenci S....
    1.1-1.11页
    查看更多>>摘要：© 2024 Elsevier LtdIn engineering, controlling the vibration of suspended cables is crucial and urgent. Notably, prolonged exposure to varying temperatures alters the vibration characteristics of suspended cables, impacting the selection and effectiveness of control strategies. Given the advancements in temperature-sensitive materials and refined engineering needs, researching temperature effects on cable vibration control is essential. Consequently, this study explores the nonlinear vibration control of suspended cables under temperature variations using a time-delay velocity feedback strategy. A nonlinear dynamic model of time-delay vibration considering temperature effects is established based on Hamilton's principle. Comparative analysis quantitatively characterizes how temperature variations affect the inherent properties, nonlinear dynamics, and control strategies of suspended cables. Using the method of multiple scales, this study obtains analytical solutions for the primary resonance response. Analysis of three critical variables, sag-to-span ratio, control gain, and time delay under temperatures of −40∘C, 0‘∘C and +40∘C led to an optimal control parameter design that achieves a vibration control efficiency of 93.6%, underscoring the effectiveness of the time-delay feedback strategy.
      原文链接:
    • NETL
    • NSTL
    • Elsevier

    Torsional vibration behavior of compressor shaft system considering variable inertia characteristics of crank-connecting rod mechanisms

    Peng, FeiHuang, Yong
    1.1-1.14页
    查看更多>>摘要：The differential equation for the torsional vibration of the shaft system, which takes into account the variable inertia and nonlinear friction of the cylinder, has been established. This study investigates the influence of the connecting rod ratio, motor speed, reciprocating mass of the piston assembly, and cylinder damping on the vibration characteristics of the shaft system. First, the expression for the instantaneous moment of inertia of the crank-connecting rod-piston mechanism, which accounts for the connecting rod ratio, has been derived. Second, an experimental study on the vibration of the shaft system was conducted. The results indicated that the relative error between the numerical model calculations and the experimental data was 8.2%, demonstrating that the numerical model possesses good computational accuracy. Subsequently, the impact of the connecting rod ratio on the unbalance moment, torsional stress, and speed inhomogeneity within the shaft system was investigated. The findings reveal that an increase in the connecting rod ratio leads to an increase in the amplitude of these three parameters, and that the vibration energy shifts from low frequencies to high frequencies. The shaft system is more susceptible to high-frequency resonance phenomena, which can lead to velocity inhomogeneity and result in distortion phenomena. Ultimately, the effects of rotational speed, reciprocating mass of the piston assembly, and cylinder damping on the vibration behavior of the shaft system were analyzed using bifurcation and phase trajectory diagrams. The results indicate that a high rotational speed n is an element of (880,1000] r/min is beneficial for controlling the vibration behavior and amplitude of the shaft system. A moderate reciprocating mass mp is an element of [170, 270] kg can maintain the shaft's vibration behavior and amplitude within an optimal range. Enhancing the cylinder damping can transform it into an energy-dissipating element, thereby improving the vibration behavior of the shaft system. The research findings presented in this paper not only offer guidance for the design of the crank-rod structure but also provide a means to control the shaft system's vibration amplitude, preventing the occurrence of the "burning tile" phenomenon.
      原文链接:
    • NETL
    • NSTL
    • Elsevier