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
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    A Lorenz model for an anelastic Oberbeck-Boussinesq system

    Grandi D.Passerini A.Trullo M.
    1.1-1.6页
    查看更多>>摘要：© 2024 The AuthorsIn an Oberbeck–Boussinesq model, rigorously derived, which includes compressibility, one could expect that the onset of convection for Bénard's problem occurs at a higher critical Rayleigh number with respect to the classic O–B solutions. The new partial differential equations exhibit non constant coefficients and the unknown velocity field is not divergence-free. By considering these equations, the critical Rayleigh number for the instability of the rest state in Lorenz approximation system is shown to be higher than the classical value, so proving increased stability of the rest state as expected.
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    A generalized incremental harmonic balance method by combining a data-driven framework for initial value selection of strongly nonlinear dynamic systems

    Li Y.L.Huang J.L.Zhu W.D.
    1.1-1.22页
    查看更多>>摘要：© 2024 Elsevier LtdThe incremental harmonic balance (IHB) method is a semi-analytical and semi-numerical method that consists of the harmonic balance process and the Newton–Raphson iteration process, which can accurately obtain solutions of strongly nonlinear dynamic systems, and has been successfully applied to many practical problems. However, it is difficult to choose proper initial values for the Newton–Raphson iteration process, especially for strongly nonlinear dynamic systems, which can cause divergence of the IHB method. A novel generalized IHB method by combining a data-driven framework to obtain feasible initial values for strongly nonlinear dynamic systems is proposed in this work. In the proposed data-driven framework, an artificial neural network (ANN) is trained to learn the mapping between small system parameters of a weakly nonlinear dynamic system and corresponding solutions of the IHB method. The amount of data required for training is determined by the number of system parameters, which is usually only a few hundreds to a few thousands, making the training process very expeditious. Once the trained ANN receives other system parameters of a nonlinear dynamic system, it can immediately output a set of feasible initial values for the IHB method, which can make the IHB method quickly converge. Results from extensive testing indicate that the mapping learned by the ANN is effective not only for weakly nonlinear dynamic systems that are characterized by smaller system parameters, but also for strongly nonlinear dynamic systems in most cases that involve larger system parameters. During the testing for strongly nonlinear dynamic systems, successful convergences generate new training data. These data can be leveraged to further fine-tune the ANN to yield an improved ANN, which allows continuous refinement of the ANN and enhances prediction of initial values for strongly nonlinear dynamic systems. With the introduction of this simple yet highly efficient data-driven initial value selection framework, the applicability of the IHB method can be significantly enhanced. Three numerical examples are presented to show the efficiency and advantages of the present methodology.
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    Experimental and numerical investigations of the effects of bundled conductor on seismic responses of interconnected electrical equipment

    He C.Guo Y.Zhou C.Jiang L....
    1.1-1.17页
    查看更多>>摘要：© 2024 Elsevier LtdWith a main function of power transmission, bundled conductors bring in strong nonlinearity for the connected electrical equipment in substations. Investigations of their effects on seismic responses of interconnected electrical equipment (IEEQ) are few in literature, lacking studies from an experimental perspective. Thus, shaking table tests were performed on a scaled ultra-high voltage IEEQ. The tests examine the effects of slackness, bending stiffness, number of spacers, and damping of the bundled conductors. Besides, the influence of earthquake input directions is also analysed. Moreover, a numerical model is developed to conduct parameter analyses to investigate the influence of bundled spacing and equipment frequency. The results indicate that the connection of the conductors reduces the IEEQ relative displacement. It overall increases the stress responses of the higher-frequency equipment while reduces those of the low-frequency equipment. The effects of slackness are related to the damping and stiffness effects of bundled conductors, since the latter can decrease the seismic responses of the IEEQ. Besides, the effects of bundled conductors on the out-of-plane and vertical responses of the IEEQ can be neglected per the test results. Finally, bundled conductors may twist during earthquakes, the spacers thereby should be positioned appropriately to prevent this issue.
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    Universal relations for electroactive solids undergoing shear and triaxial extension

    Rajagopal K.R.Wineman A.
    1.1-1.5页
    查看更多>>摘要：© 2024In this article we establish universal relations for a cube of a nonlinear elastic isotropic electroactive solid that undergoes a homogeneous deformation due to shear tractions but no normal tractions. When there is no electric field, in addition to a shearing deformation, the cube's dimensions change because of the Poynting effect. In this work, we study the influence of the electric field vector on these dimensional changes using a previously developed constitutive equation for nonlinear electroactive solids. Expressions are obtained for these dimensional changes that depend the amount of shear for different directions of the electric field vector relative to the shearing direction. In addition, universal relations are obtained when there is no electric field and are extended for different electric field directions.
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    Research on lateral–torsional coupled vibration induced by substantial imbalance in an overhung flexible rotor

    Yu P.Jiang Z.Tao X.Li S....
    1.1-1.16页
    查看更多>>摘要：© 2024 Elsevier LtdSubstantial imbalance is a real possibility in aero–engines and is usually caused by blade off, bird strikes, etc. A substantially unbalanced rotor system will exhibit extremely complicated nonlinear lateral–torsional behavior, and the related dynamics are critical to the safe design of a rotor system. In this paper, a comprehensive nonlinear model of an imbalanced flexible rotor system is proposed, in which translational–torsional coupling and angular–torsional coupling are introduced simultaneously. Based on the model, the lateral–torsional coupling features are discussed, and the lateral as well as the torsional vibration behaviors are further analyzed in detail. The results show that the lateral–torsional coupling factors only exist under the nonsynchronous whirl condition. Thus, if the imbalance is small, the lateral vibration exhibits the linear feature of a traditional unbalanced response, and the torsional vibration does not occur in steady state. However, under substantially unbalanced conditions, the vibration responses are significantly changed. In lateral vibration, many combined frequency components between rotation frequency (fu) and torsional natural frequency (ft1 and ft2) such as fu-ft1, fu-2ft1 and fu-ft2 can be induced, which can lead to combined resonance phenomena and many additional resonance peaks. The lateral–torsional coupling effect is strong at that time. Both the lateral translational–torsional coupling excitation and lateral angular–torsional coupling excitation exhibits the multiple harmonics whose frequencies are closely related to ft1 and ft2. Consequently, the torsional vibration in those combined resonance regions can be very high. The corresponding vibration exhibits the steady harmonic feature with vibration frequency being ft1 or ft2.
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    A general solution procedure for nonlinear single degree of freedom systems including fractional derivatives

    Yildiz B.Sinir S.Sinir B.G.
    1.1-1.16页
    查看更多>>摘要：© 2024 Elsevier LtdThis paper considers oscillations of systems with a single-degree-of-freedom (SDOF) including fractional derivatives. The system is assumed to be an unforced condition. A general solution procedure that can be effectively applied to various types of fractionally damped models, where damping is defined by a fractional derivative, in engineering and physics is proposed. The nonlinearity of the mentioned models contains not only damping but can also consist of acceleration or displacement. This study proposed a new general model that includes but not limited to modified fractional versions of the well-known linear, quadratic, Coulomb and negative damped models. The method of multiple time scales is performed to obtain approximate analytical solutions. The solution, the amplitude, and the phase in the applications are plotted for various fractional derivative parameter values. In order to confirm their validity, our results for the case of the fractional derivative parameter equal to one are compared with others available in the literature.
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    Surface instability of a finitely deformed magnetoelastic half-space

    Shahsavari D.Saxena P.
    1.1-1.16页
    查看更多>>摘要：© 2024 The AuthorsMagnetorheological elastomers (MREs) are soft solids that can undergo large and reversible deformation in the presence of an externally applied magnetic field. This coupled magneto-mechanical response can be used for active control of surface roughness and actuation in engineering applications by exploiting the reversible instabilities in these materials. In this work, we develop a general mathematical formulation to analyse the surface instabilities of a finitely deformed and magnetised MRE half-space and find the critical stretch that causes bifurcation of the solution of the resulting partial differential equations. The equations are derived using a variational approach in the reference configuration and the null-space relating the incremental solutions is presented to provide a basis for post-bifurcation analysis. Details of the numerical calculations are presented to clearly identify and discount non-physical solutions. Stability phase diagrams are presented to analyse the effect of material parameters and strength/direction of magnetic field.
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    Corrigendum to “Slip with friction boundary conditions for the Navier–Stokes-α turbulence model and the effects of the friction on the reattachment point” [Int. J. Non–Linear Mech. 159 (2024) 104614] (International Journal of Non-Linear Mechanics (2024) 159, (S0020746223002664), (10.1016/j.ijnonlinmec.2023.104614))

    Ilhan O.
    1.1-1.1页
    查看更多>>摘要：© 2024 Elsevier LtdThings to be requested changes: 1. Review article [Formula presented] Research article 2. Department of Mathematics, Faculty of Scie, Mugla Sitki Kocman University, Mugla, 48000, Turkiye.[Formula presented] Department of Mathematics, Faculty of Science, Mugla Sitki Kocman University, Mugla, 48000, Turkiye. The authors regret < insert corrigendum text>. The authors would like to apologise for any inconvenience caused.
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    Derivation of a stability and non-bifurcation criterion for frictional contact problems

    Antoni N.
    1.1-1.12页
    查看更多>>摘要：© 2024 Elsevier LtdBifurcation and stability of irreversible systems in plasticity have widely been studied in the literature devoted to Solid Mechanics and are now well understood. The same criteria are of great importance in frictional contact problems as they define the allowable limits of the service domain for frictional contact interfaces prior to their failure due to those mechanisms. In this paper, it is shown that uniqueness, bifurcation and stability in the sense of Hill can be obtained for associated friction, via the established asymptotic equivalence with elastic-perfect plasticity, when the intermediate elastic-plastic layer tends towards the contact interface. The problem formulation and its discretization by the finite element method then lead to the solving of an eigenvalue problem in the vicinity of the limit state for which a static condensation can be performed on the discrete contact interface. The application of the derived stability and non-bifurcation criterion is finally illustrated through two worked examples.
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    Nonlinear dynamics and motion bifurcations of 12-pole variable stiffness rotor active magnetic bearings system under complex resonance

    Ma W.S.Liu F.H.Lu S.F.Huang S....
    1.1-1.18页
    查看更多>>摘要：© 2024 Elsevier LtdIn this study, we analyze the nonlinear dynamic characteristics of a 12-pole variable stiffness rotor active magnetic bearings (rotor-AMBs) under intricate resonance conditions. Using the principles of electromagnetic bearings, a model for the 12-pole variable stiffness rotor-AMBs system is developed. Next, the dynamic equations for a two-degree-of-freedom 12-pole variable stiffness rotor-AMBs system are derived, incorporating both quadratic and cubic nonlinearities, through Newton's second law. Considering the primary parametric resonance, 1:1 internal resonance, and 1/2 subharmonic resonance, the multiple time scale perturbation method is applied to derive the average equation of the system. Based on these averaged equations, the characteristics and complex dynamics of the system are analyzed. Finally, MATLAB software is employed for numerical simulations of the 12-pole variable stiffness rotor-AMBs system. The simulation results indicate that the nonlinear control parameters can modify the system's softening and hardening spring behaviors. Varying the parametric excitation amplitude leads to diverse dynamic behaviors, including single-periodic motion, double-periodic motion, and chaotic vibrations.
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