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The aim of this paper is to investigate the dynamic response of the resilient wheel equipped on the intercity train at the rail weld. A vehicle-track coupling dynamics model with resilient wheels is developed. A rigid multi-body system with 55 degrees of freedom is utilized to model the vehicle system. The rubber layer of the resilient wheel is modeled as a three-directional spring-damper unit between the wheel rim and the wheel core. For the track sub-model, the rails were modelled as Euler Beam and supported by concrete sleepers modelled as mass block. The vehicle and track motion equations are represented as mass-stiffness-damping matrixes. The accuracy of this modeling method at low frequencies is verified via the comparison between the field measured data and numerical results. The dynamic results of the rigid wheel are compared with those of the resilient wheel. Results show that the dynamic wheel-rail force of the rigid wheel is slightly higher than that of the resilient wheel. Furthermore, the mass factor is introduced to investigate the effect of the rubber layer position on the tire acceleration and the wheel-rail impact force. The numerical simulation results are expected to provide references for resilient wheel application into the intercity train.

Transverse vibration of a circular cross sectional micro-rod subjected to a new kind of boundary constraints with elastic torsional springs is presented based on nonlocal elasticity. A nonl...

The one-dimensional nanoscaled bar is commonly seen in current nanodevices, and it plays a significant role in nanoelectromechanical system (NEMS) and related nanotechnology. Motivated by this, the paper is concerned with the bending and stability of a nanoscaled bar especially a flexible bar subjected to vertical concentrated, vertical linearly distributed, and horizontal concentrated forces simultaneously. The theoretical model is developed by employing Eringen’s nonlocal differential law. Hence, the nonlocal differential constitutions in terms of stress and bending moment at a nanoscale are applied to the classical equilibrium formulation in order to construct the nonlocal constitutive model and then determine the analytical solutions for bending of such a nanoscale bar. Subsequently, the effect of a nonlocal scale on the midpoint deflections and internal forces is shown numerically, and the internal and external characteristic length scales are also examined. It is revealed that the capacity of resisting compression decreases with increasing the nonlocal effect since the internal characteristic scale cannot be neglected by comparing with the external characteristic scale. There exists a threshold value for bending stiffness. Both the midpoint deflection and bending moment vary monotonously when the material bending stiffness exceeds the threshold value, while the mechanical quantities fluctuate when the bending stiffness is less than its threshold value, namely, for a flexible nanoscaled bar. Accordingly, two different kinds of nonlocal predictions and the related disputes are resolved in the context of Eringen’s nonlocal differential law. The work is expected to be useful for the design, application, and optimization of nanoscaled bars sustaining bending with linear vertical and horizontal forces.

The present study is motivated by the shock response of a nano-cantilever component in nano-scaled electromechanical system (NEMS). For this purpose, the mechanical properties of a cantilevered nano-beams subjected to impact load are presented for the first time. Our work is concerned with the special moment that the impact deformation gets most and the impact velocity reduces to zero. The nonlocal theory proposed by Eringen is applied to reveal the nonlocal effect involved in impact behaviors at nano-scale. To this end, the classical impact stress is determined first using the law of conservation of energy. Subsequently, the nonlocal impact stress is obtained from the nonlocal constitutive equation and clamped-free boundary constraints of cantilevered nano-beams, where an imaginary equivalent symmetrical nano-structure is constructed to solve the unknown coefficients in general solution of stress of nonlocal field. The bending moment in nonlocal theory is gained from the stress of nonlocal field and the deflection in nonlocal field under impact load is calculated. Finally, the nonlocal dynamical load coefficient is derived via the maximal nonlocal impact deflection divided by the corresponding traditional static deflection at free edge. In numerical examples, the maximal stress of nonlocal field, the maximal nonlocal impact deflection, and the nonlocal dynamical load coefficient are calculated, respectively, to show the significant nonlocal small-scale effect in cantilevered nano-beams subjected to impact load. The conclusion is that the nonlocality plays a remarkable role in nano-scaled impact behaviors and it cannot be neglected. The existence of scale coefficient decreases the nonlocal impact stress, deflection, and dynamical load coefficient. On the contrary, the impact velocity results in a higher nonlocal impact stress, deflection, and dynamical load coefficient. With increasing the scale coefficient, the nonlocal effect increases and the strengthening physical manifestation of nano-structural equivalent stiffness becomes even more pronounced. The results reported herein are expected to provide a useful reference for understanding the scale effect in dynamic impact that often occurs in the working process of NEMS.

Based on the nonlocal elasticity theory, the vibration behavior and wave propagation of functionally graded Euler nanobeams with axial motion are investigated. Assuming that the axial velocity of nanobeams is a constant and the graded material parameters vary along the thickness direction in terms of power index, we apply the hypothesis of neutral plane to derive the axial displacement of geometry surface caused by non-uniformity of graded materials. Effects of graded index, axial velocity and nonlocal scale parameter on natural frequencies are analyzed through numerical examples. Also, the relationship between wave propagation frequency, wave velocity and wave number is revealed. The complex mode method is utilized to solve the governing equation, and the natural frequencies and wave velocity are obtained accordingly. To solve the derived transcendental equations, the Newton iteration method is used and a detailed solution flowchart is provided. For vibration, with the increase of non-dimensional axial velocity, non-dimensional nonlocal parameter and gradient index, natural frequencies decrease. For wave propagation, with the increase of wave number, frequency of wave propagation increases. However, with the increase of wave number, velocity of wave propagation decreases. Moreover, increasing the gradient index causes a decrease in frequency and velocity of wave propagation, increasing the axial velocity causes an increase in frequency and velocity of wave propagation, and increasing the nonlocal parameter causes a decrease in frequency and velocity of wave propagation.

The transverse free vibration and wave propagation of functionally graded microbeams with an axial motion are investigated based on a nonlocal theory and the Timoshenko beam model. It is assumed the material properties of functionally graded microbeams vary along the thickness direction. The neutral plane of functionally graded materials is introduced, and the inhomogeneity of functionally graded Timoshenko microbeams is considered. The governing equations are derived using Hamilton’s principle, and the differential quadrature method is utilized to determine the first three-order natural frequencies of the microbeams with simply supported and clamped boundary conditions, respectively. The effects of gradient index, nonlocal parameter and axial velocity on natural frequencies are investigated. Moreover, the wave propagation characteristics of functionally graded Timoshenko microbeams are analyzed, and the significant influences of wave number and other variables on wave propagation frequencies and wave velocities are studied. The different influence patterns of nonlocal effect are observed in transverse vibration and wave propagation. The nonlocality shows a weakening phenomenon in transverse vibration of axially moving functionally graded Timoshenko microbeams, while it reveals both weakening and strengthening phenomena in wave propagation. Therefore, two kinds of existing nonlocal scale effects are further confirmed and this is an additional contribution of the present paper.

To clarify the train-track traction behaviour in the low adhesion zone, a three-dimensional (3D) train-track coupling dynamic model was developed, in which the train was modelled as a rigid multi-body system with 8 vehicles. The vehicles are connected through coupler devices, which are simplified as nonlinear springs and dampers. The modified FASTSIM algorithm is utilized to obtain the wheel/rail creep force, which can consider the interfacial conditions. A new anti-slip control algorithm was proposed where the traction power could be adjusted to ensure the maximum utilization of wheel/rail adhesion. This control algorithm is achieved by iterating among the traction power, rotational speed and rotational acceleration of each wheelset. Numerical simulation results showed that the traction force would be reduced to a certain level to achieve maximum admissible force when the anti-slip control algorithm is activated. The rotational speed, traction force, creep force, creepages, and coupler force in contaminated conditions were investigated. The results show that the model can effectively simulate the traction process under the low adhesion state, which provides a certain theoretical reference for railway applications.

Nowadays, numerous supervised deep learning models have been applied to bearing fault diagnosis. However, labelling the health states of the bearing vibration data is a time-consuming work and dependent on expert experience. In order to tackle this problem, a novel unsupervised bearing fault diagnosis method named adversarial flow-based model is explored in this paper. Flow-based model is a type of generative models that is proved to be better than other types in many aspects. This paper introduces the flow-based model into the field of machinery fault diagnosis, and designs an appropriate model architecture so as to train the model in unsupervised and adversarial ways. The proposed model contains an autoencoder (AE), a flow-based model, and a classifier. Firstly, the AE maps the vibration data from signal space to latent vector space. Then, the flow-based model aligns the distributions of the latent vectors of different bearing states with specific prior distributions. Finally, the classifier tries to discriminate the aligned latent vectors from the vectors sampled from the prior distributions. With the help of distinguishable prior distributions and the adversarial training mechanism between the classifier and the flow-based model together with the AE, the bearing data with the same health states are clustered into the same areas. The good clustering performance of the adversarial flow-based model is verified by a dataset with 10 health states from a bearing test rig.

A semi-continuum dynamical model involving the relaxation effects is constructed to investigate the mechanical properties of the lateral bending vibration of an ultra-thin beam with a nanoscale thickness. The governing equation of vibration is derived based on the Hamilton principle. Three different kinds of end supporting conditions including fully clamped, simply supported and cantilevered nanoscale ultra-thin beams are considered and various numerical results are analyzed and discussed in detail. Some comparisons between the semi-continuum and classical continuum models are presented. It is concluded that the variational tends of natural frequencies depend on the values of relaxation coefficient. For different relaxation coefficients, the natural frequencies may decrease or increase with an increase in the number of atomic layers. Hence an explanation is proposed for some contradictions that the bending stiffness of the nanoscale beams should be enhanced or weakened in current non-local elasticity theory. Moreover, the relations between the Young's modulus and the number of atomic layers are developed and it is clearly seen that the small scale has a significant effect on the Young's modulus. When the number of atomic layers, or the thickness of the beam is sufficiently large, the small scale effects disappear and the value of the Young's modulus is just recovered to the corresponding classical bulk material, which also proves the validity of the semi-continuum dynamical model proposed in this study.

Recently, there have been an increasing number of studies on nonlocal theoretical models, of which different kinds of nonlocal elasticity approaches including softening and hardening models have been investigated extensively. In the present work, the longitudinal dynamic behaviors of some common one-dimensional nanostructures (e.g. nanorods/nanotubes) were examined using the hardening nonlocal approach. The hardening nonlocal longitudinal stress was employed and an eigenvalue analysis method was utilized in deriving some dynamic characteristics of the minute structures at nanoscale. The effects of a dimensionless nonlocal small scale parameter at molecular level unavailable in classical rods/tubes were investigated. Subsequently, nonlocal longitudinal vibration responses under various boundary conditions including soft and hard constraints were determined through a numerical method. The correlations between natural frequencies and the nonlocal nanoscale parameter were obtained and discussed in detail. Within the framework of hardening nonlocal stress theory, it concludes for the first time that the longitudinal free vibration frequencies of nanorods/nanotubes are higher than those based on the classical continuum mechanics but they are quite different from the softening nonlocal model. The strengthening effects on nonlocal stiffness of nanorods/nanotubes are observed and they are consistent with some other theoretical approaches or atomistic simulations. In particular, a case study on nonlocal natural frequencies of carbon nanotubes (CNTs) was presented and the results were calculated by atomistic simulations, classical continuum theory, softening and hardening nonlocal models, respectively. The validity of both existing softening and hardening nonlocal models was confirmed in comparison with the atomistic simulations. In addition, a comparative calculation for dimensional natural frequencies with respect to length of CNTs by different methodologies was provided to explain why the softening and hardening nonlocal models are both correct in nonlocal elasticity theory.

This paper presents eight-node solid-shell elements for geometric non-linear analyze of piezoelectric structures. To subdue shear, trapezoidal and thickness locking, the assumed natural strain method and an ad hoc modified generalized laminate stiffness matrix are employed. With the generalized stresses arising from the modified generalized laminate stiffness matrix assumed to be independent from the ones obtained from the displacement, an extended Hellinger-Reissner functional can be derived. By choosing the assumed generalized stresses similar to the assumed stresses of a previous solid element, a hybrid-stress solid-shell element is formulated. The presented finite shell element is able to model arbitrary curved shell structures. Non-linear numerical examples demonstrate the ability of the proposed model to analyze nonlinear piezoelectric devices.

This paper investigates dynamic behavior of multilayered piezoelectric diaphragms that are simplified as laminated plates. The validity of the dynamic analysis based on the simplified clamped multilayered plate model has first been studied using ANSYS finite element (FE)-codes. The simplified, clamped, multilayered plate model has been verified to be a reasonable one in comparison with the exact model. Subsequently, the frequency characteristics of clamped rectangular piezoelectric laminated plates were further analytically investigated. Using the classical laminated plate theory, mechanical, electrical, and electromechanical characteristics of the multilayered piezoelectric diaphragms were studied. For ease of calculation, the dimensionless method was adopted. Furthermore, numerical analysis was carried out using the Rayleigh-Ritz method. Influence of dimensions of the laminar diaphragm on natural frequencies also was studied. The thickness ratio of the PZT layer to the total thickness of the laminar diaphragm has been optimized to obtain the largest deflection.