DYNAMIC BEHAVIORS OF CONDUCTIVE CIRCULAR PLATE IN TIME-VARYING MAGNETIC FIELDS

In this study, we proposed an analytical solution for eddy currents as well as electromagnetic forces of a conductive circular plate in a time varying magnetic field. Specifically, an analytical series solution for eddy currents in a circular plate subjected to an axisymmetrie time varying magnetic field has been proposed based on the T-method that has been widely used in the eddy current analysis of conductive and superconductive structures. Accordingly, the dynamic response, the dynamic instability and the magnetic damping of a circular plate in a transverse transient magnetic field as well as a stationary in-plane magnetic field have also been obtained. The analytical series solution proposed in this work as well as the subsequent numerical analysis not only confirmed the emergence of dynamic instability of a circular plate in a strong transverse magnetic field, but also demonstrated the existence of magneto-damping of a circular conductive plate in an in-plane magnetic field. The method developed in this paper provides a potential new possible way by which the analysis of the electromagnetic coupling problems of conductive structures can be simplified.     

基于绝对节点坐标的多柔体系统动力学高效计算方法

绝对节点坐标法已经被广泛应用于柔性多体系统的动力学研究之中, 但是其计算效率问题尚未得到很好的解决. 基于绝对节点坐标方法计算弹性力及其对广义坐标的偏导数矩阵(Jacobi矩阵), 通常是基于第二类Piola-Kirchhoff应力张量来完成, 计算效率不高.根据虚功原理并采用第一类Piola-Kirchhoff应力张量的方法直接推导得到了弹性力及其Jacobi矩阵的解析表达式. 基于不同方法所得的数值算例结果对比研究表明, 该方法可使计算效率大大提高.      

Analytical formulations of image forces on dislocations with surface stress in nanowires and nanorods

The interaction between dislocations and surfaces is usually characterized by image forces. Most analytical solutions to image forces could be found in literatures for two-dimensional (2D) solids with or without the consideration of surface stress. This work provides alternative analytical formulations of image forces for nanowires which are in more flexible forms compared with the infinite power series solutions from complex variable method. Moreover, this work proposes analytical formulations of image forces for nanorods (3D) by approximating the 3D shape effect as a height-dependent shape function, which is obtained through curve fitting of the finite element results of image forces without surface stress. The results of nanowires are demonstrated to be acceptable compared with the classical solution and complex variable method. More importantly, the analytical formulation of nanorods has not been found in other literatures so far. This work could contribute to nanostructure design and provide guidance for the fabrication of high quality nanostructures.     

Tire-soil interaction model for turning (steered) tires

A review of the experimental information on the development of lateral forces on tires traveling at an angle to their center plane is presented and the usefulness of the consideration of the lateral forces for the development of an analytical model is evaluated. Major components of the lateral force have been identified as the forces required to balance the tractive force and the drawbar pull vectorially. The lateral forces are generated by the shear stresses developing in the contact area and the horizontal component of the normal stresses acting on the in-ground portion of the curved side walls of the tire. The tire-soil interaction model for steady state straight travel has been expanded to include the necessary algorithms for the calculation of these lateral forces. The pattern of tractive force-slip and longitudinal-lateral force relationships is in general agreement with experiments.     

Mechanics of thermophoretic and thermally induced edge forces in carbon nanotube nanodevices

A double walled carbon nanotube thermal actuator consisting of a short outer tube sliding along a long inner tube under a temperature gradient is used as a model system to investigate the mechanics of thermophoretic and thermally induced edge forces in nanoscale contact based on the theory of lattice dynamics. It is shown that the total thermophoretic force has two components: a gradient force due to the change in van der Waals energy in the direction of temperature gradient and an unbalanced edge force due to the temperature difference between the two tube ends. Closed-form analytical expressions are derived for the gradient and unbalanced edge forces, with results in excellent agreement with molecular dynamics simulations. This study represents a first analytical study of thermophoretic and thermally induced edge forces between two solid bodies, and may have far reaching implications on thermomechanical nanodevices and nanoscale contact.     

Passage of a subsonic flow around V-shaped wings

In view of the problems involved in the design of hypersonic aircraft great interest has arisen in recent years as to the behavior of wings in fast supersonic flows. Two main approaches have been used: a study of hypersonic flow around traditional wings, and a search for new configurations with optimum aerodynamic properties. Aerodynamic [1, 2], heat-transfer [3], and stability investigations (for V-shaped wings in super- and hypersonic flows) belong to the latter category. Before attaining supersonic flight the aircraft has to overcome the range of subsonic velocities. In this connection it is important to study flow around V-shaped wings at M < 1. Little research has been devoted to flow around such configurations at subsonic velocities, principal attention having been directed at the study of rapid flow around aircraft configurations with V-shaped wings or tails. The results of analytical and numerical calculations allowing for the interference of transient aerodynamic forces acting on a V-shaped and mutiple-fin tail group in combination with the fuselage were presented in [4, 5]. An experimental study of V-shaped wings as regards the influence of the wing dihedral angle on the aerodynamic characteristics of a model aircraft was presented in [6, 7].Translated from Zhurnal Prikladnoi Mekhaniki i Technicheskoi Fiziki, No. 4, pp. 102–106, July–August, 1975.     

Electrical body forces and electrical tractions in the nonlinear response of ferroelectric actuators

The influence of the electrical body forces and electrical tractions on the nonlinear response of ferroelectric stack actuators is analytically investigated. While the role of the electrical body forces and tractions in the response of piezoelectric actuators is well documented (and in many cases is not significant), the questions of their effect on ferroelectric active materials is still of interest. To examine this influence, the analytical model for the electro-mechanical behavior of a ferroelectric stack actuator is augmented to account for the electrical body forces along the actuator and the electrical tractions at the material–electrode interfaces. Focusing on the effect of the electrical forces and tractions on the ferroelectric domain switching phenomenon, the model is used for the numerical analysis of a ferroelectric layer and for the comparison with the case that neglects the electrical body forces and traction. The comparison theoretically designates cases in which the effect of the electrical body forces and tractions may be prominent and other cases where the classical approach that neglects these effects can be adopted.     

Hydrodynamics of flow along the wall of a rotating cup

A study has been carried out of the influence of inertial and Coriolis forces on the hydrodynamics of flow along the inner wall of a rotating cup. It is shown that when these forces are pronounced, the liquid velocity components may be considerably less than those predicted from simple analyses based solely upon a balance of centrifugal and viscous forces, and the velocity at the lip may consequently be critically dependent upon the position of the feed.     

Interaction of an edge dislocation with a coated elliptic inclusion

This paper presents an analytical solution for plane elasticity problems of an elliptically cylindrical layered media subject to an arbitrary edge dislocation. Based on the technique of conformal mapping and the method of analytical continuation in conjunction with the alternating technique, the general expressions of the displacements and stresses, where an edge dislocation is located in matrix, coating layer and inclusion are obtained. The numerical results of image forces exerted on a generalized edge dislocation are carried out by using the generalized Peach–Koehler equation. As a numerical illustration, both the image forces and equilibrium positions are presented for different material combinations and relative thickness of a coating layer. The result shows that the thickness and the shear modulus of the coating layer have a strong influence on the stability of dislocation.     

FLUTTER INSTABILITY OF SUPPORTED PIPES CONVEYING FLUID SUBJECTED TO DISTRIBUTED FOLLOWER FORCES

In the past decades,it has been reported that divergence is the expected form of instability for fluid-conveying pipes with both ends supported.In this paper,the form of instability of supported pipes ...     

Analytical models and laboratory measurements of the soil-tool interaction force to push a narrow tool through JSC-1A lunar simulant and Ottawa sand at different cutting depths

Excavation equipment for developing NASA’s lunar outpost must be carefully designed to reduce launch cost, minimize operation cost, and enhance reliability. Excavation equipment requires knowledge of the stresses and strains in the equipment caused by the forces experienced during excavation. The types of excavation anticipated indicate that blade tools would move the most material. There are several analytical models available to predict forces from blade tools interacting with soil; however, it is not clear which if any, can predict lunar excavation forces precisely enough. Consequently, we measured the forces to push narrow (2.5-cm wide) square and round rods through a control material, Ottawa sand, and JSC-1A lunar mare regolith simulant at different cut depths in a controlled laboratory setting. The measurement results were compared with the forces predicted by eight analytical models. The Zeng, Luth and Wismer, and the Qinsen and Suren models fit the measurements best, considering that our study was limited to pushing stimulant and sand with small rods. The results show that depth of cut has a dramatic effect on the soil-tool interaction forces. Consequently, lunar missions should use a series of shallow cuts to reduce equipment size and power requirements.     

Noise influenced elastic cantilever dynamics with nonlinear tip interaction forces

In this work, the authors study the influence of noise on the dynamics of base-excited elastic cantilever structures at the macroscale and microscale by using experimental, numerical, and analytical means. The macroscale system is a base excited cantilever structure whose tip experiences nonlinear interaction forces. These interaction forces are constructed to be similar in form to tip interaction forces in tapping mode atomic force microscopy (AFM). The macroscale system is used to study nonlinear phenomena and apply the associated findings to the chosen AFM application. In the macroscale experiments, the tip of the cantilever structure experiences long-range attractive and short-range repulsive forces. There is a small magnet attached to the tip, and this magnet is attracted by another one mounted to a high-resolution translatory stage. The magnet fixed to the stage is covered by a compliant material that is periodically impacted by the cantilever’s tip. Building on their earlier work, wherein the authors showed that period-doubling bifurcations associated with near-grazing impacts occur during off-resonance base excitations of macroscale and microscale cantilevers, in the present work, the authors focus on studying the influence of Gaussian white noise when it is included as an addition to a deterministic base excitation input. The repulsive forces are modeled as Derjaguin–Muller–Toporov (DMT) contact forces in both the macroscale and microscale systems, and the attractive forces are modeled as van der Waals attractive forces in the microscale system and magnetic attractive forces in the macroscale system. A reduced-order model, based on a single mode approximation is used to numerically study the response for a combined deterministic and random base excitation. It is experimentally and numerically found that the addition of white Gaussian noise to a harmonic base excitation facilitates contact between the tip and the sample, when there was previously no contact with only the harmonic input, and results in a response that is nominally close to a period-doubled orbit. The qualitative change observed with the addition of noise is associated with near-grazing impacts between the tip and the sample. The numerical and experimental results further motivate the formulation of a general analytical framework, in which the Fokker–Planck equation is derived for the cantilever-impactor system. After making a set of approximations, the moment evolution equations are derived from the Fokker–Planck equation and numerically solved. The resulting findings support the experimental results and demonstrate that noise can be added to the input to facilitate contact between the cantilever’s tip and the surface, when there was previously no contact with only a harmonic input. The effects of Gaussian white noise are numerically studied for a tapping mode AFM application, and it is shown that contact between the tip and the sample can be realized by adding noise of an appropriate level to a harmonic excitation.     

Peristaltic flow of Walter’s B fluid in endoscope

The peristaltic flow of a Walter’s B fluid in an endoscope is studied.The problem is modeled in a cylindrical coordinate system.The main theme of the present analysis is to study the endoscopic effects on the peristaltic flow of the Walter’s B fluid.To the best of the authors’ knowledge,no investigation has been made so far in the literatures to study the Walter’s B fluid in an endoscope.Analytical solutions are obtained using the regular perturbation method by taking δ as a perturbation parameter.The appro...     

Control with trim tabs and history-dependent aerodynamic forces

This analytical study addresses three different, but closely related problems: time-history dependence of aerodynamic forces acting on a moving control surface, control by means of trim tabs, and control surface reaction upon abrupt actuator failure. Closed-form solutions are proposed to each of these problems. Perhaps the most conspicuous result is our conclusion that history-dependent aerodynamic effects have no significant influence on the transfer function between the trim tab and the surface it drives, provided that the chord of the surface is sufficiently small compared to the total chord.     

Flow of a mixture of a viscous fluid and a granular solid in an orthogonal rheometer

In this paper, we study the flow of a linearly viscous fluid and a granular solid, consisting of many particles, situated between two parallel plates rotating about different axes. Flow in orthogonal rheometers has been studied for many viscoelastic fluids so that their rheological properties can be measured. The mixture is modeled using the theory of interacting continua, and constitutive relations for the fluid phase, the granular phase, and the interaction forces are provided. For a very special case, an analytical solution to the equations of motion is also provided.     

Stability and dynamic analysis of partially cracked thin orthotropic microplates under thermal environment: an analytical approach

Abstract

An analytical model is proposed to analyze the vibration and buckling problem of partially cracked thin orthotropic microplate in the presence of thermal environment. The differential governing equation for the cracked plate is derived using the classical plate theory in conjunction with the strain gradient theory of elasticity. The crack is modeled using appropriate crack compliance coefficients based on the simplified line spring model. The influence of thermal environment is incorporated in governing equation in form thermal moments and in-plane compressive forces. The governing equation for cracked plate has been solved analytically to get fundamental frequency and central deflection of plate. To demonstrate the accuracy of the present model, few comparison studies are carried out with the published literature. The stability and dynamic characteristics of the cracked plate are studied considering various parameters such as crack length, plate thickness, change in temperature, and internal length scale of microstructure. It has been concluded that the frequency and deflection are affected by crack length, temperature, and internal length scale of microstructure. Furthermore, to study the buckling behavior of cracked plate, the classical relations for critical buckling load and critical buckling temperature is also proposed considering the effect of crack length, temperature, and internal length scale of microstructure.     

Analytical solution of the spherical indentation problem for a half-space with gradients with the depth elastic properties

The contact problem for the impression of spherical indenter into a non-homogeneous (both layered and functionally graded) elastic half-space is considered. Analytical methods for solving this problem have been developed. It is assumed that the Lame coefficients vary arbitrarily with the half-space depth. The problem is reduced to dual integral equations. The developed methods make it possible to find the analytical asymptotically exact problem solution, suitable for a PC. The influence of the Lame coefficients variation upon the contact stresses and size of the contact zone with different radius of indenter as well as values of the impressing forces are studied. The effect of the non-homogeneity is examined. The developed method allows to construct analytical solutions with presupposed accuracy and gives the opportunity to do multiparametric and qualitative investigations of the problem with minimal computation time expenditure.     

The strain energy release rates in adhesively bonded balanced and unbalanced specimens and lap joints

An analytical model is developed to determine the strain energy release rate in adhesive joints of various configurations such as the double-cantilever beam and single-lap joints. The model is based on asymptotic analysis of adhesive layer stresses and Irwin’s crack closure integral. Closed-form solutions are presented for balanced and unbalanced joints under mode I, II and mixed-mode I/II that take into account the influence of the shear force on the adhesive stresses, and its influence on the strain energy release rate. The accuracy of the model is tested against the classical beam theory expressions for double-cantilever beam and end-notch flexure specimens. In fact, classical beam theory’s expressions are found to be the lower bound of the proposed model solutions, and the two methods converge as the adhesive layer thickness decreases. Analysis of single-lap joints reveals the influence of edge shear forces on the total strain energy release rate, and more importantly on the ratio between modes I and II. Results from the proposed analytical model are in good agreement with finite element results and with analytical models found in the literature.     

Track-terrain modelling and traversability prediction for tracked vehicles on soft terrain

Skid-steered tracked vehicles are the favoured platform for unmanned ground vehicles (UGVs) in poor terrain conditions. However, the concept of skid-steering relies largely on track slippage to allow the vehicle to conduct turning manoeuvres potentially leading to overly high slip and immobility. It is therefore important to predict such vulnerable vehicle states in order to prevent their occurrence and thus paving the way for improved autonomy of tracked vehicles. This paper presents an analytical approach to track-terrain modelling and a novel traversability prediction simulator for tracked vehicles conducting steady-state turning manoeuvres on soft terrain. Traversability is identified by predicting the resultant track forces acting on the track-terrain interface and the adopted models are modified to provide an analytical generalised solution. The validity of the simulator has been verified by comparison with available data in the literature and through an in-house experimental study. The developed simulator can be employed as a traversability predictor and also as a design tool to test the performance of tracked vehicles with different vehicle geometries operating on a wide range of soil properties.     

Rankine pseudo-static earth pressure for c–ϕ soils

This study provides an analytical solution for calculation of seismic active earth pressure on the back of a rigid wall retaining cohesional–frictional (c–φ) soil. The proposed formulation is based on the conjugate stress concept, without employing any additional assumptions, similar to Rankine's original earth pressure formulation. The effects of sloping backfill and wall inclination are considered. In addition, a closed form solution has been derived for the soil–wall friction angle as a function of inertial forces and problem geometry for any given pseudo-static acceleration, as opposed to the constant value commonly employed in practice. The net seismic active force calculated based on the proposed formulations is found to be comparable with those obtained from previously published methods.