The toppling of a vertical slender rod occurs in a short period of time, the mechanical analysis of this process is made in this paper. Firstly, a theoretical model of the cylindrical rod, the hollow cylindrical rod, the rod with variable cross section and the rod with a mass on the top is constructed. Then, based on experiments, the strain distribution along the axis and the variation of the strain in these rods are obtained,which are found to be consistent with the theoretical model. Finally, the distribution and the variation of the strain in a toppling vertical slender rod are obtained.
This paper first discusses the intrinsic distinction of the term "ideal constraint" used both in analytical mechanics and in the work-energy theorem in theoretic mechanics. The possible misunderstanding due to the use of the same term with different connotations is illustrated. In this setting, a new technical term "null-work constraint" is suggested instead in the work-energy theorem for the sake of the uniqueness and consistency of terminology in mechanics. Then the differential form of the work-energy theorem is transformed into a sum form indexed by the generalized coordinates, and the reason why the general dynamic equations of the system cannot be obtained from this sum form as in the general equation of dynamics is analyzed and illustrated by a comparison with the Lagrange equation method. The arguments for the two problems both involve the concepts of real displacement and virtual displacement, accordingly, they may serve as a way to understand and distinguish the concepts of displacement and virtual displacement.
Since PMMA (polymethyl-methacrylate) is an important material used for the aircraft windshield and canopy, it is necessary to study its mechanical properties. This paper reviews the studies of mechanical properties of PMMA. Constitutive models on viscoelasticity, inelasticity, yield stress and module related to tem-perature are summarized. Recent quasi-static and dynamic experiments are discussed, while several examples in molecular dynamic simulation and finite element analysis are described. The new research directions are commented.
This paper uses analytical geometry and analytical mechanics to obtain the conditions of a homo-geneous slender rod in a state of balance and in the stable equilibrium when it is in the inner wall of a smooth conic curve , as well as the static properties of the conic curve. When the homogeneous slender rod goes through the focus and is in the inner wall of a smooth conic curve aslant, the homogeneous slender rod will be in a state of stable equilibrium. Its mechanical properties are also proven by using its optical properties.
With ever increasing threat during terrorism war and regional conflict, providing improved pro-tection for vehicle and its passengers is the common challenge for researchers in materials science, mechanical engineering, biomedical engineering and many other disciplines. This article presents an overview of the po-tential threat of common explosives to vehicle safety, the underlying mechanisms, the influence of key factors on explosive loading, and the different types of blast injury to armored vehicles and passengers. Based on the analysis of existing experimental technology, characterization methods and finite element simulation results,the current research status of explosion protection designs for both military and civil vehicles are summarized,including the development trend of novel lightweight protective materials and structures, and future trends in explosion-protection design for armored vehicles are discussed.
For the Newton's pendulum, a new model is established using the Hertzian contact theory to represent the interactions between adjacent balls. This model is applied to solve the problems of a ball chain collision, with the impulse wave propagation in the chain. By changing the number of the balls, the influence of the ball-chain length is studied. Numerical calculations provide information of the position, the velocity of each ball, and the deformations and the interaction forces between the adjacent balls, as functions of time. A computer tool with graphic user interface (GUI) is developed to solve the ball-chain impact problems in different situations. The high speed camera is used in the collision experiments to study the detailed process, showing that the numerical model gives good predictions.
A simplified adaptive mesh method is applied to solve the two-dimensional convection -diffusion model of batching. In this method, the density of the mesh is controlled by the velocity and the concentration gradient, and the traditional fixed grid is replaced by the dynamic mesh. In the two-dimension model, the velocity field and the turbulent diffusion rate is derived based on the mixed length theory，with the consideration of the influence on the mixing oil by its viscosity variation. The goal is to improve the computation precision and reduce the calculation amount to make it suitable for batching simulations in long distance pipelines. The effectiveness of this method is verified by the comparative analysis of the numerical experiment. The numerical analysis shows how the Reynolds number, the product sequence and the transportation distance influence the results.
Overlapping grid techniques, from two major aspects, the grids assembly process and the interpo-lating computations in the numerical iterations, are reviewed in this paper. First, the grid assembly algorithms in the preconditioning step are discussed from two aspects, including the hole-cutting algorithms and the node-searching algorithms for building inter-grid links. Secondly, the interpolation methods for communication among overset grids in the numerical computations are illustrated. Meantime, the issues of conservative laws for in-compressible and compressible flows are discussed and the accuracy of interpolation is analyzed. The parallel implementations of overset grids and achievements in engineering applications are also reviewed. Finally, some conclutions are reached. There are wide spaces for further studies of overlapping grid techniques, such as the improvements of grid assembly,the interpolation and the parallel computations.
This paper reviews the background and the significance of the flexible-structures-fluid coupling problems, and the current related studies, including the coupling movement of one single flexible body in a uniform flow, the multiple flexible bodies in a uniform flow, and the flexible bodies in a non-uniform flow.From the review, the progress of the research methods and results, and the main influencing factors and their problems are revealed. The future research directions are proposed.
The instability of an axially moving liquid fiber in a crimping stuffer box is studied, and its critical load is obtained. The effects of spinning conditions on the critical load are studied. This theory can be used to design an optimal stuffer box or improve the product quality.
The transverse buckling of a strip involves a serious flatness defect, and its mechanism of production is still unclear. Based on Airy stress function and Timoshenko's principle of least work, a new mechanical model of transverse pre-buckling is established, and the stress field in the strip prebuckling state is obtained. The mathematical model of the critical buckling stress is also built by Galerkin's principle of virtual displacement.The results of the analysis could be used for prediction of the transverse buckling in the annealing furnace.
An online fault diagnosis method is proposed to make sure that the aircraft flight is safe as the failure occurs in the control surface, and the evaluation of the flight performance can be made based on the fault diagnosis information. Firstly, in order to overcome the shortcoming of the filtering performance of the UKF (unscented kalman filter), which will be decreased as the system state has higher dimensions, a fault diagnosis method based on the cubature Kalman filter algorithm is designed. The problem that the filtering effect of the UKF with a high dimensional state is not ideal can be solved by using the spherical integral criterion and the radial integral criterion to optimize the Sigma point sampling strategy and the weight distribution of the UKF. Secondly, according to the characteristics of the aircraft leveled off with a constant velocity, the lift and drag coeflcients can be computed and the flight envelope is established to reflect the flight performance. Lastly, the simulation results verify that the proposed method is practical.
The trajectory tracking control and the vibration suppression of a free floating space-based manip-ulator with elastic base are discussed in this paper. According to the geometric feature and the momentum conservation, the generalized Jacobian matrix is derived, And the Lagrangian method and the momentum con-servation are adopted in building the dynamic equations. Based on the results and under the assumption of two kinds of time scale, a singular perturbation model of the free floating space manipulator system is built. The slow-subsystem describes the tracking control of rigid motion while the fast-subsystem describes the vibration of elastic base. The computed torque control of the free floating space-based robot with elastic base is designed for the low-subsystem. The linear-quadratic optimal control is designed for the fast-subsystem. The simulation results show that the proposed control scheme is feasible for the tracking control and the vibration suppression.
Based on the potential energy principle, a frictionless elastic contact problem quadratic program-ming model is constructed by treating the nodal displacements as the variables and the contact conditions as the constraint equation. On the basis of the model, the particular solution and the base solutions of the linear constraint equation of the force balance are used to construct the singular modal matrix, and then the freedom reduction method based on a singular coordinate transformation is proposed, which greatly reduces the dimension of the quadratic programming, and leaves the quadratic programming with no dominance equality constraint. According to the characteristics of the elastic contact mechanical system, and the contact freedom displacement mode generally assumed，a simple and eflcient singular modal matrix calculation method is pro-posed. The solution of the elastic contact problem is verified through comparison and analysis of two numerical cases of the contact problems of two cylinders and the axle hole clearance fit. The reduction of the quadratic programming method overcomes the problems of large amount of work, the sensitivity to the parameter settings and the convergence diflculties inherent in the traditional method.
In using the resonance theory to study the motion of a space vehicle, the corresponding non-Keplerian orbits are named the resonance orbits. In this paper the general dynamical model for resonance orbits is established through a judicious choice of orbit parameters，the time scale，and the thrust representation. An analysis of the influence of the resonance frequency is made based on simulations. The possibility and the effect of the resonance orbits to be used in the deep space exploration through analyzing an Earth-Mars mission are explored. It is shown that, changing the circle frequency will influence the peak thrust; it is possible to use the resonance orbits in the deep space exploration, and its energy consumption is less than using a Lambert orbit.
The paper defines two elements of an airdrop system. They are the aircraft for carrying and load.Two modeling methods for airdrop dynamics are introduced. They are the single-body model and the multi-body model. The two methods are shown to be equivalent in the translation motion, but not in rotation,because the single-body model does not always exist.
The entire elasto-plastic process of loading and deformation of a beam with one degree of indeter-minacy under a concentrated load is analyzed. Based on the deformation feature, the up-loading process can be divided into four stages: the elastic stage, the second stage when the beam region near the fixed end is in the plastic propagation state, the third stage when both the beam regions near the fixed end and near the point where the concentrated load acts are in the plastic propagation state, and the fourth stage when the fixed end behaves as a plastic hinge while the plastic region near the fixed end is unloaded and the plastic region near the mid-point is propagating to the emergence of the second plastic hinge. In the elastic stage, the relation between the moment and the load is proportional, so is that between the deflection and the load. In the second and third stages, the relation between the moment and the load is complicated and nonlinear, so is that between the deflection and the load. In the fourth stage, the relation between the moment and the load is linear but not proportional, while the relation between the deflection and the load is much complicated and nonlinear. The formulas of the moment and the deflection at an arbitrary point at each stage are derived. The formulas can be applied to the engineering structure design.
For a symmetrical structure under symmetrical load, the internal force and the displacement are symmetrical; under anti-symmetric loads, the internal force and the displacement are anti-symmetrical. Accord-ingly, the structural analysis can be simplified. In this paper the above conclusions are proved mathematically.On this basis, the theory of the internal forces and the displacements of a symmetrical structure under an arbitrary load is discussed.
The critical axial pressures of an Euler's pole in some constraint conditions are well known. According to the derivation, the Euler's staight pole might be in a curved static state and lose stability only if the axial pressure is equal to some integer multiple of the critical axial pressure value. When the pressure is between two integer multiples of the critical value, the pole might not be in a curved static state. In other words, it will remain in a straight state and will not lose stability. This is obviously not consistent with the reality. The problem is discussed in this paper by using the exact formula of the pole's curvature. The reason why the pull-pole will not lose stability is explained. Meanwhile, the variation of the pole's deflection curve with the increase of the axial pressure is discussed.
In this paper, based on three aspects, it is shown that in Pfaff-Birkhoof principle, the end-point conditions are not fixed, but semi-fixed. The corresponding natural end-point conditions for non-fixed variables at the end-points are deduced, and the general forms of the conditions are given.