Ride dynamics mathematical model for a single station representation of tracked vehicle

Tracked vehicles are exposed to severe ride environment due to dynamic terrain-vehicle interactions. Hence it is essential to understand the vibration levels transmitted to the vehicle, as it negotiates different types of terrains at different speeds. The present study is focused on the development of single station representation of tracked vehicles with trailing arm hydro-gas suspension systems, simulating the ride dynamics. The kinematics of hydro-gas suspension system have been derived in order to determine the non-linear stiffness characteristics at various charging pressures. Then, incorporating the actual suspension kinematics, non-linear governing equations of motion have been derived for the sprung and unsprung masses and solved by coding in Matlab. Effect of suspension non-linear dynamics on the single station ride vibrations have been analyzed and validated with a multi-body dynamics model developed using MSC.ADAMS. The above mathematical models would help in estimating the ride vibration levels of the tracked vehicle, negotiating different types of terrains at various speeds and also enable the designers to fine-tune the suspension characteristics such that the ride vibrations are within acceptable limits. The mathematical ride model would also assist in development of non-linear ride vibration model of full tracked vehicle and estimate the sprung mass dynamics.     

Effects of vertical exciting force of a tracked vehicle on the dynamic compaction of a high lifted decomposed granite

The main purpose of this paper is to evaluate the effects of a jumping action of a tracked vehicle mounted with a vertical oscillator on vibro-compaction of a high lifted decomposed granite. A vibro-compaction test was executed using a model tracked vehicle of 4.9 kN weight under a condition of frequency of 16 Hz and load ratio of maximum vertical exciting force to vehicle weight of 0.2–2.0. As a result, it was observed that both the amount of sinkage of terrain surface and the dry density of soil increased hyperbolically with increment of the load ratio and the dry density distribution with depth became uniform for the whole depth of the soil stratum. It was confirmed that the volume shrinkage of soil was succeeded by the propagation of acceleration to deep stratum due to the jumping action and the dilatancy phenomenon due to an alternative shear stress. The optimum load ratio obtaining a maximum dry density at the frequency of 16 Hz was judged to be 2.0 within this experiment. In the application of these test results to an actual prototype tracked vehicle of 39.2 kN weight, it was estimated that the degree of compaction of a high lifted soil stratum of 90 cm became over 90% at the load ratio of 2.0.     

Effects of a roller and a tracked vehicle on the compaction of a high lifted decomposed granite sandy soil

The aim of this research was to innovate a new compaction machinery by comparing experimentally the effects of a two-axle, two wheel road roller and a tracked vehicle on the compaction of a decomposed granite sandy soil with a high spreading lift. By measuring the amount of sinkage of the terrain surface, the dry density distribution versus depth using a cone penetrometer, the normal earth pressure distribution versus depth using a stress state transducer (SST), the effects of the road roller and the tracked vehicle on the increment of the soil dry density were considered theoretically. It was observed that the tracked vehicle showed a larger amount of sinkage and a larger dry density distribution versus depth than the roller. The ratio of shear stress to normal stress was still large enough at the deep stratum, so that an optimal shear strain was developed on the whole range of the high lifted stratum and it increased the soil compaction density due to the dilatancy effect.     

On numerical solution of dynamic problems in the theory of reinforced shells

Dynamic problems for cylindrical shells reinforced with discrete ribs are examined. A numerical algorithm based on Richardson extrapolation is developed. Specific problems are solved, and the results are analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 50–56, May 2006.     

An eight noded composite plate element for the dynamic analysis of spatial mechanism systems

The development of a shear-deformable laminated plate element, based on the Mindlin plate theory, for use in large reference displacement analysis is presented. The element is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotrophic material property sets. Coordinate mapping is utilized so that non-rectangular elements may be modeled. The Gauss quadrature method of numerical integration is utilized to evaluate volume integrals. A comparative study is done on the use of full Gauss quadrature, reduced Gauss quadrature, mixed Gauss quadrature, and closed form integration techniques for the element. Dynamic analysis is performed on the RSSR (Revolute-Spherical-Spherical-Revolute) mechanism, with the coupler modeled as a flexible plate. The results indicate the differences in the dynamic response of the transverse shear deformable eight-noded element as compared to a four-noded plate element. Dynamically induced stresses are examined, with the results indicating that the primary deformation mode of the eight-noded Mindlin plate model being bending.     

Numerical solution of singular perturbation problems for the fourth-order elliptic differential equations

In this paper we construct the finite-difference scheme for the singularly perturbedboundary value problem for the fourth-order elliptic differential equation on the basis ofpaper[1],and prove the uniform convergence of this scheme with respect to the smallparameterεin the discrete energy norm,Finally,we give a numerical example.     

具有奇异位置的多体系统动力学方程的隐式算法

本文研究了在运动过程中具有奇异位置的多体系统动力学方程的隐式算法，给出了隐式算法所用的Ｊａｃｏｂｉ矩阵，并建立了该矩阵中各子矩阵间的计算关系，提高了计算效率，计算结果表明隐式算法的计算速度和精度明显优于显式算法。     

An optimal method for the design of a robotic tracked vehicle to operate over fresh concrete under steering motion

The objective of this paper is to find an optimal method for the design of tracked base travel systems for special purpose vehicles and robotic machines that may be required to steer over a light bonded terrain composed of fresh concrete. For the case of a vehicle traveling on a weak fresh concrete during construction, the paper presents detailed comparative studies of the steering performances of a small model tracked test vehicle with alternative amount of steering ratio for various concrete slump values. For these studies a detailed simulation analytical method has been developed. From this work it is proven, in comparison to experiment, that the simulation analytical method is useful for predicting various steering performances of a test tracked vehicle running upon soft fresh concrete of various consistencies.     

On a representation of the solution of the linear elasticity equations

A new representation of the stress tensor in the linear theory of elasticity is proposed. The representation satisfies the equilibrium equations and the compatibility conditions for strains. In this representation, the stress tensor is expressed in terms of a harmonic vector. The second boundary-value problem for an elastic half-space and elastic layer is considered as an example.Translated from Prikladnaya Mekhanika, Vol. 40, No. 11, pp. 85–91, November 2004.This revised version was published online in April 2005 with a corrected cover date.     

Modified augmented Lagrangian preconditioners for the incompressible Navier–Stokes equations

We study different variants of the augmented Lagrangian (AL)‐based block‐triangular preconditioner introduced by the first two authors in [SIAM J. Sci. Comput. 2006; 28 : 2095–2113]. The preconditioners are used to accelerate the convergence of the Generalized Minimal Residual method (GMRES) applied to various finite element and Marker‐and‐Cell discretizations of the Oseen problem in two and three space dimensions. Both steady and unsteady problems are considered. Numerical experiments show the effectiveness of the proposed preconditioners for a wide range of problem parameters. Implementation on parallel architectures is also considered. The AL‐based approach is further generalized to deal with linear systems from stabilized finite element discretizations. Copyright © 2010 John Wiley & Sons, Ltd.     

New numerical method for volterra integral equation of the second kind in piezoelastic dynamic problems

The elastodynamic problems of piezoelectric hollow cylinders and spheres under radial deformation can be transformed into a second kind Volterra integral equation about a function with respect to time, which greatly simplifies the solving procedure for such elastodynamic problems. Meanwhile, it becomes very important to find a way to solve the second kind Volterra integral equation effectively and quickly. By using an interpolation function to approximate the unknown function, two new recursive formulae were derived, based on which numerical solution can be obtained step by step. The present method can provide accurate numerical results efficiently. It is also very stable for long time calculating.     

Effect of the deformation in the inertia forces on the inverse dynamics of planar flexible mechanical systems

The inverse dynamics problem for articulated structural systems such as robotic manipulators is the problem of the determination of the joint actuator forces and motor torques such that the system components follow specified motion trajectories. In many of the previous investigations, the open loop control law was established using an inverse dynamics procedure in which the centrifugal and Coriolis inertia forces are linearized such that these forces in the flexible model are the same as those in the rigid body model. In some other investigations, the effect of the nonlinear centrifugal and Coriolis forces is neglected in the analysis and control system design of articulated structural systems. It is the objective of this investigation to study the effect of the linearization of the centrifugal and Coriolis forces on the nonlinear dynamics of constrained flexible mechanical systems. The virtual work of the inertia forces is used to define the complete nonlinear centrifugal and Coriolis force model. This nonlinear model that depends on the rate of the finite rotation and the elastic deformation of the deformable bodies is used to obtain the solution of the inverse dynamics problem, thus defining the joint torques that produce the desired motion trajectories. The effect of the linearization of the mass matrix as well as the centrifugal and Coriolis forces on the obtained feedforward control law is examined numerically. The results presented in this investigation are obtained using a slider crank mechanism with a flexible connecting rod.     

Control structure interaction in the nonlinear analysis of flexible mechanical systems

The effect of the control structure interaction on the feedforward control law as well as the dynamics of flexible mechanical systems is examined in this investigation. An inverse dynamics procedure is developed for the analysis of the dynamic motion of interconnected rigid and flexible bodies. This method is used to examine the effect of the elastic deformation on the driving forces in flexible mechanical systems. The driving forces are expressed in terms of the specified motion trajectories and the deformations of the elastic members. The system equations of motion are formulated using Lagrange's equation. A finite element discretization of the flexible bodies is used to define the deformation degrees of freedom. The algebraic constraint equations that describe the motion trajectories and joint constraints between adjacent bodies are adjoined to the system differential equations of motion using the vector of Lagrange multipliers. A unique displacement field is then identified by imposing an appropriate set of reference conditions. The effect of the nonlinear centrifugal and Coriolis forces that depend on the body displacements and velocities are taken into consideration. A direct numerical integration method coupled with a Newton-Raphson algorithm is used to solve the resulting nonlinear differential and algebraic equations of motion. The formulation obtained for the flexible mechanical system is compared with the rigid body dynamic formulation. The effect of the sampling time, number of vibration modes, the viscous damping, and the selection of the constrained modes are examined. The results presented in this numerical study demonstrate that the use of the driving forees obtained using the rigid body analysis can lead to a significant error when these forces are used as the feedforward control law for the flexible mechanical system. The analysis presented in this investigation differs significantly from previously published work in many ways. It includes the effect of the structural flexibility on the centrifugal and Coriolis forces, it accounts for all inertia nonlinearities resulting from the coupling between the rigid body and elastic displacements, it uses a precise definition of the equipollent systems of forces in flexible body dynamics, it demonstrates the use of general purpose multibody computer codes in the feedforward control of flexible mechanical systems, and it demonstrates numerically the effect of the selected set of constrained modes on the feedforward control law.     

Theoretical statistical solution and numerical simulation of heterogeneous brittle materials

The analytical stress-strain relation with heterogeneous parameters is derived for theheterogeneous brittle materials under a uniaxial extensional load, in which the distributions of theelastic modulus and the failure strength are assumed to be statistically independent. This theoreticalsolution gives an approximate estimate of the equivalent stress-strain relations for 3-D heterogeneousmaterials. In one-dimensional cases it may provide comparatively accurate results. The theoreticalsolution can help us to explain how the heterogeneity influences the mechanical behaviors, Further, anumerical approach is developed to model the non-linear behavior of three-dimensional heterogeneousbrittle materials. The lattice approach and statistical techniques are applied to simulate the initialheterogeneity of heterogeneous materials. The load increment in each loading stage is adaptivelydetermined so that the better approximation of the failure process can be realized. When the maximumtensile principal strain exceeds the failure strain, the elements are considered to be broken, which canbe carried out by replacing its Young‘s modulus with a very small value. A 3-D heterogeneous brittlematerial specimen is simulated during a full failure process. The numerical results are in good agreementwith the analytical solutions and experimental data.     

On the numerical solution of the equations of propagation by the method of characteristics

Summary A new application of the method of characteristics for the numerical solution of the problems of one-dimensional propagation is stated. The main concept is to consider a Massau grid and to compel it into a net of rectangles, having the sides parallel to the axes of the space-time plane.     

Three-Dimensional Large Deformation Analysis of the Multibody Pantograph/Catenary Systems

To accurately model the nonlinear behavior of the pantograph/catenary systems, it is necessary to take into consideration the effect of the large deformation of the catenary and its interaction with the nonlinear pantograph system dynamics. The large deformation of the catenary is modeled in this investigation using the three-dimensional finite element absolute nodal coordinate formulation. To model the interaction between the pantograph and the catenary, a sliding joint that allows for the motion of the pan-head on the catenary cable is formulated. To this end, a non-generalized arc-length parameter is introduced in order to be able to accurately predict the location of the point of contact between the pan-head and the catenary. The resulting system of differential and algebraic equations formulated in terms of reference coordinates, finite element absolute nodal coordinates, and non-generalized arc-length and contact surface parameters are solved using computational multibody system algorithms. A detailed three-dimensional multibody railroad vehicle model is developed to demonstrate the use of the formulation presented in this paper. In this model, the interaction between the wheel and the rail is considered. For future research, a method is proposed to deal with the problem of the loss of contact between the pan-head and the catenary cable.     

On the numerical solution of partial differential equations of the elliptic type. I

Summary The potential equation and some connected problems in which the unknown function is given on the boundary is solved by using the properties of a special class of matrices which have the same structure as the coefficient matrix of the system of linear difference equations resulting from the differential equation.     

Improving the dynamic stability of a workpiece dominated turning process using an adaptronic tool holder

In this contribution, inside turning of a thin-walled cylinder is investigated in simulation. Self-excited vibrations can arise due to repeated cutting of the same surface, that lead to instability. A flexible multibody system model of the system is the basis for a subsequent analysis of the stability of the process. Stability analysis is done using an approximation as a time-discrete system via the semi-discretization method. An adaptronic turning chisel comprising a piezo actuator and sensors is then used in combination with different control concepts to improve the stability of the process. The effectiveness of the different strategies is compared based on the influence on the stability charts. A classic H_∞ controller based on a model of the coupled system of workpiece and tool can only yield some improvements, when an additional measurement of the workpiece displacement is added. Incorporating knowledge on the cutting process coupling workpiece and tool using a gain scheduled H_∞ controller allows further improvements. However, robustness with respect to model uncertainties, notably concerning the force law, remains an issue.     

On the numerical solution of the turbulence energy equations for wave and tidal flows

This paper deals with the numerical solution, using finite difference methods, of the hydrodynamic and turbulence energy equations which describe wind wave and tidally induced flow. Calculations are performed using staggered and non-staggered finite difference grids in the vertical, with various time discretizations of the production and dissipation terms in the turbulence energy equations. It is shown that the time discretization of these terms can significantly influence the stability of the solution. The effect of time filtering on the numerical stability of the solution is also considered. The form of the mixing length is shown to significantly influence the bed stress in wind wave problems. A no-slip condition is applied at the sea bed, and the associated high-shear bottom boundary layer is resolved by transforming the equations onto a logarithmic or log-linear co-ordinate system before applying the finite difference scheme. A computationally economic method is developed which remains stable even when a very fine vertical grid (over 200 points) is used with a time step of up to 30 min.     

ON THE NUMERICAL SOLUTION OF QUASILINEAR WAVE EQUATION WITH STRONG DISSIPATIVE TERM

The numerical solution for a type of quasilinear wave equation is studied. The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved. The error of the difference solution is estimated. The theoretical results are controlled on a numerical example.