Implementation of configuration dependent stiffness proportional damping for the dynamics of rigid multi-block systems

The distinct element method(DEM)has been used successfully for the dynamic analysis of rigid block sys- tems.One of many difficulties associated with DEM is modeling of damping.In this paper,new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid muhi-block systems.The stiff- ness proportional damping is constructed for the prescribed damping ratio,based on the non-zero fundamental frequency ef- fective during the time interval while the boundary conditions remain essentially constant.At this time interval,the funda- mental frequency can be estimated without complete eigenvalue analysis.The damping coefficients will vary while the damp- ing ratio remains the same throughout the entire analysis.A new numerical procedure is developed to prevent unnecessary energy loss that can occur during the separation phases.These procedures were implemented in the development of the dis- tinet element method for the dynamic analyses of piled multi-block systems.The analysis results |or the single-block and two-block systems were in a good agreement with the analytic predictions.Applications to the seismic analyses of piled four- block systems revealed that the new procedures can make a significant difference and may lead to much-improved results.

A TENSOR METHOD FOR THE DERIVATION OF THE EQUATIONS OF RIGID BODY DYNAMICS

A tensor method for the derivation of the equations of rigid body dynamics, based on the concepts of continuum mechanics, is presented. The formula of time derivative of the inertia tensor with zero corotational rate is used to prove the equivalences of five methods, namely, Lagrange's equations, Nielsen's equations, Gibbs-Appell's equations, Kane's equations and the generalized momentum type of Kane's equations. Some differential identities on angular velocity and angular acceleration are given.

TORSIONAL VIBRATIONS OF A RIGID CIRCULAR PLATE ON SATURATED STRATUM OVERLAYING BEDROCK

The torsional vibration of a rigid plate resting on saturated stratum overlaying bedrock has been analysed for the first time. The dynamic governing differential equations for saturated poroelastic medium are solved by employing the technology of Hankel transform. By taking into account the boundary conditions, the dual integral equations of torsional vibration of a rigid circular plate are established, which are further converted into a Fredholm integral equation of the second kind. Subsequently, the dynamic compliance coefficients of the foundation on saturated stratum, the contact shear stress under the foundation and the angular amplitude of the foundation are evaluated. Numerical results indicate that, when the dimensionless height is bigger than 5, saturated stratum overlaying bedrock can be treated as saturated half space approximately. When the dimensionless frequency is low, the permeability of the soil must be taken into account. Furthermore, when the vibration frequency is a constant, the height of the saturated stratum has a slight effect on the dimensionless contact shear stress under the foundation.

Dynamic modeling and simulation for the flexible spacecraft with dynamic stiffening

A rigid flexible coupling physical model which can represent a flexible spacecraft is investigated in this paper. By applying the mechanics theory in a non-inertial coordinate system,the rigid flexible coupling dynamic model with dynamic stiffening is established via the subsystemmodeling framework. It is clearly elucidated for the first time that,dynamic stiffening is produced by the coupling effect of the centrifugal inertial load distributed on the beamand the transverse vibration deformation of the beam. The modeling approach in this paper successfully avoids problems which are caused by other popular modeling methods nowadays： the derivation process is too complex by using only one dynamic principle; a clearly theoretical explanation for dynamic stiffening can＇t be provided. First,the continuous dynamic models of the flexible beamand the central rigid body are established via structural dynamics and angular momentumtheory respectively. Then,based on the conclusions of orthogonalization about the normal constrained modes,the finite dimensional dynamic model suitable for controller design is obtained. The numerical simulation validations showthat： dynamic stiffening is successfully incorporated into the dynamic characteristics of the first-order model established in this paper,which can indicate the dynamic responses of the rigid flexible coupling system with large overall motion accurately,and has a clear modeling mechanism,concise expressions and a good convergence.

DYNAMIC MODELING AND SIMULATION OF FLEXIBLE CABLE WITH LARGE SAG

Discrete model of flexible cable with large sag is established by using multiple rigid body-spherical hinge model, and dynamic equation of that discrete model is derived according to dynamics theory of multiple rigid body system. Displacement and velocity of system are revised to eliminate violation phenomenon of the differential-algebra equation in numerical simulation based of the theory of generalized inverse of matrices. Numerical simulation proves the validity of our method.

THE INVARIANT MANIFOLD METHOD AND THE CONTROLLABILITY OF NONLINEAR CONTROL SYSTEM

The problem of controllability of nonlinear control system is a significant field which has an extensive prospect of application. A. M. Kovalev of Ukraine Academy of Science applied the oriented manifold method developed in dynamics:of rigid body to nonlinear control system for the first time,and obtained a series of efficient results. Based on Kovalev's oriented manifold method, firstly, by invariant manifold method the problem of controllability of nonlinear control system was studied and the necessary condition of the controllability of a kind of affine nonlinear system was given out. Then the realization of the necessary condition wars discussed. At last, the motion of a rigid body with two rotors,vas, investigated and the necessary condition which is satisfied by this system,vas proved.

Modified RATTLE Method for Rigid Body Dynamics in Cartesian Coordinates

In this paper,we describe a modified RATTLE(M-RATTLE)method for rigid body dynamics directly in Cartesian coordinates.The M-RATTLE method introduces a new way of resetting the coordinates to satisfy the constraints at each step,which is designed for the rigid body dynamics calculations in the Cartesian coordinates.M-RATTLE is algebraically equivalent to the RATTLE method and the cost of performing rigid body dynamics by M-RATTLE is independent of the number of constraints.The interaction forces between atoms belonging to the same rigid molecule do not need to be computed and explicit expressions of the constraints of internal degrees of freedom are unnecessary.The performance and sampling results of the proposed method are compared with those of the symplectic splitting method for an isolated rigid benz molecule and for a cluster of twenty-seven benz molecules.

DRIFT MOTION OF FREE-ROTOR GYROSCOPE WITH RADIAL MASS-UNBALANCE

The motion of a rigid body about fixed point with small radial mass-unbalance in homogeneous gravitational field was discussed. The dynamical equations described by state variables of the body were established, and approximate analytical solutions for a spinning body with high speed were obtained by use of the average method. The influence of the radial mass-unbalance of the rotor to the precession character of a free-rotor gyroscope was analyzed. And a physical explanation of the drift phenomenon of the gyro was given. An applicable formula of gyro's constant drift in analytical form was obtained, which is perfectly coincident with the numerical calculation.

Pose Synchronization of Multiple Rigid Bodies Under Average Dwell Time Condition

This paper considers the pose synchronization problem of a group of moving rigid bodies under switching topologies where the dwell time of each topology may has no nonzero lower bound. The authors introduce an average dwell time condition to characterize the length of time intervals in which the graphs are connected. By designing distributed control laws of angular velocity and linear velocity,the closed-loop dynamics of multiple rigid bodies with switching topologies can be converted into a hybrid dynamical system. The authors employ the Lyapunov stability theorem, and show that the pose synchronization can be reached under the average dwell time condition. Moreover, the authors investigate the pose synchronization problem of the leader-following model under a similar average dwell time condition. Simulation examples are given to illustrate the results.

EXPERIMENTAL AND NUMERICAL INVESTIGATIONS ON SECONDARY FLOWS AND SEDIMENTATIONS BEHIND A SPUR DIKE

For a physical model of the approach navigation channel of Three Gorges Project（TGP）, flow patterns around a non-submerged spur dike placed as a mountain in a long rectangular glass flume were experimentally investigated with and without ＂sucking-spouting＂ water respectively. Based on rigid lid assumption and Dynamic Smagorinsky Model, all these vortex flows around the spur dike were numerically simulated and analyzed, which probably affect the whole flow field and then probably lead to sedimentations for silt-laden two-phase flows. Meanwhile, silt-laden flows were also investigated experimentally. Both the secondary flow region and the silt sedimentations downstream of the spur dike decrease greatly with ＂sucking-spouting＂ water compared to those ones without ＂sucking-spouting＂ water. The Finite Volume Method （FVM） was used to discretize the governing equations together with a staggered grid system, where the second order difference is employed for the diffusion terms and the source terms while the upwind difference QUICK is used for the convection terms. The computational results are all in fairly good agreement with the experimental data.

Micromechanical investigation of granular ratcheting using a discrete model of polygonal particles

We use a two-dimensional model of polygonal particles to investigate granular ratcheting. Ratcheting is a long-term response of granular materials under cyclic loading, where the same amount of permanent deformation is accumulated after each cycle. We report on ratcheting for low frequencies and extremely small loading amplitudes. The evolution of the sub-network of sliding contacts allows us to understand the micromechanics of ratcheting. We show that the contact network evolves almost periodically under cyclic loading as the sub-network of the sliding contacts reaches different stages of anisotropy in each cycle. Sliding contacts lead to a monotonic accumulation of permanent deformation per cycle in each particle. The distribution of these deformations appears to be correlated in form of vortices inside the granular assembly.

DESIGN AND IMPLEMENTATION OF REAL-TIME PHYSICS SIMULATION ENGINE FOR e-ENTERTAINMENT

We present our recent research results regarding the designing and implementation of real-time physics simulation engines,which aim at developing physics-inspired e-entertainment such as computer games,mobile applications,interactive TV and other smart media in Korea.Our real-time physics engine consists of three functional components:rigid body dynamics simulation,deformable body simulation,and data-driven physics simulation.The core simulation techniques to realize these simulation components include real-time collision detection and response,large-scale model simulation,and character model control.In this paper,we highlight these features and demonstrate their performances.We also showcase some of the gaming applications that we have integrated our physics engine into.