... at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running...

...Suying Zhang; Jiangdan Li The precise integration method can give precise numerical result for linear invariant dynamical system, and can be used to solve stiff linear invariant dynamical system. In this paper, precise integration is compounded with Runge–Kutta method and a new effective...

...Nick Schafer; Dan Negrut Implicit integration, unencumbered by numerical stability constraints, is attractive in molecular dynamics (MD) simulation due to its presumed ability to advance the simulation at large step sizes. It is not clear what step size values can be expected and if the larger step...

... that exploit the modular structure of coupled systems are frequently used as alternatives to classical time integration methods. The numerical stability and convergence of such modular time integration methods is studied for a class of sequential modular methods for coupled multibody system models. Theoretical...

...Peter Betsch; Christian Hesch; Nicolas Sänger; Stefan Uhlar This work contains a comparison between variational integrators and energy-momentum schemes for flexible multibody dynamics. In this connection, a specific “rotationless” formulation of flexible multibody dynamics is employed. Flexible...

... for the determination of permanent (plastic) deformations of the rivet when hitting the bucking bar. For simulation, numerical integration algorithms are applied to solve the impact dynamic model and determine the riveting time according to riveting specifications. Riveting tests are carried out for model validation...

...Dan Negrut; Laurent O. Jay; Naresh Khude The premise of this work is that the presence of high stiffness and/or frictional contact/impact phenomena limits the effective use of high order integration formulas when numerically investigating the time evolution of real-life mechanical systems...

... the dependency of this Jacobian on physical properties, further improving the numerical conditioning of the resulting linearized equations. Because the scaling of the equations is performed before the time and space discretizations, its benefits are reaped for all time integration schemes. The augmented...

...F. Khouli; F. F. Afagh; R. G. Langlois An energy decaying integration scheme for an intrinsic, geometrically exact, multibody dynamics model with composite, dimensionally reducible, active beamlike structures is proposed. The scheme is based on the first order generalized- α method...

...Jay L. Adams; Tom T. Hartley In this paper, the conditions that lead to a system output remaining at zero with zero input are considered. It is shown that the initialization of fractional-order integrators plays a key role in determining whether the integrator output will remain at a zero with zero...

... fractional integral and derivative that generalize those for the integer-order operators. The new transforms unify the initialization of systems of fractional and ordinary differential equations. The paper provides background on past work in the area and determines the Laplace transforms for the initialized...

...Dan Negrut; Rajiv Rampalli; Gisli Ottarsson; Anthony Sajdak The paper presents theoretical and implementation aspects related to a numerical integrator used for the simulation of large mechanical systems with flexible bodies and contact/impact. The proposed algorithm is based on the Hilber-Hughes...