van Dh Dick Campen

Bifurcations in Nonlinear Discontinuous Systems

This paper treats bifurcations of periodic solutions indiscontinuous systems of the Filippov type. Furthermore, bifurcations offixed points in non-smooth continuous systems are addressed. Filippovstheory for the definition of solutions of discontinuous systems issurveyed and jumps in fundamental solution matrices are discussed. It isshown how jumps in the fundamental solution matrix lead to jumps of theFloquet multipliers of periodic solutions. The Floquet multipliers canjump through the unit circle causing discontinuous bifurcations.Numerical examples are treated which show various discontinuousbifurcations. Also infinitely unstable periodic solutions are addressed.

Stick-Slip Vibrations Induced by Alternate Friction Models

In the present paper a simple and efficient alternate friction model is presented to simulate stick-slip vibrations. The alternate friction model consists of a set of ordinary non-stiff differential equations and has the advantage that the system can be integrated with any standard ODE-solver. Comparison with a smoothing method reveals that the alternate friction model is more efficient from a computational point of view. A shooting method for calculating limit cycles, based on the alternate friction model, is presented. Time-dependent static friction is studied as well as application in a system with 2-DOF.

A mixture approach to the mechanics of skin

Skin can be considered to be a mixture of a solid and a fluid. A general theory for the description of the behaviour of mixtures is presented and applied to a mixture of a solid and a fluid. A numerical procedure is presented to solve the non-linear field equations describing such a mixture. The abilities of the procedure are demonstrated by means of a confined compression test.

Stick-slip Whirl Interaction in Drillstring Dynamics

A Stick-slip Whirl Model is presented which is a simplification of an oilwell drillstring confined in a borehole with drilling fluid. The disappearance of stick-slip vibration when whirl vibration appears is explained by bifurcation theory. The numerical results are compared with the experimental data from a full-scale drilling rig.

An Approximate Analysis of Dry-Friction-Induced Stick-Slip Vibrations by a Smoothing Procedure

This paper deals with a systematic procedure to find both stable and unstable periodic stick-slip vibrations of autonomous dynamic systems with dry friction. In this procedure, the discontinuous friction forces are approximated by smooth functions. Using the simple shooting method with a stiff-ODE solver, in combination with a path following algorithm, branches of periodic solutions are computed for a changing design variable. For testing purposes, both 1 and 2-DOF autonomous block-on-belt models and a 1-DOF autonomous drill string model from literature are investigated. Comparison of the results shows that the smoothing procedure accurately describes the behavior of the discontinuous systems. The proposed procedure can also easily be applied to more complex MDOF models, as well as to nonautonomous dynamic systems.

Long term structural dynamics of mechanical systems with local nonlinearities

This paper deals with the long term behavior of periodically excited mechanical systems consisting of linear components and local nonlinearities. The number of degrees of freedom of the linear components is reduced by applying a component mode synthesis technique. Lyapunov exponents are used to identify the character of the long term behavior of a nonlinear dynamic system, which may be periodic, quasi-periodic or chaotic. Periodic solutions are calculated efficiently by solving a two-point boundary value problem using finite differences. Floquet multipliers are calculated to determine the local stability of these solutions and to identify local bifurcation points. The methods presented are applied to a beam system supported by a one-sided linear spring, which reveals very rich, complex dynamic behavior.

Optimization of multibody systems using approximation concepts

Sequential approximate optimization is used to solve multibody optimum design problems. The transient optimization problem is formulated such that approximation concepts can be incorporated. Two multibody design examples illustrate the effectiveness of the approach.

In vitro compression of a soft tissue layer on a rigid foundation

In vitro compression studies have been performed on layers of porcine skin and fat. The tissue layers have been loaded by means of various indentors. Indentor displacements and interstitial fluid pressures have been measured. The results have been compared to finite element calculations with mixture elements. A qualitative agreement between calculations and measurements is found. The results support the hypothesis that skin and fat behave like solid/fluid mixtures.

Discontinuous bifurcations of periodic solutions

This paper discusses different aspects of bifurcations of periodic solutions in discontinuous systems. It is explained how jumps in the fundamental solution matrix lead to jumps of the Floquet multipliers of periodic solutions. A Floquet multiplier of a discontinuous system can jump through the unit circle causing a discontinuous bifurcation. Numerical examples show discontinuous fold and symmetry-breaking bifurcations. The discontinuous fold bifurcation can connect stable branches to branches with infinitely unstable periodic solutions.

Low Reynolds number steady state flow through a branching network of rigid vessels: I. A mixture theory

A mixture theory has been used to formulate a theory of blood perfusion. By means of a formal averaging procedure the discrete network of microvessels is transformed into a continuum. During this procedure, the distinction between arterioles, capillaries and venules is preserved by means of an arteriovenous parameter. In this paper, two equations are derived for the case of low Reynolds number steady-state flow through a rigid vessel network: the extended Darcy equation and the continuity equation. A verification of the theory is presented, on the basis of a network analysis.