de A Bram Kraker

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.

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.

Integrating experimentation into control courses

The Department of Mechanical Engineering at the Technische Universiteit Eindhoven, the Netherlands, aims to provide a stimulating educational environment that emphasizes the role of hands-on experiments. To achieve this goal, the Department integrated an experimentation program with courses in the mechanical engineering bachelors curriculum, starting in the first year and gradually building in complexity through the third year. To make it possible for students to perform experiments, a new approach, which include a personal notebook, a set of 30 portable data acquisition devices, a varied set of small-scale systems, and MATLAB-based software, was introduced. This approach allow the students to plan, prepare and analyze the experiments on their own notebook computers whenever they wish. While this approach has broken through the practical barriers to large-scale experimenting, the success of further integration of student experimentation into mechanical engineering curriculum ultimately depends on the efforts and creativity of staff members.

Steady-State Behaviour of Flexible Rotordynamic Systems with Oil Journal Bearings

This paper deals with the long term behaviour of flexible rotor systems, which are supported by nonlinear bearings. A system consisting of a rotor and a shaft which is supported by one oil journal bearing is investigated numerically. The shaft is modelled using finite elements and reduced using a component mode synthesis method. The bearings are modelled using the finite-length bearing theory. Branches of periodic solutions are calculated for three models of the system with an unbalance at the rotor. Also self-excited oscillations are calculated for the three models if no mass unbalance is present. The results show that a mass unbalance can stabilize rotor oscillations.

Application of hybrid frequency domain substructuring for modelling an automotive engine suspension

A practical application of hybrid FRF-coupling (Frequency Response Function) in the development of a passenger car is presented. First, a short review is given about FRF-coupling in general. Next, some problems are discussed which may be encountered when both analytical and experimental FRF-data is used in FRF-coupling. This is also known as hybrid modelling. The main part of this paper presents a successful application of hybrid FRF-coupling to analyze and solve an interior noise problem of a passenger car. Both analytical and experimental FRFs were used to create a hybrid dynamic model of a complete passenger car. The engine and its suspension system were modelled using finite elements, while the remainder of the car was modelled by experimentaly derived FRFs. This hybrid model was then used to compute the response of the vehicle due to the engine excitation. Measured noise transfer function were used next to compute the interior sound pressure level using forced response results of the hybrid car model. Subsequently, the hybrid model was used to analyze the problem, and to predict the effects of an alternative design of the engine suspension on interior noise. Numerical results indicated that the alternative design would have a significant positive effect on noise. This was confirmed by verification measurements on a car.

Experimental verification of the steady-state behavior of a beam system with discontinuous support

This article deals with the experimental verification of the long-term behavior of a periodically excited linear beam supported by a one-sided spring. Numerical analysis of the beam showed subharmonic, quasi-periodic, and chaotic behavior. Further, three different routes leading to chaos were found. Because of the relative simplicity of the beam system and the variety of calculated nonlinear phenomena, an experimental setup is made of this beam system to verify the numerical results. The experimental results correspond very well with the numerical results as far as the subharmonic behavior is concerned. Measured chaotic behavior is proved to be chaotic by calculating Lyapunov exponents of experimental data.

Rubin's CMS reduction method for general state-space models

Abstract In this paper the Rubin CMS procedure for the reduction and successive coupling of undamped structural subsystems with symmetric system matrices will be modified for the case of general damping. The final coordinate transformation is based on the use of complex (residual) flexibility modes, state-space rigid body modes and complex free-free dynamic modes. The dynamic modes are selected using a specific eigenvalue selection criterion. Some examples will be presented and discussed showing the potential of this extension of the Rubin CMS-procedure.

Vibration Control of Periodically Excited Nonlinear Dynamic Multi-dof Systems

For nonlinear mechanical systems, which have stable subharmonic resonance peaks and one or more coexisting unstable harmonic solutions, a large reduction of maximum subharmonic, quasi-periodic, or chaotic displacement can be established if the coexisting unstable harmonic solution could be made stable. The control effort to obtain this goal can be very small in that case. In this article, a method for controlling nonlinear multi-degree-of-freedom (multi-dof) systems to unstable periodic solutions is developed. This is established by putting a single control force somewhere on the system. Because the selected control method uses the full state of the system and because only measured displacements and accelerations of a very limited number of dofs are assumed to be available, a reconstruction method has to be used for estimating the full state on-line. Simulations are done using a beam system supported by a one-sided spring that is control led to the unstable harmonic solution. The robustness of the method with respect to model errors, system disturbance, and measurement errors is examined. Further, the performance of the method in case of a varying excitation frequency during the control is investigated.

Parameter variation methods for cell mapping

In the study of nonlinear dynamic systems, the influence of system parameters on the long term behaviour plays an important role. In this paper, parameter variation methods are presented which can be used when investigating a nonlinear dynamic system by means of simple or interpolated cell mapping. In the case of coexisting attractors, the proposed methods determine the evolution of the basin boundaries when a system parameter is varied. Application of the methods to a modified Duffing equation is performed. It is concluded that the proposed methods are very efficient and accurate.