Nonlinear Normal Modes, Part I: An Attempt To Demystify Them

in 26th International Modal Analysis Conference, Orlando, 2008 (2008)

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companions, Parts II and III. Because there is virtually no application of the NNMs to large-scale engineering ... [more ▼]

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companions, Parts II and III. Because there is virtually no application of the NNMs to large-scale engineering structures, these papers are an attempt to highlight several aspects that might drive their development in the future. Specifically, we support that (i) numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs, and (ii) time-frequency analysis is particularly suitable for the analysis of the resulting dynamics. Another objective of the present paper is to describe, in simple terms, and to illustrate the fundamental properties of NNMs. This is achieved to convince the structural dynamicist not necessarily acquainted with them that they are a useful framework for the analysis of nonlinear vibrating structures. [less ▲]

On the numerical damping of time integrators for coupled mechatronic systems

in Computer Methods in Applied Mechanics & Engineering (2008), 197(6-8), 577-588

The generalized-alpha time integrator is considered for the simulation of mechatronic systems. In this context, the fundamental concept of numerical damping is analysed for coupled sets of first and ... [more ▼]

The generalized-alpha time integrator is considered for the simulation of mechatronic systems. In this context, the fundamental concept of numerical damping is analysed for coupled sets of first and second-order differential-algebraic equations. First, it appears that the algebraic variables do not influence the spectral properties of the dynamic variables. Second, we demonstrate that the coupling between the dynamic variables does not influence the high-frequency spectral response, so that the numerical damping can be determined as usual from elementary characteristic polynomials. Those results are exploited to assess the stability properties of the scheme and to select an algorithm with optimal damping properties. [less ▲]

Microbeam pull-in voltage topology optimization including material deposition constraint

in Computer Methods in Applied Mechanics & Engineering (2008), 197

Because of the strong coupling between mechanical and electrical phenomena existing in electromechanical microdevices, some of them experience, above a given driving voltage, an unstable behavior called ... [more ▼]

Because of the strong coupling between mechanical and electrical phenomena existing in electromechanical microdevices, some of them experience, above a given driving voltage, an unstable behavior called pull-in effect. The present paper investigates the application of topology optimization to electromechanical microdevices for the purpose of delaying this unstable behavior by maximizing their pull-in voltage. Within the framework of this preliminary study, the pull-in voltage maximization procedure is developed on the basis of electromechanical microbeams reinforcement topology design problem. The proposed sensitivity analysis requires only the knowledge of the microdevice pull-in state and of the first eigenmode of the tangent stiffness matrix. As the pull-in point research is a highly non-linear problem, the analysis is based on a monolithic finite element formulation combined with a normal flow algorithm (homotopy method). An application of the developed method is proposed and the result is compared to the one obtained using a linear compliance optimization. Moreover, as the results provided by the developed method do not comply with manufacturing constraints, a deposition process constraint is added to the optimization problem and its effect on the final design is also tested. [less ▲]

COMPUTATION OF NONLINEAR NORMAL MODES, PART I: NUMERICAL CONTINUATION IN MATLAB

in Sixth EUROMECH Nonlinear Dynamics Conference, Saint Petersbourg, 2008 (2008)

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II. Because there is virtually no application of the NNMs to large-scale engineering structures ... [more ▼]

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part II. Because there is virtually no application of the NNMs to large-scale engineering structures, these papers are an attempt to highlight one aspect that might drive their development in the future. Specifically, we support that numerical methods for the continuation of periodic solutions pave the way for an effective and practical computation of NNMs. In this context, we show that the NNM computation is possible with limited implementation effort. The proposed algorithm, implemented in MATLAB, relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. The algorithm is demonstrated using a 2DOF nonlinear system. A comparison with the results given by the AUTO software is achieved in Part II. [less ▲]

Computation of Nonlinear Normal Modes using Numerical Continuation Techniques

in International Confernce on Advanced Computational Methods in Engineering, Liège, 2008 (2008)

Modelling the electromechanical coupling of RF switch using Extended Finite Element

(2008)

Nonlinear Normal Modes, Part II: Practical Computation using Numerical Continuation Techniques

in 26th International Modal Analysis Conference, Orlando, 2008 (2008)

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is ... [more ▼]

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is often regarded as impractical. However, when resorting to numerical algorithms, we show that the NNM computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed algorithm relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. The algorithm is demonstrated using two different mechanical systems, a nonlinear two-degree-of-freedom system and a nonlinear cantilever beam discretized by the finite element method. [less ▲]

Model of electrostatic actuated deformable mirror using strongly coupled electro-mechanical finite element

in Analog Integrated Circuits and Signal Processing (2007), 53(2-3), 129-135

The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well ... [more ▼]

The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena appear and interact. Because of their microscopic scale, strong coupling effects arise between the different physical fields, and some forces, which were negligible at macroscopic scale, have to be taken into account. In order to accurately design such micro-electro-mechanical systems, it is of primary importance to be able to handle the strong coupling between the electric and the mechanical fields. In this paper, the finite element method (FEM) is used to model the strong coupled electro-mechanical interactions and to perform static and transient analyses taking into account large mesh displacements. These analyses will be used to study the behaviour of electrostatically actuated micro-mirrors. [less ▲]

Non-conforming element for accurate modelling of MEMS

in Finite Elements in Analysis & Design (2007), 43(10), 749-756

In this work different modelling techniques are investigated to simulate the dynamic behaviour of slender structures on which electrostatic forces are acting. In particular, non-conforming elements are ... [more ▼]

In this work different modelling techniques are investigated to simulate the dynamic behaviour of slender structures on which electrostatic forces are acting. In particular, non-conforming elements are tested to model micro- mechanical devices (or MEMS) having a very large aspect ratio. These elements are constructed on linear shape functions enriched by internal second-order polynomials. As a consequence the element compatibility is not exactly satisfied, but such elements can efficiently model beam- or shell-like structures with a small number of degrees of freedom. The advantage of non-conforming elements compared to shell or beam elements is that they are volume elements and can therefore easily be combined with other volume finite elements. For micro-mechanical systems the structure must be coupled to the electrostatic domain with the so-called electro-mechanical elements that solve for the electrostatic potential and generate the electrostatic forces. This paper shows that constructing coupled electro-mechanical models for high aspect ratio systems is then greatly simplified when non-conforming finite elements are used. The theory is presented for small deformations and also for large displacements where geometric non-linearities must be accounted for. The elements proposed in this paper are based on non-conforming formulations published earlier. The efficiency of the non-conforming approach combined with specific electro-mechanical elements is highlighted in the analysis of two simple MEMS for which the pull-in voltage is computed. (C) 2007 Elsevier B.V. All rights reserved. [less ▲]

Identification of Linear and Nonlinear Systems using Signal Processing Techniques

in 26th Benelux Meeting on Systems and Control, Lommel, 2007 (2007)