Luc Masset

Performance, robustness and sensitivity analysis of the nonlinear tuned vibration absorber

Abstract The nonlinear tuned vibration absorber (NLTVA) is a recently developed nonlinear absorber which generalizes Den Hartog׳s equal peak method to nonlinear systems. If the purposeful introduction of nonlinearity can enhance system performance, it can also give rise to adverse dynamical phenomena, including detached resonance curves and quasiperiodic regimes of motion. Through the combination of numerical continuation of periodic solutions, bifurcation detection and tracking, and global analysis, the present study identifies boundaries in the NLTVA parameter space delimiting safe, unsafe and unacceptable operations. The sensitivity of these boundaries to uncertainty in the NLTVA parameters is also investigated.

Isolated Response Curves in a Base-Excited, Two-Degree-of-Freedom, Nonlinear System

In the present paper, isolated response curves in a nonlinear system consisting of two masses sliding on a horizontal guide are examined. Transverse springs are attached to one mass to provide the nonlinear restoring force, and a harmonic motion of the complete system is imposed by prescribing the displacement of their supports. Numerical simulations are carried out to study the conditions of existence of isolated solutions, their bifurcations, their merging with the main response branch and their basins of attraction. This is achieved using tools including nonlinear normal modes, energy balance, harmonic balance-based continuation and bifurcation tracking, and global analysis.Copyright

The universal projection for computing data carried on the hemisphere

For many years, important efforts have been devoted to efficiently compute the view factors in the frame of radiative heat exchanges. This subject has also received special attention in the more recent development of global illumination methods. Basically two techniques are available; the first one is based on projections and the second one on ray tracing methods. Here we will present a new algorithm dealing with projections and show that we can solve both the problems of computing view factors and solid angles by using the same projection. The proposed method is precise and fast, so it can be used in interactive design software.

The Harmonic Balance Method for Bifurcation Analysis of Nonlinear Mechanical Systems

Because nowadays structural engineers are willing to use or at least understand nonlinearities instead of simply avoiding them, there is a need for numerical tools performing analysis of nonlinear large-scale structures. Among these techniques, the harmonic balance (HB) method is certainly one of the most commonly used to study finite element models with reasonably complex nonlinearities. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. For this reason, the present paper proposes to extend the method to the detection and tracking of codimension-1 bifurcations in the system parameters space. As an application, the frequency response of a spacecraft is studied, together with two nonlinear phenomena, namely quasiperiodic oscillations and detached resonance curves. This example illustrates how bifurcation tracking using the HB method can be employed as a promising design tool for detecting and eliminating such undesired behaviors.

Enrichment of the visual experience by a wider choice of projections

Collaborative work is very important in engineering and architecture because of the many disciplines involved in the design process. For this reason, it is necessary to deliver to all the actors of the system not only relevant data, but also information corresponding to their specific skills. Because in architecture the visual experience is mainly based on projections, we want to show that a wider choice of them is the best way to improve the data exchanges. We choose the simple geometric problem of solar illumination. Because it is essential to take it into account from the first steps of the design to the final project, the partners have to communicate with several kinds of projections that are not always the most standard ones. In this process all the collaborators are expected to contribute to the fluency of the exchanges with the consequence that, in order to magnify some aspects of the design, they are induced to define new representations.

Bifurcation Analysis of a Spacecraft Structure Using the Harmonic Balance Method

The harmonic balance (HB) method has been widely used in the past few years, as a numerical tool for the study of nonlinear models. However, in its classical formulation the HB method is limited to the approximation of periodic solutions. The present paper proposes to extend the method to the detection and tracking of bifurcations in the codimension-2 system parameters space. To validate the methodology, the forced response of a real spacecraft is examined. The paper first provides some numerical evidence of the presence of quasiperiodic oscillations and isolated solutions. It then demonstrates how the tracking of Neimark-Sacker and fold bifurcations can help get a deeper understanding of these attractors.Copyright

Proper Orthogonal Decomposition for Nonlinear Radiative Heat Transfer Problems

Analysing large scale, nonlinear, multiphysical, dynamical structures, by using mathematical modelling and simulation, e.g. Finite Element Modelling (FEM), can be computationally very expensive, especially if the number of degrees-of-freedom is high. This paper develops modal reduction techniques for such nonlinear multiphysical systems. The paper focuses on Proper Orthogonal Decomposition (POD), a multivariate statistical method that obtains a compact representation of a data set by reducing a large number of interdependent variables to a much smaller number of uncorrelated variables. A fully coupled, thermomechanical model consisting of a multilayered, cantilever beam is described and analysed. This linear benchmark is then extended by adding nonlinear radiative heat exchanges between the beam and an enclosing box. The radiative view factors, present in the equations governing the heat fluxes between beam and box elements, are obtained with a ray-tracing method. A reduction procedure is proposed for this fully coupled nonlinear, multiphysical, thermomechanical system. Two alternative approaches to the reduction are investigated, a monolithic approach incorporating a scaling factor to the equations, and a partitioned approach that treats the individual physical modes separately. The paper builds on previous work presented previously by the authors. The results are given for the RMS error between either approach and the original, full solution.Copyright