Olivier Dessombz

Stochastic Analysis of the Eigenvalue Problem for Mechanical Systems Using Polynomial Chaos Expansion— Application to a Finite Element Rotor

This paper proposes to use a polynomial chaos expansion approach to compute stochastic complex eigenvalues and eigenvectors of structures including damping or gyroscopic effects. Its application to a finite element rotor model is compared to Monte Carlo simulations. This lets us validate the method and emphasize its advantages. Three different uncertain configurations are studied. For each, a stochastic Campbell diagram is proposed and interpreted and critical speeds dispersion is evaluated. Furthermore, an adaptation of the Modal Accordance Criterion is proposed in order to monitor the eigenvectors dispersion.

Structural Design of Uncertain Mechanical Systems Using Interval Arithmetic

This paper deals with a method to analyze the modal characteristics of structures including bounded uncertain parameters. These parameters can be uncertain, variable or not set at a design stage. We will use interval theory to propose a formulation adapted to finite element mechanical problems, taking into account the construction of mass and stiffness matrices. We will consider two kinds of problems: finding the bounds of static problem solutions, and the envelopes for transfer functions. A new numerical method will be used, based on the formulation proposed above. We will emphasize the efficiency of this method on simple mechanical problems. A frame structure will be studied, for which an overlap phenomenon appears on the transfer function envelope.

Acoustical Radiation Calculation of Complex Structures Using Finite Element Methods

Predicting noise is a step that cannot be ignored in automotive industry during vehicle design cycle. This is classically achieved through Finite Element and Boundary Element methods. When dealing with exterior problems, Boundary Element Method is quite efficient but may induce ill-conditioned equations. On the other hand, Finite Element Method, if easier to handle is not basically adapted to unbounded media. In this paper a new method, which tries to combine advantages of both techniques is presented. This method, inspired from Substructure Deletion Method, which is well-known in Civil Engineering, consists in dividing a complex unbounded problem into two easier ones to solve finite and infinite problems. Instead of considering a geometrically complex structure straightforward, a prismatic bounding volume is first studied using BEM. Then a classical Finite Element computation is performed on the volume left between the box and the structure of interest. Advantage of this technique is that when testing and comparing several geometries contained in such a box, only one boundary element calculation is needed. Efficiency of this method is discussed in the present document. Here instead of using Boundary Element Methods to solve the exterior problem, an original use of Finite Elements is made. Efficiency of this new version of the Substructure Deletion Method is discussed.Copyright