Global and bifurcation analysis of a structure with cyclic symmetry

International audienceIntroducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions--where T is known--of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited

Stochastic study of a non-linear self-excited system with friction

ThispaperproposestwomethodsbasedonthePolynomialChaostocarryout the stochastic study of a self-excited non-linear system with friction which is commonly used to represent brake-squeal phenomenon. These methods are illustrated using three uncertain configurations and validated using comparison with Monte Carlo simulation results. First, the stability of the static equilibrium point is examined by computing stochastic eigenvalues. Then, for unstable ranges of the equilibrium point, a constrained harmonic balance method is developed to determine subsequent limit cycles in the deterministic case; it is then adapted to the stochastic case. This demonstrates the effectiveness of the methods to fit complex eigenmodes as well as limit cycles dispersion with a good accuracy

A Case of Trisomy D 1

ABSTRACTA case of D1 trisomy is reported. The patient suffered of multiple congenital anomalies, which formed a characteristic pattern known as the « Patau's syndrome ».Chromosome analysis from blood cultures showed a modal number of 47; the additional chromosome was a 13 (D1).The aneuploidy origin and the probable mechanism, through which the malformations typical of Patau's syndrome might be produced, are discussed