is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. Summary A flexible cable is modeled by a geometrically exact beam model with 3D rotations described using quaternion parameters. The boundary value problem is then discretized by the finite element method. The use of an asymptotic numerical method to solve the problem, requiring quadratic equations, is well suited to the quaternion parametrization. This combination of methods leads to a fast, robust and accurate algorithm very well-adapted for the simulation of the assembly process of cables. This is proved by running many examples involving complicated solutions.

A time-domain numerical modeling of brass instruments is proposed. On one hand, outgoing and incoming waves in the resonator are described by the Menguy-Gilbert model, which incorporates three key issues: nonlinear wave propagation, viscothermal losses, and a variable section. The nonlinear propagation is simulated by a TVD scheme well-suited to non-smooth waves. The fractional derivatives induced by the viscothermal losses are replaced by a set of local-in-time memory variables. A splitting strategy is followed to couple optimally these dedicated methods. On the other hand, the exciter is described by a one-mass model for the lips. The Newmark method is used to integrate the nonlinear ordinary differential equation so-obtained. At each time step, a coupling is performed between the pressure in the tube and the displacement of the lips. Finally, an extensive set of validation tests is successfully completed. In particular, self-sustained oscillations of the lips are simulated by taking into account the nonlinear wave propagation in the tube. Simulations clearly indicate that the nonlinear wave propagation has a major influence on the timbre of the sound, as expected. Moreover, simulations also highlight an influence on playing frequencies, time envelopes and on the playability of the low frequencies in the case of a variable lips tension.