José Vieira Antunes (Centro de Ciências e Tecnologias Nucleares, Instituto Superior Técnico, Lisbon, Portugal). The Udwadia-Kalaba formulation and its application for the physical modelling of string instruments.

Most structures consist of dynamical subsystems connected at a number of constraining points through which energy flows. One important difficulty deals with enforcing these coupling constraints. While standard techniques include the use of Lagrange multipliers or penalty methods, another interesting approach will be discussed, the Udwadia-Kalaba (U-K) formulation, which is rooted on analytical dynamics but avoids the explicit use of Lagrange multipliers. This general and elegant formulation has been nearly exclusively used for conceptual systems of discrete masses or articulated rigid bodies, namely, in robotics. However its natural extension to deal with continuous flexible systems is nearly absent from the literature. Such a modeling strategy is presented and the potential of combining the U-K equation for constrained systems with the modal description is shown, in particular, to simulate musical instruments.

Moreover, constraints often display intermittent contact phenomena, such as arising from joints or supports with clearances. The dynamical analysis of these highly nonlinear systems is typically performed in the time-domain, with the difficulty of enforcing intermittent coupling constraints. The Udwadia-Kalaba (U-K) analytical framework, can be extended to deal with such a problem, by addressing subsystems modelled through their unconstrained modes and coupled at one or more intermittent point-constraints. A crucial aspect is that constraint violations must be prevented, not only at the acceleration level, but also at the velocity and displacement levels, in order to avoid computational drift.

These developments will be illustrated in the context of musical instrument modelling, more specifically string instruments. An industrial application will be also discussed, concerning the nonlinear dynamics of clearance-supported tubes of nuclear steam-generators subjected to flow excitation.