Development of a computationally efficient dynamical model of constrained flexible  systems  using  a  modal  udwadia-kalaba formulation

Most structures consist on dynamical subsystems connected at constraining points. While standard modelling techniques use Lagrange multipliers or penalty methods, Udwadia & Kalaba (U-K) encapsulated the constraints into a single dynamical equation. We extended their approach to continuous flexible systems, through modal description, while addressing highly nonlinear intermittent constraints. Efficient numerical simulations performed include the (1) dynamics of a complete guitar, incorporating many modes and linear constraints; (2) flow-excited vibro-impact responses of multi-supported tubes with clearances, typical of nuclear steam generators.