Resposta dinâmica e estabilidade de tubos com escoamento interno

Abstract

In this work, a finite element model is developed to analyze: linear and non-linear transient response and free vibrations problems and dynamic stability of pipes conveying fluid. Making use of an updated lagrangian formulation for the principle of virtual work the incremental equations of motion are deduced. These equations are linearized about the equilibrium configuration and the free vibration problem is discussed, showing that an integral of motion exists when the pipes have fixed supports. Expressions for the hamiltonian, the lagrangian and the Hamilton's principle are then derived. A generalized Rayleigh quotient is used to study the influence of flow velocity on the eigenvalues behaviour, and theoretical estimates for the stability of the equilibrium position are obtained. It is shown that, for a periodic flow velocity, parametric resonance occurs and the boundaries of these instability regions are determined. A computer program was developed and used to get some numerical results namely: stability maps for pipes with different support conditions;existence of a limit cycle flutter in a non-linear problem vibration, for a cantilever pipe; comparison of linear and non-linear solutions for a transient dynamic response problem.