Linear fluid-structure stability analysis with transpiration. Part II: numerical analysis and applications

This paper constitutes the numerical counterpart of the mathematical framework introduced in Part I. We address the problem of flutter analysis of a coupled fluid–structure system involving an incompressible Newtonian fluid and a reduced structure. We use the Linearization Principle approach developed in Part I, particularly suited for fluid–structure problems involving moving boundaries. Thus, the stability analysis is reduced to the computation of the leftmost eigenvalues of a coupled eigenproblem of minimal complexity. This eigenproblem involves the linearized incompressible Navier–Stokes equations and those of a reduced linear structure. The coupling is realized through specific transpiration interface conditions. The eigenproblem is discretized using a finite element approximation and its smallest real part eigenvalues are computed by combining a generalized Cayley transform and an implicit restarted Arnoldi method. Finally, we report three numerical experiments: a structure immersed in a fluid at rest, a cantilever pipe conveying a fluid flow and a rectangular bridge deck profile under wind effects. The numerical results are compared to former approaches and experimental data. The quality of these numerical results is very satisfactory and promising.