Numerical investigation of the effects of compressibility on the flutter of a cantilevered plate in an inviscid, subsonic, open flow

Numerical investigation of the effects of compressibility on the flutter of a three-dimensional, cantilevered plate in an inviscid, subsonic, open flow

“…In this work, we extend the investigations of [28,30,41] by performing a parametric study of the flutter speed and the flutter frequency of a plate cantilevered at the leading edge in a three-dimensional, inviscid, compressible, subsonic flow as a function of its mechanical properties and the upstream Mach number. For that purpose, we have developed a numerical scheme based on discretizing the plate equations through a spectral Galerkin formulation and on solving the (linear) aerodynamic equations with a slight modification of the Ueda-Dowell doublet point method [42].…”

“…Therefore, in order to deal with compressibility effects at higher Mach numbers, some investigators have tried an approach based on the direct discretization in space and in time of the linearized, compressible, potential flow equations. This is done, for example, in the papers of Li and Yang -who implemented a differential quadrature method restricted to panels wetted by one side-, Huang and Zhang [26] -who formulated a Chebyshev pseudospectral method-and of Colera and Pérez-Saborid [27,28] -who employed finite differences. Apparently, only the latter authors effectively applied their method to compressible flows and panels wetted by the two sides -Huang and Zhang only considered the case of zero Mach number-, although their results were restricted to the two-dimensional case.…”

“…For that purpose, we have developed a numerical scheme based on discretizing the plate equations through a spectral Galerkin formulation and on solving the (linear) aerodynamic equations with a slight modification of the Ueda-Dowell doublet point method [42]. It must be pointed that the methodology and the parametric study presented here are clearly inspired on those of a previous work [28], with the difference that here we employ a three-dimensional formulation instead of a two-dimensional one. To the best of our knowledge, this is the first computational investigation of the effects of compressibility on the flutter of a plate cantilevered at the leading edge in a three dimensional, inviscid, subsonic flow carried out in the literature.…”

PDEs on deformable domains: Boundary Arbitrary Lagrangian-Eulerian (BALE) and Deformable Boundary Perturbation (DBP) methods

“…Partial differential equations whose domains are a priori unknown arise in a plethora of physical configurations where geometrical nonlinearities, free interfaces and shape optimisation matter. Geometrical nonlinearities are of crucial importance for the proper description of stability problems involving (i) deformable solids such as beam buckling, first described by Leonhard Euler [36], or follower loads [23], (ii) solid-gas interactions, such as the flutter of Tacoma Narrows bridge which led to its collapse, the flutter of airwings [9], or cantilevered pipes conveying fluids [29], and (iii) fluid interfaces with surface tension, such as liquid bridges [25], vibration and break up of liquid domains [27] or capillary waves [20].…”

“…Analytical changes of variables and description at the boundary further allow to carry out linearisation of model equations in canonical geometries [27,20,6], and in more involved geometries such as in stretched axisymmetric jets [16,33], curve jets and pipes [1,29], planar plates [9] or coflowing liquids [5], with the help of methods developed on purpose for those specific geometries. Despite this concept was developed shortly after the development of perturbation techniques [13], they are either analytical [13,10] or they depend on the numerical method used to solve the equations.…”