a 2023 06 12 text

Page 1

STRUCTURAL DYNAMICS AND AEROELASTICITY Prof. Giuseppe Quaranta, June 12, 2023 Exercise 1: Static aeroelasticity Consider the structure shown in the Figure. The wing, to be considered rigid, with span b and chord c, is placed in a wind tunnel and is attached to the wall by two beams, one of length L and the other of length b, both with constant stiffnesses EJ and GJ placed at 90 deg. between them. The flexible beam is attached at a distance e from the aerodynamic centre of the wing. To model aerodynamic forces use strip theory for incompressible flow. 1.a) Compute the dynamic divergence pressure qD. 1.b) Identifying which is the only geometric parameter that may prevent the occurrence of divergence. Exercise 2: Dynamic stability Consider the structure shown in the figure. The wing, to be considered rigid, with span b, chord c and uniform mass per unit area mw, is placed in a wind tunnel and is constrained by means of support consisting of two beams (placed at 90 deg. to each other with length L, bending stiffness EJ uni- form, torsional stiffness to be considered infinite and mass per unit of length m) and a beam of length b to be considered rigid and massless. At point B is placed a spring which al- lows the wing to rotate around the y axis. To model elastic deformation use the Ritz Galerkin approximation with a sin- gle, well-chosen, polynomial shape function for each portion of the flexible beam. The quasi-steady strip theory for an incom- pressible field should be adopted as an aerodynamic model. It is required to: 2.a) Write the equations of motion and illustrate how to eval- uate the possible instabilities. 2.b) Modify the equations and the solution methodology in the case of using Theodorsen’s theory to model aerody- namic unsteady forces. Exercise 3: Stochastic…