By Earl H. Dowell, Howard C. Curtiss Jr. (auth.), Earl H. Dowell, Howard C. Curtiss Jr., Robert H. Scanlan, Fernando Sisto (eds.)
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Extra resources for A modern course in aeroelasticity
They are 'primitive functions' for a variable property wing even though eigenfunctions for a constant property wing. 3 Rolling 01 a straight wiIlg We shall now consider a more complex physical and mathematical variation on our earlier static aeroelastic lifting surface (wing) studies. For variety, we treat a new physical situation, the rolling of a wing (rotation about the root axis). Nevertheless, we shall meet again our old friends, 'divergence' and 'control surface effectiveness' or 'reversal' .
2 P3, P4 -±I-m * Timoshenko and Gere . 5) or convert them into an integral equation to be solved by the 'Iumped element' method. 6) we may determine that 2 Al =A =A4 =O and either A 3 = 0 or sin Ä = 0 For non trivial solutions and sin Ä =0 or Ä = 1',21',31', etc. , w == o. 8) Note that Ä 2 is a nondimensional ratio of aerodynamic to elastic stiffness; we shall call it and similar numbers we shall encounter an 'aeroelastic stiffness number'. It is as basic to aeroelasticity as Mach number and Reynolds number are to fluid mechanics.
This problem is one of a type known as 'Sturm-Liouville Problems'. 25) where GJ (GJ)ref 'Y=-- Let as before. 25), multiplying by a m and J~ ... 26) The first and se co nd terms cannot be simplified further unless the eigenfunctions or 'modes' employed are eigenfunctions for the variable property wing. Hence, an is not as simply related to An as in the constant property wing example. 26) represents a system of equations for the an. 29) which is a polynomial in A2. , are infinite systems of equations (in an infinite number of unknowns).