GENERAL FORMULATION OF AEROELASTIC. PROBLEMS
In the previous chapters several types of aeroelastic problems are treated. A large number of other problems can be formulated, the practical importance of which depends on the type of the structure and the conditions of the flow. In order to clarify the basic features of any problem, and to determine the degree of approximation of an analysis, it is desirable to have the formulation as general as possible at the beginning, and then to specialize in particular cases by introducing further assumptions. In this way the relationship between various approaches to the problem can be understood, and, if an improvement on a known theory is desired, one can locate the restrictive assumptions and decide which one should be relaxed.
In § 11.1 the feedback nature of aeroelastic systems and their representation by functional diagrams are considered. The functional operators concept is then introduced in § 11.2 to reduce the pictorial representations of functional diagrams into algebraic equations. The operators entering aeroelastic analysis are examined in greater detail in §§ 11.3 to 11.5.
Knowing the form of the operators involved, we will have no difficulty in writing down the governing equations according to the functional diagrams and the operational equations. The accuracy of the formulation of each problem is clearly indicated by the assumptions used in deriving the operators.
The mathematical characteristics of aeroelastic problems are briefly discussed in § 11.6.