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This chapter presents details of deriving a structural dynamics model for use in aeroelastic and aeroservoelastic applications. Beginning with an introduction on assumptions and idealizations required for modeling aircraft structures, the principles of static load-displacement relations, flexibility influence coefficients, virtual work, strain energy, and stiffness influence coefficients are described. For the dynamic case, the structural dynamics equations are derived from both Lagrange’s energy approach and Newton’s laws. A large part of the chapter presents the various discretization schemes for structural modeling. These include the lumped parameter approximation, the finite-element method, and the Rayleigh-Ritz method. Emphasis is placed on the finite element method, with details of Euler-Bernoulli beam-shaft model of two-noded elements for high aspect-ratio wings, and the Poisson-Kirchoff (CPT) plate theory for low aspect-ratio wings with triangular and rectangular elements.
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In a steady flow, we have \(\alpha_i\simeq\theta_i\), which is why most textbooks on aeroelasticity use the two angles interchangeably. However, we will distinguish the angles α i and θ i here, because we are mainly concerned with unsteady flow.
A more general boundary-value problem has time-varying governing equations and boundary conditions specified at discrete times, which implies explicit dependence of the partial differential operators on time, \(f(u,t),g_k(u,t)\). While such a problem can be posed for the general aeroservoelastic case in which the control inputs produce a certain desired behavior in time, it is not relevant in structural modeling applications.
One can alternatively specify a variation of the material properties by smooth functions, EI( y) and GJ( y), which are then included in the integration over each element.
Since the elements are arranged sequentially in a spanwise direction, only the adjacent elements can have a shared degree of freedom.
- Structural Modeling
- Springer New York
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