Aeroelastic Problem: Formulation of Static and Dynamic Response Problems Flashcards
What is the response analysis?
Once the stability analysis is over and we have assessed that there is no flutter/divergence, it is possible to move to response analysis. The analysis of the response is meaningful only for flight conditions where the aircraft is stable. The types of inputs can be:
*Controls (ie movable surfaces)
*Gusts
*Exciters (vibrating masses, bonkers, etc)
What is an equilibrium or steady maneuver?
The aircraft is in a steady maneuver, so it is balanced, or trimmed, so no changed in times must be considered. Examples are steady level flight, pull-up push-down, banked turn. The assumption is that the dynamics are fast enough. Consequently, the problem could be approached using static aeroelasticity methods. The problem could be approached:
a) Retaining a rigid aircraft model and modifying the aerodynamics to keep into account the flexibility
b) Using a fully flexible model
For the aerodynamics it is possible to use a quasti-steady behavior since the frequency of the forces is 0, which means that the structure repsonds instantaneously to the forcing.
How are equilibrium maneuvers calculated?
The problem is:
Mq_dot_dot + Cq_dot - q/UCaq_dot + Kq - qKaq = Fe.
The modes are decomposed into rigid and elastic modes. There is no stiffness and damping associated with rigid modes. Also, the elastic velocity and acceleration is negligible, because elastic dofs are faster than structural dofs.
KAE (KEE - qKaEE) is the aeroelastic stiffness (that is singular at the divergence dynamic pressure) and for low dynamic pressures, KAE ~ KEE.
It is possible to see the deformation of the structure as the combined effect of external loads, inertia forces due to rigid movements and aerodynamic loads due to rigid movements. From the equation KEE is calculated and substituted in the rigid body equation.
If the vehicle changes shape., new terms proportional to the dynamic pressure appear in the first rigid equation. The equation has the same format of the rigid ones, but the matrixes contain new aerodynamic derivative terms. If Mer = 0, then there are no aerodynamic stability derivatives that are proportional to rigid accelerations. If the proper orthogonal modes of a free-free structure are used, Mer = 0 by default.
What are dynamic maneuvers?
When we are interested in dynamic maneuvers, we will consider the application of a time history of a control surface movement to see what happens to loads.
It is essential to model the behavior of a control surface and its actuation behavior.
How can a control surface be modelled?
Specific shape functions are used to represent the rigid rotations of the movable surface will be added to the usual shape functions. In this way, a specific degree of freedom associated with the rotation of the movable surface will be defined. The set of shape functions will be the union of blocked-surface shape functions and movable surface shape functions.
ηs = Nq + Νδ*δ, where d represents the rotation of surface.
How can an ideal servo actuator be modelled?
If we consider an ideal servo actuator that can keep exactly any required position, independently from the load applied on it, it is possible to consider the control rotation δ an an input.
z{q;δ} = {Feq;Feδ}. The second equation could be used to identify the load Fδ that must be applied by the actuator/pilot to keep the position δ. This load is in general a function of time.
Discuss about control chain and servo-actuators.
For light aircraft a direct mechanical contron chain connects the actuators with the control sticks in the cockpit.
For larger aircraft, the forces to be sustained are too big, so a hydraulic system with irreversible actuators is installed. An example is a duplex actuator, where two valves are supplied by different hydraulic circuits. If there is a pressure loss in one valve, the other one will keep working without obstructing the flow.
How can a servo-controlled surface be modelled?
In order to improve the approximation, it is possible to include the dynamics of the actuator through a servo-system transfer function. This model is still ideal, because also in this case, the force Feδ must change instantaneously to adapt to changes of v.
δ = Hservo(s)δc
How can a flight control system be modelled?
When there is a flight control system, things become more cumbersome because the controller request is the result of what is applied by the pilot, through a transfer function that represents the flexibility of the control chain and what is required by the flight control system that is again governed by the transfer funtion.
δc = Hp(s)δpilot + HFCS(s)Hsensors(s){q;q_dot;q_dot_dot}
How can a dynamic compliance surface be modelled?
It is also possible to include the effect of elasticity to the control chain. In the case where there is no servo-actuator, it is possible to have δ and δc different because the control chain is in reality an elastic system. Feδ/κ = (δ - δc) -> δ = Hs(s)δc + Hc(s)Feδ/κ, Hc admittance or dynamic compliance.
What is the gust response?
For design purposes, atmospheric change of wind speed is divided in two ideal categories:
1) Discrete gusts, where the gust velocity varies in a deterministic manner (typically 1-cosine shape). The intensity of gust and length to consider are assigned by the certification standards as function of altitude and speed.
2) Continuous gusts, where the gust velocity is assumed to vary in a randon manner. The Von Karman PSD for turbulence can be used.
