Full exam for Dynamics and Control of Space Structures in the Aerospace Engineering degree programme at Politecnico di Milano. The document covers: Continue on the next page. DCASF A ID codes: 072652, 081225, 091932 Date: 15 July 2016 Instructor: Lorenzo Dozio 1. A straight wing is modeled as a cantilever beam of span b, torsional stiffness GJ(y) and bending stiffness EJ (y). Let e(y) be the distance between the elastic axis
Full exam for Dynamics and Control of Space Structures in the Aerospace Engineering degree programme at Politecnico di Milano. The document covers: Continue on the next page. DCASF A ID codes: 072652, 081225, 091932 Date: 15 July 2016 Instructor: Lorenzo Dozio 1. A straight wing is modeled as a cantilever beam of span b, torsional stiffness GJ(y) and bending stiffness EJ (y). Let e(y) be the distance between the elastic axis
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Continue on the next page. DCASF A ID codes: 072652, 081225, 091932 Date: 15 July 2016 Instructor: Lorenzo Dozio 1. A straight wing is modeled as a cantilever beam of span b, torsional stiffness GJ(y) and bending stiffness EJ (y). Let e(y) be the distance between the elastic axis and the axis of aerodynam ic centers, and c(y) the chord of the generic wing section. (a) According to the strip theory, derive the equations to study t he aeroelastic divergence of the wing using an admissible one-term approximation for the transverse disp lacement w(y) of the elastic axis and the twist angle θ(y) about the elastic axis. (b) Compute from the previous equations the dynamic pressure qD corresponding to the torsional diver- gence condition when the elastic and aerodynamic properties of the wing are assumed to be constant in the spanwise direction. x y z e(y) c(y) b V∞ axis of aerodynamic centers – elastic axis fixed root section 2. The bending vibrations of a slender cantilever lightly-damped beam are represented by a finite element model based on two-nodes 1-D elements. The beam is equipped at th e tip with a voltage-driven inertial actuator and a single-axis accelerometer. The actuator is modeled as a single-degree-of-freedom system with mass ma, damping ca and stiffness ka and the force transmitted between the actuator and the beam is expressed as F (s) = ( ka + sca)δ(s) − b0 s3 + a2s2 + a1s + a0 V (s) where δ is the total elongation of the actuator and V is the control voltage. (a) Derive the set of differential equations describing the overall d ynamics of the system when a reduced- order modal model of the beam is used. (b) Write a state-space representation of the previous set. 1 (c) Show the equations required for the design of an optimal outpu t feedback controller aimed at…
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