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An aerofoil of mass 20 kg is suspended in a wind tunnel by a spring, which deflects by 20 mm under the static load of the aerofoil. The viscous damping ratio is estimated to be 0.1. During a test, the amplitude of vibration of the aerofoil is measured to be 10 mm at an excitation frequency of 10 Hz. Assuming the excitation is harmonic, calculate the maximum value of disturbing force.
A machine of mass 70 kg is mounted on three identical springs, each having a stiffness of 9 kN/m, with a damper. If the amplitude of the oscillations of the machine decreases from 30 mm to 5 mm in two complete oscillations, calculate the damping coefficient and the frequency of the damped motion in Hz.
(b) For leading edge components for hypersonic applications, a company wants to fabricate composites consists of 20 vol % of SiC fibres reinforced HfB2 matrix. The elastic modulus of SiC fibre is 410 GPa and HfB2 is 520 GPa. Compute the modulus of elasticity of this composite in the longitudinal direction.
(c) If the composite in Q8 (b) subjected to a stress of 800 MPa in longitudinal direction and behaves linearly elastic, compute the strain on the longitudinal direction and the true stress in the longitudinal direction.
9. If the cross sectional area of the composites in (Q8 (c) is 240 mm2 and is subjected to a stress of 400 MPa in longitudinal direction, compute the magnitude of the load carried by the each of the fibre and matrix phases.
A gas turbine rotor consists of a compressor, a turbine and a generator mounted on a uniform flexible shaft simply supported in its bearings as shown in Figure Q11. The mass of the shaft is negligible in comparison to the masses of the other components. The shaft is of length of 6 m and diameter of 100 mm. The masses and locations of the compressor, turbine and generator are shown on the diagram.
(a) Use Dunkerley’s method to estimate the lowest natural frequency of the rotor.
(b) Discuss other methods such as Rayleigh’s method (Do not calculate, but assemble the equations) which could be used to estimate the lowest natural frequency of the rotor.
AE5022: Aerospace Structures Materials And Dynamics