A turbine blade in a rotor of a gas turbine experiences the force (Table P3.4) during each
Question:
A turbine blade in a rotor of a gas turbine experiences the force (Table P3.4) during each rotation. An SDOF model of the turbine blade is described in Figure P3.4a where \(m=1 \mathrm{~kg}, k=80,000\) \(\mathrm{N} / \mathrm{m}\), and \(c=3 \mathrm{~N}-\mathrm{sec} / \mathrm{m}\). The clearance is \(0.0002 \mathrm{~m}\). The force \(f(t)\) is described by data in Table P3.4, where the locations of the pressure measurements are shown in P3.4b.
Table P3.4
Figure P3.4a
Figure P3.4b
Figure P3.4c
The gas turbine is stationary. You are in charge of starting the engine and operating the gas turbine at a steady rotational speed equal to \(60 \mathrm{~Hz}\). Using the velocity profile (Figure P3.4c), determine the smallest angular acceleration of the turbine so that the blade never hits the casing.
At the steady speed of \(60 \mathrm{~Hz}\), compute the Fourier coefficients and the steady-state response analytically. Compare your steady-state response to that from ODE23 or ODE45.
Step by Step Answer:
