In Example 3.1.4, the second nozzle is inadvertently closed. Find the Fourier coefficients of the force experienced by each blade. Also, find the maximum steady-state amplitude using the natural frequency and the damping ratio provided in Example 3.1.5.

Example 3.1.4

Example 3.1.5

Transcribed Image Text:

Consider the rotor and the stator of a turbomachine (Figure 3.1.9). The schematic drawings of the stator and the rotor are shown in Figure 3.1.10. The stator consists of four equi-spaced nozzles, with each nozzle having a 45 degrees sector. The rotor is a bladed disk with a rotational speed of 2 cps (Hz). When the blade comes in front of the nozzle, it experiences a constant force p due to fluid flow. The temporal variation of the force experienced by each blade is periodic and is shown in Figure 3.1.11. The force pattern is repeated four times during one full rotation. As a result, the time period 7 of the forcing function is 1 T = sec 452 And the fundamental frequency 2 @= = 8 rad/sec T