Question 1 To study drone propeller noise, a propeller test rig has been developed for the anechoic wind tunnel at UNSW, as shown in Figure 1. The rig consists of an 8 inch diameter, 2-bladed propeller and motor attached to the end of a 468 mm long steel shaft (beam) with diameter of 10 mm (I = 1.2(107) mm, E = 200(109) Pa and p = 7850 kg/m). Shaft Housing Propeller outer diameter and motor assembly Microphone arrays Test rig Figure 1. Drone propeller rig and rig installation in the UNSW anechoic wind tunnel. We need to understand the vibrational characteristics of the shaft as noise measurements will be impacted if the rig vibrates excessively. a) Analyse the transverse free vibration of the shaft by determining the first 5 natural Wn frequencies, the mode shape equation, and plot the first 5 mode shapes for the following B two cases: i. ii. The shaft alone when it is fixed at both ends of x = 0 and 1. The shaft when it is fixed at x = 0 in the housing and has the 0.45 kg drone propeller and motor mass assembly attached at the free end. You can assume the propeller Hailneton's and motor mass assembly is concentrated at x = 1 and ignore gravity. b) Consider the natural frequencies of the shaft you calculated in ii. If the propeller rotates at 8000 RPM, is it likely that the first blade pass frequency will excite a resonance condition and cause excessive vibration? method.