Wave propagation in a rotating disc of polygonal cross-section immersed in an inviscid fluid

Figures & data

Table 1. The non-dimensional frequency of triangular and square cross-sectional disc with fluid and without rotation for different aspect ratios

Mode	Triangle			Square
	a/b = 1.0	a/b = 1.5	a/b = 2.0	a/b = 1.0	a/b = 1.5	a/b = 2.0
S1	3.5251	3.6403	3.4426	3.2076	3.0775	3.2511
S2	4.8474	4.9872	4.8692	4.7112	4.8430	4.9522
S3	5.5647	5.6966	5.6625	5.4685	5.4844	5.8029
S4	6.2604	6.2625	6.3683	6.1122	6.1911	6.3618
S5	6.9675	6.9685	7.0676	6.8276	6.8976	7.0225

Table 2. The non-dimensional frequency of pentagon and hexagon cross-sectional disc with fluid and without rotation for different aspect ratios

Mode	Pentagon			Hexagon
	a/b = 1.0	a/b = 1.5	a/b = 2.0	a/b = 1.0	a/b = 1.5	a/b = 2.0
S1	4.2469	4.1053	4.2473	4.2469	4.2426	4.3841
S2	4.9545	4.9501	5.0964	4.9511	4.9497	5.0927
S3	5.6625	5.6556	5.8041	5.6624	5.6593	5.8041
S4	6.3693	6.2288	6.3712	6.3668	6.2257	6.5118
S5	7.0732	6.9290	7.2125	7.0680	6.9366	7.0704

Table 3. The non-dimensional frequency of triangular and square cross-sectional disc without fluid and without rotation for different aspect ratios

Mode	Triangle			Square
	a/b = 1.0	a/b = 1.5	a/b = 2.0	a/b = 1.0	a/b = 1.5	a/b = 2.0
A1	4.1440	4.1536	4.2475	4.0336	4.0978	4.2434
A2	4.8602	4.8621	4.9428	4.7134	4.8007	4.9526
A3	5.5753	5.5712	5.6615	5.4087	5.5055	5.6599
A4	6.2691	6.2785	6.3704	6.1590	6.2154	6.3711
A5	6.9696	6.9857	7.0715	6.8707	6.9220	7.0726

Table 4. The non-dimensional frequency of pentagon and hexagon cross-sectional disc without fluid and without rotation for different aspect ratios

Mode	Pentagon			Hexagon
	a/b = 1.0	a/b = 1.5	a/b = 2.0	a/b = 1.0	a/b = 1.5	a/b = 2.0
A1	4.2377	4.1785	4.3766	4.2480	4.2232	4.3144
A2	4.9598	4.8095	5.0695	4.9535	4.8513	5.2585
A3	5.6645	5.5171	5.8027	5.6723	5.5509	5.8042
A4	6.3672	6.2246	6.3815	6.5083	6.1846	6.5117
A5	7.0761	6.9380	7.2124	7.0833	7.0781	7.2201

Figure 1. Rotating disc of (a) Triangle (b) Square (c) Pentagon (d) Hexagonal cross-sections.

Figure 2. Variation of non-dimensional wave number vs. non-dimensional frequency of rotating disc of triangular cross-section.

Figure 3. Variation of non-dimensional wave number vs. non-dimensional frequency of rotating disc of square cross-section.

Figure 4. Variation of non-dimensional wave number vs. non-dimensional frequency of rotating disc of pentagonal cross-section.

Figure 5. Variation of non-dimensional wave number vs. non-dimensional frequency of rotating disc of hexagonal cross-section.

Figure 6. Variation of relative frequency shift vs. non-dimensional frequency of rotating disc of triangular cross-section.

Figure 7. Variation of relative frequency shift vs. non-dimensional frequency of rotating disc of square cross-section.

Figure 8. Variation of relative frequency shift vs. non-dimensional frequency of rotating disc of pentagonal cross-section.

Figure 9. Variation of relative frequency shift vs. non-dimensional frequency of rotating disc of hexagonal cross-section.