Dynamic Behavior of Axially Functionally Graded Pipes Conveying Fluid

Table 7

The variation of natural angular frequencies for different material distributions and mass ratios when flow velocity is 20 m/s.

(mm)
1.0	0.796		22.1835	23.8868	24.9026	26.4715	27.4513	28.1186	28.8294	29.4111
			61.5036	65.7479	68.3906	72.7928	76.1318	79.0050	81.8223	83.2525
			120.732	128.668	133.700	142.428	149.573	156.161	162.514	165.285
			199.693	212.486	220.721	235.305	247.679	259.404	270.748	275.362
			298.392	317.258	329.420	351.361	370.905	389.776	407.194	413.686
2.0	0.672		22.2976	23.8315	24.6962	25.9020	26.4864	26.7497	27.1061	27.5738
			61.5972	65.3592	67.5855	71.0306	73.3695	75.2171	77.0180	78.0331
			120.825	127.785	131.993	138.872	144.125	148.770	153.121	155.007
			199.781	210.932	217.798	229.340	238.617	247.159	255.195	258.328
			298.477	314.839	324.951	342.322	357.127	371.143	383.736	388.144
3.0	0.587		22.3317	23.7692	24.5496	25.5605	25.9443	26.0152	26.2112	26.6270
			61.6283	65.1117	67.1047	70.0359	71.8650	73.2123	74.5377	75.3643
			120.856	127.252	131.000	136.890	141.179	144.870	148.272	149.752
			199.812	210.013	216.115	226.033	233.735	240.712	247.171	249.620
			298.508	313.428	322.400	337.340	349.740	361.370	371.651	375.089