Theoretical and Numerical Studies on Damped Nonlinear Vibration of Orthotropic Saddle Membrane Structures Excited by Hailstone Impact Load

Table 4

Frequencies (rad/s) under different hailstone diameters and time instants.

Order	Time (s)	Hailstone diameter (cm)
		1.0	2.0	3.0	4.0	5.0	6.0
1st order	0.000	767.153	764.210	756.556	743.197	725.732	711.945
	0.005	767.153	764.206	756.494	742.780	724.029	706.369
	0.010	767.153	764.203	756.449	742.480	722.781	702.175
	0.050	767.153	764.197	756.347	741.767	719.633	690.749
	0.100	767.153	764.196	756.341	741.714	719.358	689.520
		767.153	764.196	756.340	741.712	719.345	689.445
2nd order	0.000	900.943	897.476	888.331	871.663	847.390	819.091
	0.005	900.943	897.475	888.306	871.495	846.699	816.760
	0.010	900.943	897.474	888.288	871.375	846.192	815.006
	0.050	900.943	897.471	888.248	871.088	844.914	810.228
	0.100	900.943	897.471	888.245	871.066	844.803	809.714
		900.943	897.471	888.245	871.066	844.797	809.683
3rd order	0.000	1081.37	1077.25	1066.77	1049.89	1032.55	1034.530
	0.005	1081.37	1077.24	1066.59	1048.66	1027.60	1018.990
	0.010	1081.37	1077.23	1066.45	1047.78	1023.97	1007.310
	0.050	1081.37	1077.21	1066.15	1045.68	1014.82	975.473
	0.100	1081.37	1077.21	1066.13	1045.52	1014.02	972.048
		1081.37	1077.21	1066.13	1045.51	1013.98	971.837
4th order	0.000	1105.53	1101.40	1092.06	1083.13	1094.00	1100.19
5th order	0.000	1184.02	1179.48	1167.68	1147.15	1120.50	1165.05
6th order	0.000	1190.68	1186.16	1174.99	1158.63	1147.61	1171.37
7th order	0.000	1395.95	1390.65	1377.50	1358.04	1344.08	1369.30