Table 9: Typical relative deviation between present NTM and finite element (3D) results. Lowest three nonzero modes for two categories of single-step F-F beam; see Figure 13.

MethodModal frequencies in Hz
 mm mm
123123

0.5NTM0.1217.034635.6041267.5901878.3025163.8609645.650
0.4232.036797.5431834.1101995.4976510.74013831.40
0.7447.6291037.2702253.9403813.426816015739.200
FE(3D)0.1216.987634.8501263.2591876.2675123.7909448.138
0.4229.554785.7221819.3051930.1666271.64513642.314
0.7437.5911033.9152245.1253583.0148091.33015706.439
% dev.0.1−0.022−0.119−0.343−0.108−0.782−2.090
0.4−1.082−1.504−0.814−3.385−3.812−1.386
0.7−2.294−0.324−0.392−6.431−0.849−0.208

0.625NTM0.1283.930812.3571608.2202446.3476532.94011979.500
0.4308.616991.9552074.8902639.6387837.58015025.700
0.7495.7921128.8202333.2904167.3858797.25016074.300
FE(3D)0.1283.898811.7951604.9562445.4586509.82111855.709
0.4305.955981.3472072.5542570.4087647.97915037.839
0.7489.2341121.4522336.1774021.3018655.04216159.248
% dev.0.1−0.011−0.069−0.203−0.036−0.355−1.044
0.4−0.870−1.081−0.113−2.693−2.4790.080
0.7−1.341−0.6570.123−3.633−1.6430.526

0.750NTM0.1355.027993.2791944.0903030.2227818.40014004
0.4381.6391149.7202248.1103236.3678841.60015842.900
0.7511.2271230.8902406.1904268.2729431.64016437.800
FE(3D)0.1355.036993.1791943.0163031.6577819.72213978.716
0.4379.5831144.1592251.3513181.2918759.63415934.664
0.7508.4391224.3962410.0394205.9309312.42516529.197
% dev.0.10.002−0.010−0.0550.0470.017−0.181
0.4−0.542−0.4860.144−1.731−0.9360.576
0.7−0.548−0.5300.160−1.482−1.2800.553

0.875NTM0.1429.2731177.8202274.8603616.2129013.57015741.600
0.4448.1341269.8402419.6903759.2959566.42016569.700
0.7511.3801312.6602498.4604253.6609878.82016849.800
FE(3D)0.1429.3471178.4462277.0133621.2759047.34715829.045
0.4447.2581269.2732423.6953739.8349595.93416695.492
0.7510.7781310.7382502.1534247.1819870.04516963.843
% dev.0.10.0170.0530.0940.1400.3730.552
0.4−0.196−0.0450.165−0.5200.3080.753
0.7−0.118−0.1460.148−0.153−0.0890.672