Shock and Vibration / 2017 / Article / Tab 9 / Research Article
A Normalized Transfer Matrix Method for the Free Vibration of Stepped Beams: Comparison with Experimental and FE(3D) Methods 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 .
Method Modal frequencies in Hz 1 2 3 1 2 3 0.5 NTM 0.1 217.034 635.604 1267.590 1878.302 5163.860 9645.650 0.4 232.036 797.543 1834.110 1995.497 6510.740 13831.40 0.7 447.629 1037.270 2253.940 3813.426 8160 15739.200 FE(3D) 0.1 216.987 634.850 1263.259 1876.267 5123.790 9448.138 0.4 229.554 785.722 1819.305 1930.166 6271.645 13642.314 0.7 437.591 1033.915 2245.125 3583.014 8091.330 15706.439 % 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 0.625 NTM 0.1 283.930 812.357 1608.220 2446.347 6532.940 11979.500 0.4 308.616 991.955 2074.890 2639.638 7837.580 15025.700 0.7 495.792 1128.820 2333.290 4167.385 8797.250 16074.300 FE(3D) 0.1 283.898 811.795 1604.956 2445.458 6509.821 11855.709 0.4 305.955 981.347 2072.554 2570.408 7647.979 15037.839 0.7 489.234 1121.452 2336.177 4021.301 8655.042 16159.248 % 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 −2.479 0.080 0.7 −1.341 −0.657 0.123 −3.633 −1.643 0.526 0.750 NTM 0.1 355.027 993.279 1944.090 3030.222 7818.400 14004 0.4 381.639 1149.720 2248.110 3236.367 8841.600 15842.900 0.7 511.227 1230.890 2406.190 4268.272 9431.640 16437.800 FE(3D) 0.1 355.036 993.179 1943.016 3031.657 7819.722 13978.716 0.4 379.583 1144.159 2251.351 3181.291 8759.634 15934.664 0.7 508.439 1224.396 2410.039 4205.930 9312.425 16529.197 % dev. 0.1 0.002 −0.010 −0.055 0.047 0.017 −0.181 0.4 −0.542 −0.486 0.144 −1.731 −0.936 0.576 0.7 −0.548 −0.530 0.160 −1.482 −1.280 0.553 0.875 NTM 0.1 429.273 1177.820 2274.860 3616.212 9013.570 15741.600 0.4 448.134 1269.840 2419.690 3759.295 9566.420 16569.700 0.7 511.380 1312.660 2498.460 4253.660 9878.820 16849.800 FE(3D) 0.1 429.347 1178.446 2277.013 3621.275 9047.347 15829.045 0.4 447.258 1269.273 2423.695 3739.834 9595.934 16695.492 0.7 510.778 1310.738 2502.153 4247.181 9870.045 16963.843 % dev. 0.1 0.017 0.053 0.094 0.140 0.373 0.552 0.4 −0.196 −0.045 0.165 −0.520 0.308 0.753 0.7 −0.118 −0.146 0.148 −0.153 −0.089 0.672
