Journal of Engineering / 2016 / Article / Tab 3 / Research Article
A Higher-Order Thermomechanical Vibration Analysis of Temperature-Dependent FGM Beams with Porosities Table 3 Temperature and material graduation effect on first dimensionless natural frequency of S-S FG porous beam with different FG type and porosity parameter and thermal loading
.
FGM type Load type FGM (I) 0 UTR 6.30389 5.55814 5.07272 4.27875 3.72764 3.33104 3.01417 LTR 6.35804 5.61591 5.13240 4.3404 3.78911 3.39085 3.07191 NLTR 6.35804 5.61697 5.13418 4.34337 3.79269 3.39432 3.07434 STR 6.39220 5.64920 5.16525 4.37267 3.82089 3.42192 3.10216 0.1 UTR 6.88939 5.91101 5.3085 4.36908 3.74463 3.30844 2.96886 LTR 6.93701 5.96243 5.36189 4.4244 3.79971 3.3618 3.02011 NLTR 6.93701 5.96350 5.36368 4.42737 3.80327 3.36525 3.02251 STR 6.96838 5.99263 5.39152 4.45338 3.82818 3.38953 3.04698 0.2 UTR 7.82479 6.41844 5.62782 4.47876 3.75865 3.27411 2.90872 LTR 7.86594 6.46361 5.67541 4.52784 3.80743 3.32111 2.95356 NLTR 7.86594 6.46470 5.67681 4.53081 3.81097 3.32451 2.95592 STR 7.89494 6.49085 5.70149 4.55354 3.83259 3.34551 2.97705 FGM (II) 0 UTR 6.30389 5.55814 5.07272 4.27875 3.72764 3.33104 3.01417 LTR 6.35804 5.61591 5.1324 4.3404 3.78911 3.39085 3.07191 NLTR 6.35804 5.61697 5.13418 4.34337 3.79269 3.39432 3.07434 STR 6.39220 5.64920 5.16525 4.37267 3.82089 3.42192 3.10216 0.1 UTR 6.64111 5.78821 5.24673 4.38047 3.79112 3.37261 3.04242 LTR 6.69138 5.84218 5.30264 4.43828 3.84865 3.42818 3.09605 NLTR 6.69138 5.84326 5.30446 4.44130 3.85227 3.43189 3.09850 STR 6.72276 5.97465 5.33263 4.46770 3.87758 3.45659 3.12341 0.2 UTR 7.04845 6.05522 5.44397 4.49154 3.85843 3.41549 3.0708 LTR 7.09505 6.10561 5.49630 4.5457 3.91222 3.46742 3.12050 NLTR 7.09505 6.10673 5.49818 4.54880 3.91590 3.47098 3.12300 STR 7.12377 6.34578 5.52354 4.57237 3.93839 3.49287 3.14509 ( FGM (I) 0 UTR 6.03310 5.29292 4.81092 4.02257 3.47629 3.08492 2.77209 LTR 6.21394 5.48065 5.00243 4.21813 3.67152 3.27641 2.95925 NLTR 6.21396 5.48282 5.00610 4.22427 3.67893 3.28361 2.96429 STR 6.28428 5.54918 5.07003 4.28455 3.73697 3.34046 3.02173 0.1 UTR 6.64113 5.67142 5.07315 4.14065 3.52152 3.09079 2.75553 LTR 6.80158 5.83808 5.24377 4.31487 3.69508 3.26037 2.92054 NLTR 6.80158 5.84028 5.24746 4.32099 3.70243 3.26747 2.92549 STR 6.86614 5.90014 5.30464 4.37434 3.75352 3.31734 2.97583 0.2 UTR 7.59524 6.20206 5.41874 4.27759 3.56334 3.08445 2.72346 LTR 7.73650 6.34921 5.5683 4.43094 3.71572 3.23261 2.86700 NLTR 7.7365 6.35146 5.57203 4.43704 3.72299 3.23960 2.87185 STR 7.79615 6.40512 5.6226 4.48355 3.76723 3.28260 2.91519 FGM (II) 0 UTR 6.0331 5.29292 4.81092 4.02257 3.47629 3.08492 2.77209 LTR 6.21394 5.48065 5.00243 4.21813 3.67152 3.27641 2.95925 NLTR 6.21396 5.48282 5.00610 4.22427 3.67893 3.28361 2.96429 STR 6.28428 5.54918 5.07003 4.28455 3.73697 3.34046 3.02173 0.1 UTR 6.38455 5.53844 5.00104 4.14128 3.55732 3.14447 2.81874 LTR 6.55307 5.71372 5.17992 4.32377 3.73904 3.32205 2.99163 NLTR 6.55307 5.71595 5.18367 4.32999 3.74651 3.32929 2.99671 STR 6.61767 5.81476 5.24155 4.38419 3.79848 3.38007 3.04801 0.2 UTR 6.80459 5.81974 5.21333 4.26838 3.64126 3.20441 2.8646 LTR 6.96171 5.98338 5.38036 4.43855 3.81022 3.36884 3.02398 NLTR 6.96171 5.98569 5.38423 4.44491 3.81781 3.37617 3.02913 STR 7.02082 6.12458 5.43628 4.49324 3.86390 3.42107 3.07452 ( FGM (I) 0 UTR 5.43496 4.70068 4.2211 3.43413 2.88836 2.49999 2.18730 LTR 5.90834 5.193784 4.72667 3.95840 3.42142 3.03282 2.71915 NLTR 5.90834 5.19842 4.73454 3.97159 3.43739 3.04839 2.73012 STR 6.0582 5.33956 4.87041 4.09972 3.56096 3.16977 2.85332 0.1 UTR 6.10107 5.14332 4.55118 3.62453 3.00865 2.58294 2.25038 LTR 6.51530 5.19378 4.99411 4.08325 3.47372 3.04569 2.70968 NLTR 6.51530 5.57993 5.00197 4.09628 3.48941 3.06092 2.72034 STR 6.65232 5.70667 5.12286 4.20898 3059742 3.16660 2.82749 0.2 UTR 7.10358 5.73356 4.95971 3.83009 3.12151 2.64928 2.29333 LTR 7.46336 6.10799 5.34342 4.22684 3.52258 3.04631 2.68480 NLTR 7.46336 6.11276 5.35131 4.23973 3.53799 3.06119 2.69516 STR 7.58973 6.22605 5.45779 4.33741 3.63088 3.15163 2.78670 FGM (II) 0 UTR 5.43496 4.70068 4.2211 3.43413 2.88836 2.49999 2.18730 LTR 5.90834 5.193784 4.72667 3.95840 3.42142 3.03282 2.71915 NLTR 5.90834 5.19842 4.73454 3.97159 3.43739 3.04839 2.73012 STR 6.0582 5.33956 4.87041 4.09972 3.56096 3.16977 2.85332 0.1 UTR 5.82315 4.98619 4.45317 3.59813 3.01746 2.61003 2.28715 LTR 6.26055 5.44199 4.92030 4.08135 3.50684 3.09673 2.77022 NLTR 6.26055 5.44675 4.92831 4.09464 3.52284 3.11228 2.78118 STR 6.39781 5.59874 5.05092 4.20937 3.63293 3.22008 2.89057 0.2 UTR 6.27567 5.30382 4.70389 3.76693 3.14561 2.71632 2.38167 LTR 6.68027 5.72544 5.13573 4.21244 3.59493 3.16080 2.82025 NLTR 6.68027 5.73036 4.14395 4.22595 3.61109 3.17644 2.83130 STR 6.80568 5.64570 5.25388 4.32784 3.70829 3.27130 2.92754
