Advances in Acoustics and Vibration / 2019 / Article / Tab 3 / Research Article
Buckling Temperature and Natural Frequencies of Thick Porous Functionally Graded Beams Resting on Elastic Foundation in a Thermal Environment Table 3 Effect of the porosity volume fraction
the power law index
and the thermal field on the fundamental dimensionless frequency of P-FGB, subjected to different temperature changes
for (
(a) Uniform porosity distribution
Porosity volume fraction Thermal load type UTR 6.5813 5.7743 4.8752 4.3840 3.7859 3.0276 2.8606 LTR 6.6030 5.7923 4.8889 4.3953 3.7943 3.0330 2.8652 STR 6.6167 5.8037 4.8976 4.4024 3.7995 3.0364 2.8681 UTR 7.2139 6.1576 5.0580 4.4839 3.8055 2.9805 2.8037 LTR 7.2378 6.1768 5.0721 4.4951 3.8134 2.9852 2.8075 STR 7.2530 6.1891 5.0810 4.5023 3.8184 2.9881 2.8099 UTR 8.2198 6.7060 5.2937 4.6038 3.8206 2.9161 2.7286 LTR 8.2474 6.7271 5.3083 4.6150 3.8279 2.9198 2.7316 STR 8.2650 6.7405 5.3176 4.6222 3.8325 2.9222 2.7334 UTR 6.1875 5.3952 4.5128 4.0313 3.4468 2.7111 2.5452 LTR 6.2437 5.4428 4.5505 4.0635 3.4724 2.7308 2.5633 STR 6.2731 5.4676 4.5701 4.0801 3.4856 2.7408 2.5724 UTR 6.8441 5.8083 4.7299 4.1674 3.5043 2.7036 2.5283 LTR 6.9050 5.8581 4.7678 4.1987 3.5281 2.7207 2.5438 STR 6.9368 5.8842 4.7875 4.2150 3.5403 2.7293 2.5516 UTR 7.8658 6.3828 4.9985 4.3225 3.5568 2.6782 2.4928 LTR 7.9347 6.4364 5.0370 4.3532 3.5785 2.6924 2.5054 STR 7.9709 6.4645 5.0571 4.3692 3.5897 2.6996 2.5118 UTR 5.3070 4.5322 3.6640 3.1873 2.6072 1.8767 1.6932 LTR 5.4484 4.6581 3.7733 3.2882 2.6996 1.9680 1.7859 STR 5.5174 4.7190 3.8254 3.3357 2.7422 2.0091 1.8273 UTR 6.0363 5.0317 3.9802 3.4289 2.7782 1.9954 1.8089 LTR 6.1816 5.1563 4.0834 3.5213 2.8592 2.0716 1.8853 STR 6.2531 5.2171 4.1330 3.5652 2.8968 2.1061 1.9196 UTR 7.1104 5.6809 4.3395 3.6816 2.9356 2.0850 1.8933 LTR 7.2670 5.8079 4.4384 3.7668 3.0061 2.1477 1.9554 STR 7.3450 5.8705 4.4864 3.8076 3.0391 2.1761 1.9834
(b) Nonuniform porosity distribution
Porosity volume fraction Thermal load type UTR 6.5813 5.7743 4.8752 4.3840 3.7859 3.0276 2.8606 LTR 6.6030 5.7923 4.8889 4.3953 3.7943 3.0330 2.8652 STR 6.6167 5.8037 4.8976 4.4024 3.7995 3.0364 2.8681 UTR 6.9423 6.0210 5.0258 4.4934 3.8542 3.0590 2.8869 LTR 6.9650 6.0396 5.0397 4.5047 3.8624 3.0641 2.8913 STR 6.9795 6.0514 5.0486 4.5119 3.8676 3.0673 2.8940 UTR 7.3775 6.3067 5.1932 4.6124 3.9261 3.0902 2.9129 LTR 7.4015 6.3260 5.2074 4.6238 3.9342 3.0950 2.9169 STR 7.4167 6.3383 5.2165 4.6310 3.9393 3.0981 2.9195 UTR 6.1875 5.3952 4.5128 4.0313 3.4468 2.7111 2.5452 LTR 6.2437 5.4428 4.5505 4.0635 3.4724 2.7308 2.5633 STR 6.2731 5.4676 4.5701 4.0801 3.4856 2.7408 2.5724 UTR 6.5645 5.6605 4.6844 4.1628 3.5384 2.7674 2.5970 LTR 6.6227 5.7092 4.7222 4.1946 3.5633 2.7859 2.6139 STR 6.6532 5.7345 4.7418 4.2111 3.5760 2.7953 2.6224 UTR 7.0131 5.9630 4.8713 4.3025 3.6324 2.8222 2.6470 LTR 7.0740 6.0129 4.9093 4.3341 3.6565 2.8395 2.6627 STR 7.1058 6.0390 4.9291 4.3504 3.6689 2.8483 2.6707 UTR 5.3070 4.5322 3.6640 3.1873 2.6072 1.8767 1.6932 LTR 5.4484 4.6581 3.7733 3.2882 2.6996 1.9680 1.7859 STR 5.5174 4.7190 3.8254 3.3357 2.7422 2.0091 1.8273 UTR 5.7317 4.8521 3.8977 3.3856 2.7723 2.0187 1.8367 LTR 5.8736 4.9763 4.0030 3.4812 2.8577 2.1001 1.9185 STR 5.9432 5.0366 4.0534 3.5265 2.8974 2.1370 1.9552 UTR 6.2204 5.2027 4.1405 3.5855 2.9324 2.1494 1.9670 LTR 6.3646 5.3262 4.2426 3.6767 3.0118 2.2225 2.0398 STR 6.4357 5.3867 4.2919 3.7201 3.0489 2.2558 2.0727
