• Title/Summary/Keyword: hamilton principle

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Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC

  • Safari, Mohammad;Mohammadimehr, Mehdi;Ashrafi, Hossein
    • Advances in nano research
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    • v.10 no.2
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    • pp.115-128
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    • 2021
  • In this article, free vibration behavior of electro-magneto-thermo sandwich Timoshenko beam made of porous core and Graphene Platelet Reinforced Composite (GPLRC) in a thermal environment is investigated. The governing equations of motion are derived by using the modified strain gradient theory for micro structures and Hamilton's principle. The magneto electro are under linear function along the thickness that contains magnetic and electric constant potentials and a cosine function. The effects of material length scale parameters, temperature change, various distributions of porous, different distributions of graphene platelets and thickness ratio on the natural frequency of Timoshenko beam are analyzed. The results show that an increase in aspect ratio, the temperature change, and the thickness of GPL leads to reduce the natural frequency; while vice versa for porous coefficient, volume fractions and length of GPL. Moreover, the effect of different size-dependent theories such as CT, MCST and MSGT on the natural frequency is investigated. It reveals that MSGT and CT have most and lowest values of natural frequency, respectively, because MSGT leads to increase the stiffness of micro Timoshenko sandwich beam by considering three material length scale parameters. It is seen that by increasing porosity coefficient, the natural frequency increases because both stiffness and mass matrices decreases, but the effect of reduction of mass matrix is more than stiffness matrix. Considering the piezo magneto-electric layers lead to enhance the stiffness of a micro beam, thus the natural frequency increases. It can be seen that with increasing of the value of WGPL, the stiffness of microbeam increases. As a result, the value of natural frequency enhances. It is shown that in hc/h = 0.7, the natural frequency for WGPL = 0.05 is 8% and 14% less than its for WGPL = 0.06 and WGPL = 0.07, respectively. The results show that with an increment in the length and width of GPLs, the natural frequency increases because the stiffness of micro structures enhances and vice versa for thickness of GPLs. It can be seen that the natural frequency for aGPL = 25 ㎛ and hc/h = 0.6 is 0.3% and 1% more than the one for aGPL = 5 ㎛ and aGPL = 1 ㎛, respectively.

Calculation method and application of natural frequency of integrated model considering track-beam-bearing-pier-pile cap-soil

  • Yulin Feng;Yaoyao Meng;Wenjie Guo;Lizhong Jiang;Wangbao Zhou
    • Steel and Composite Structures
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    • v.49 no.1
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    • pp.81-89
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    • 2023
  • A simplified calculation method of natural vibration characteristics of high-speed railway multi-span bridge-longitudinal ballastless track system is proposed. The rail, track slab, base slab, main beam, bearing, pier, cap and pile foundation are taken into account, and the multi-span longitudinal ballastless track-beam-bearing-pier-cap-pile foundation integrated model (MBTIM) is established. The energy equation of each component of the MBTIM based on Timoshenko beam theory is constructed. Using the improved Fourier series, and the Rayleigh-Ritz method and Hamilton principle are combined to obtain the extremum of the total energy function. The simplified calculation formula of the natural vibration frequency of the MBTIM under the influence of vertical and longitudinal vibration is derived and verified by numerical methods. The influence law of the natural vibration frequency of the MBTIM is analyzed considering and not considering the participation of each component of the MBTIM, the damage of the track interlayer component and the stiffness change of each layer component. The results show that the error between the calculation results of the formula and the numerical method in this paper is less than 3%, which verifies the correctness of the method in this paper. The high-order frequency of the MBTIM is significantly affected considering the track, bridge pier, pile soil and pile cap, while considering the influence of pile cap on the low-order and high-order frequency of the MBTIM is large. The influence of component damage such as void beneath slab, mortar debonding and fastener failure on each order frequency of the MBTIM is basically the same, and the influence of component damage less than 10m on the first fourteen order frequency of the MBTIM is small. The bending stiffness of track slab and rail has no obvious influence on the natural frequency of the MBTIM, and the bending stiffness of main beam has influence on the natural frequency of the MBTIM. The bending stiffness of pier and base slab only has obvious influence on the high-order frequency of the MBTIM. The natural vibration characteristics of the MBTIM play an important guiding role in the safety analysis of high-speed train running, the damage detection of track-bridge structure and the seismic design of railway bridge.

Analysis of Variation for Parallel Test between Reagent Lots in in-vitro Laboratory of Nuclear Medicine Department (핵의학 체외검사실에서 시약 lot간 parallel test 시 변이 분석)

  • Chae, Hong Joo;Cheon, Jun Hong;Lee, Sun Ho;Yoo, So Yeon;Yoo, Seon Hee;Park, Ji Hye;Lim, Soo Yeon
    • The Korean Journal of Nuclear Medicine Technology
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    • v.23 no.2
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    • pp.51-58
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    • 2019
  • Purpose In in-vitro laboratories of nuclear medicine department, when the reagent lot or reagent lot changes Comparability test or parallel test is performed to determine whether the results between lots are reliable. The most commonly used standard domestic laboratories is to obtain %difference from the difference in results between two lots of reagents, and then many laboratories are set the standard to less than 20% at low concentrations and less than 10% at medium and high concentrations. If the range is deviated from the standard, the test is considered failed and it is repeated until the result falls within the standard range. In this study, several tests are selected that are performed in nuclear medicine in-vitro laboratories to analyze parallel test results and to establish criteria for customized percent difference for each test. Materials and Methods From January to November 2018, the result of parallel test for reagent lot change is analyzed for 7 items including thyroid-stimulating hormone (TSH), free thyroxine (FT4), carcinoembryonic antigen (CEA), CA-125, prostate-specific antigen (PSA), HBs-Ab and Insulin. The RIA-MAT 280 system which adopted the principle of IRMA is used for TSH, FT4, CEA, CA-125 and PSA. TECAN automated dispensing equipment and GAMMA-10 is used to measure insulin test. For the test of HBs-Ab, HAMILTON automated dispensing equipment and Cobra Gamma ray measuring instrument are used. Separate reagent, customized calibrator and quality control materials are used in this experiment. Results 1. TSH [%diffrence Max / Mean / Median] (P-value by t-test > 0.05) C-1(low concentration) [14.8 / 4.4 / 3.7 / 0.0 ] C-2(middle concentration) [10.1 / 4.2 / 3.7 / 0.0] 2. FT4 [%diffrence Max / Mean / Median] (P-value by t-test > 0.05) C-1(low concentration) [10.0 / 4.2 / 3.9 / 0.0] C-2(high concentration) [9.6 / 3.3 / 3.1 / 0.0 ] 3. CA-125 [%diffrence Max / Mean / Median] (P-value by t-test > 0.05) C-1(middle concentration) [9.6 / 4.3 / 4.3 / 0.3] C-2(high concentration) [6.5 / 3.5 / 4.3 / 0.4] 4. CEA [%diffrence Max / Mean / median] (P-value by t-test > 0.05) C-1(low concentration) [9.8 / 4.2 / 3.0 / 0.0] C-2(middle concentration) [8.7 / 3.7 / 2.3 / 0.3] 5. PSA [%diffrence Max / Mean / Median] (P-value by t-test > 0.05) C-1(low concentration) [15.4 / 7.6 / 8.2 / 0.0] C-2(middle concentration) [8.8 / 4.5 / 4.8 / 0.9] 6. HBs-Ab [%diffrence Max / Mean / Median] (P-value by t-test > 0.05) C-1(middle concentration) [9.6 / 3.7 / 2.7 / 0.2] C-2(high concentration) [8.9 / 4.1 / 3.6 / 0.3] 7. Insulin [%diffrence Max / Mean / Median] (P-value by t-test > 0.05) C-1(middle concentration) [8.7 / 3.1 / 2.4 / 0.9] C-2(high concentration) [8.3 / 3.2 / 1.5 / 0.1] In some low concentration measurements, the percent difference is found above 10 to nearly 15 percent in result of target value calculated at a lower concentration. In addition, when the value is measured after Standard level 6, which is the highest value of reagents in the dispensing sequence, the result would have been affected by a hook effect. Overall, there was no significant difference in lot change of quality control material (p-value>0.05). Conclusion Variations between reagent lots are not large in immunoradiometric assays. It is likely that this is due to the selection of items that have relatively high detection rate in the immunoradiometric method and several remeasurements. In most test results, the difference was less than 10 percent, which was within the standard range. TSH control level 1 and PSA control level 1, which have low concentration target value, exceeded 10 percent more than twice, but it did not result in a value that was near 20 percent. As a result, it is required to perform a longer period of observation for more homogenized average results and to obtain laboratory-specific acceptance criteria for each item. Also, it is advised to study observations considering various variables.