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[en] Atomic finite element simulation is applied to study the natural frequency and sensitivity of a single-layer graphene-based resonator with CCCC, SSSS, CFCF, SFSF, and CFCF boundary conditions using the commercial code ANSYS. The fundamental frequencies of the graphene sheet are compared with the results of the previous finite element study. In addition, the sensitivity of the resonator is compared with the early work based on nonlocal elasticity theory. The results of the comparison are very good in all considered cases. The sensitivities of the resonator with different boundary conditions are obtained, and the order based on the boundary condition is CCCC > SSSS > CFCF > SFSF > CFFF. The highest sensitivity is obtained when the attached mass is located at the center of the resonator. This is useful for the design of a highly sensitive graphene-based mass sensor
[en] This article theoretically analyzes the cutting depth and material removal rate of an atomic force microscope (AFM) cantilever during nanomachining. An analytical expression for the vibration frequency and displacement of the cantilever has been obtained by using the modified couple stress theory. The theory includes one additional material length scale parameter revealing the micro-scale effect. According to the analysis, the results show that the effect of size-dependent on the vibration behavior of the AFM cantilever is obvious. The maximum displacement of nanomachining with the AFM cantilever represents the cutting depth. The area under the displacement-time curve is related to the material removal rate. When the excitation frequency is closer to the nature frequency of the cantilever, a larger material removal rate is obtained
[en] Highlights: ► Time-dependent base heat flux of a functionally graded fin is inversely estimated. ► An inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied. ► The distributions of temperature in the fin are determined as well. ► The influence of measurement error and measurement location upon the precision of the estimated results is also investigated. - Abstract: In this study, an inverse algorithm based on the conjugate gradient method and the discrepancy principle is applied to estimate the unknown time-dependent base heat flux of a functionally graded fin from the knowledge of temperature measurements taken within the fin. Subsequently, the distributions of temperature in the fin can be determined as well. It is assumed that no prior information is available on the functional form of the unknown base heat flux; hence the procedure is classified as the function estimation in inverse calculation. The temperature data obtained from the direct problem are used to simulate the temperature measurements. The influence of measurement errors and measurement location upon the precision of the estimated results is also investigated. Results show that an excellent estimation on the time-dependent base heat flux and temperature distributions can be obtained for the test case considered in this study.
[en] In this study, a conjugate gradient method based on an inverse algorithm is applied to estimate the unknown space and time dependent convection heat transfer coefficient of an annular fin. While knowing the temperature or strain history at the measuring positions of the fin, the convection heat transfer coefficient between the fin and the ambient fluid can be successfully computed. No prior information is needed on the functional form of the unknown convection heat transfer coefficient; and thus, the present study is classified as the function estimation inverse calculation. A particular feature in this study is that the thermal and strain fields are coupled, which makes solving the inverse problem a highly challenging task. The accuracy of the inverse analysis is examined by using the simulated temperature or strain measurements. Results show that excellent estimations of the convection heat transfer coefficient, temperature distributions and thermal stress distributions can be obtained for all the cases considered in this study