Vibration Analysis of Variable-Thickness Multi-Layered Graphene Sheets

Central Java Province is a potential area that has an important role in national food production. El Nino and La Nina events have a very large impact if they occur in Indonesia, especially in Central Java Province. This study aims to analyze the impact of El Nino and La Nina events specifically in Central Java Province where the areas more dominantly affected by El Nino and La Nina. The research location uses 3 rainfall stations, namely the Tunggal Wulung Meteorological Station, Tegal Maritime Meteorological Station, and Tanjung Emas Maritime Meteorological Station. The method used is the Fast Fourier Transform (FFT) method and the long periodogram. The results showed that the periods of El Nino and La Nina phenomena recurring using the FFT method are forecasts for the periods 2.2428, 2.8036, and 3.7381 years. While using the lom periodogram method, namely in the periods of 2,480, 2,621, and 3:16 years. The results of the analysis of the FFT method obtained results that varied in the height of rainfall at the 3 stations, while the results of the analysis using the periodogram log showed that the Tunggal Wulung rain station had the highest peak rainfall. This study concludes that there are variations in the peak incidence using either the slow periodogram or the FFT method. However, both of these methods and based on the BMKG and TRMM, the Tunggal Wulung Meteorological Station has the highest peak between Tegal Station and Tanjung Emas Station.

The Fast Fourier Transform (FFT) method for solving the 1-D heat diffusion equation offers an efficient approach for resolving partial differential equations (PDEs) with various time steps . FFT is used to transform the 1-D heat diffusion equation into the frequency domain and back to the time domain through inverse FFT. Using mathematical modeling with initial and Dirichlet boundary conditions, the numerical solutions produced by FFT are compared with analytical solutions. The accuracy of the method is validated using MAE and MSE calculated in Matlab. At several time intervals , the obtained MAE and MSE values indicate a good agreement between the numerical and analytical solutions, with very small errors. Numerical stability analysis confirms the reliability of the FFT method across various The variation in time step has a significant impact on the accuracy and stability of the solution. Smaller time steps improve accuracy and stability but require longer computation times. The optimal time step selected in this study is Increasing the number of discretization points also enhances accuracy but implies an increase in computational load and memory usage. The FFT method demonstrates good numerical consistency with increasing

The fast Fourier transform (FFT) algorithm is widely used as a standard tool to carry out spectral analysis because of its computational efficiency. However, the presence of multiple tones frequently requires a fine frequency resolution to achieve sufficient accuracy, which imposes the use of a large number of FFT points that results in large area and power overheads. In this paper, an FFT method is proposed for on-chip spectral analysis of multi-tone signals with particular harmonic and intermodulation components. This accurate FFT analysis approach is based on coherent sampling, but it requires a significantly smaller number of points to make the FFT realization more suitable for on-chip built-in testing and calibration applications that require area and power efficiency. The technique was assessed by comparing the simulation results from the proposed method of single and multiple tones with the simulation results obtained from the FFT of coherently sampled tones. The results indicate that the proper selection of test tone frequencies can avoid spectral leakage even with multiple narrowly spaced tones. When low-frequency signals are captured with an analog-to-digital converter (ADC) for on-chip analysis, the overall accuracy is limited by the ADC's resolution, linearity, noise, and bandwidth limitations. Post-layout simulations of a 16-point FFT showed that third-order intermodulation (IM3) testing with two tones can be performed with 1.5-dB accuracy for IM3 levels of up to 50 dB below the fundamental tones that are quantized with a 10-bit resolution. In a 45-nm CMOS technology, the layout area of the 16-point FFT for on-chip built-in testing is 0.073 mm2, and its estimated power consumption is 6.47 mW.

Effect of aggregate shapes on local fields in 3D mesoscale simulations of the concrete creep behavior

In this paper, a multiplate nonlocal shear model and molecular dynamic simulations are presented to investigate the effects of interlayer shear and nonlocality on the natural frequencies of multilayer graphene sheets (MLGSs). From one aspect in the optimal design of such structures, the interaction between graphene layers, which can significantly vary the static and dynamic behavior due to lack of solidity of layers stack, should be considered. On the other hand, it is requied that the nonlocality phenomenon which has an effective role in the mechanical analysis of nanostructures is taken into account. To this aim, the equation of motion along with corresponding boundary conditions is derived by using the Kirchhoff plate model and nonlocal continuum theory to capture these effects. For a case study, the free vibration problem of simply supported MLGSs is studied by presenting the closed-form Navier’s solution of natural frequencies and carrying out Molecular dynamics (MD) simulations to estimate the value of nonlocal parameter. Finally, the influences of interlayer shear modulus, number of layers, foundation stiffness, and nonlocal parameter on the natural frequencies of such MLGSs are examined in detail. Findings show that natural frequencies including nonlocality effect become smaller than ones of the classical continuum theory and also have good agreements with MD simulations. Moreover, it is seen that the sensitivity of natural frequency to the nonlocal parameter becomes more significant when the number of layers or interlayer shear modulus increases as well as the aspect ratio or width of sheets decreases.

Maximum Entropy Spectral Analysis (MESA) Method is a powerful alternative to the traditionally used Blackman Tukey (BT) and Fast Fourier Transform (FFT) Methods in hydrologic and climatologic time series analysis. Maximum entropy spectra of annual rainfall time series measured at Mangalore and Waltair and monthly flow time series of Godavari and Krishna Rivers in India are presented and compared with the spectra obtained by using BT and FFT methods. A recently developed Bayesian decision rule is applied to determine the length of filters in MESA. Sensitivity of the maximum entropy spectra to the length of filter used is also discussed.

Nanoparticle mass detection by single and multilayer graphene sheets: Theory and simulations

Liquid metal reactors (LMR), with the significant advantages in high safety and good economic benefits, has obvious advantages and broad application prospects in the fourth generation nuclear power systems. Spiral tube steam generator is one of the most important equipment in LMR, which are composed of spiral heat transfer tubes, inner and outer cylinders, feedwater headers, steam headers, and other structures. Due to their compact structure and high heat transfer efficiency, they are conducive to equipment miniaturization and have been widely used in different reactors in various countries. Due to the impact of the shell side fluid in the steam generator on the tube bundle, it is inevitable to cause flow induced vibration (FIV), resulting in thinning or even rupture of the tube wall, thereby shortening the service life or even failure of the steam generator. Therefore, the study of the vibration characteristics of spiral tube bundles is of great significance. The natural frequency of the tube bundle is an important parameter in FIV analysis. The heat transfer tubes of the spiral tube steam generator are made of spiral winding, and the positions between adjacent tubes are complex and variable. The winding direction between adjacent layers of the spiral heat transfer tubes can be in the same or opposite direction, so their spatial structure is complex. This article simulates and calculates the natural frequency of spiral heat transfer tubes in air and lead bismuth, and studies the influence of geometric structural parameters on their natural frequency. Based on simplifying constraints at both ends of the spiral tube bundles to fixed support, the computational fluid dynamics (CFD) simulation was carried out to reveal the effect mechanism of support number, spiral radius and spiral rising angle, on natural frequency of spiral tube bundles in air. The results indicate that an increase in spiral radius leads to a decrease in natural frequency, while an increase in support number leads to a significant increase in natural frequency, and the spiral rise angle has little effect on the natural frequency. Therefore, we can improve the stability of the spiral tube bundles by increasing support number or reducing spiral radius. Through CFD simulation calculation, the influence mechanism of tube bundle structural parameters on the natural frequency of spiral tube bundles in liquid metal environments was studied. The increase of layer pitch ratio and the same layer pitch ratio led to an increase in natural frequency. The research results provide data reference for the prediction of the natural frequency of heat transfer tubes and the study of FIV of tube bundles, which are of great significance for avoiding the failure of heat transfer tubes.

In this paper,we study the quantum size effects in multilayer graphene sheets using first principles methods within the framework of density functional theory. Four different types of functionals are adopted respectively to describe the van der Waals interactions between graphene layer sheets: the DFT-GGA(PBE), the DFT-D2, the vdW-DF and the optPBE-vdW. By inspecting the binding energy as a function of increasing graphene layers, we find that the PBE functional can not well describe the van der Waals interactions between different layers of graphene sheets. In contrast, the other three methods exhibit similar results with monotonic increasing binding energy as a function of graphene layers towards the bulk limit, concluding that the layered graphene structure is stabilized by van der Waals interactions. The density of states at zero temperature indicate that the multilayer graphene sheets is a semi-metal, which is independent of sheet layers number. The finite temperature (about 200 K) density of states at Fermi surface are studied as a function of the number of stacking graphene layers. The systematic oscillating behavior of finite temperature density of states between odd and even number of layers is a demonstration of quantum size effects. The Fermi wavelength will converge to two times the inter-layer distance of graphite, which is consistent with the theory describing the motion of particles in a quantum well. Finally, we study the adsorption of single H atom on multilayer graphene sheets to test the role of quantum size effects. The adsorption energies and the vibration frequencies are calculated for comparison with experiments. Our results shed light on understanding the stacking process of multilayer graphene in vacuum both theoretically and experimentally.

Molecular dynamics (MD) approach and finite element analysis are enforced for the investigating the stress – strain fields in the proximity of the notch tip in a copper plate with single horizontal and inclined edge notches. The MD simulation embodied in a classical molecular dynamics program Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is aimed at evaluating conventional continuum linear elastic fracture mechanics key parameters, precisely stress intensity factors (SIF), T-stresses and generalized stress intensity factors (higher order factors) of the Max Williams power series expansion (WE) of the stress field adjacent with the notch tip for pure tensile (Mode I), pure shear (Mode II) and mixed mode (combinations of Mode I and Mode II) loadings of the notched specimen in linear elastic isotropic media. The paramount intent of the research is the comparability of continuum and atomistic procedures for the appraisement of the near notch tip fields exploiting the exemplification of one of the widespread cracked configurations. SIFs, T-stresses and higher order amplitude coefficients of the WE for the single-edge notched Cu plane under Mode I and Mixed Mode loadings are estimated by atomistic and finite element modelling. The wide class of the MD computations in LAMMPS is effectuated. The atomistic values of SIFs and amplitude factors of higher order terms of the WE are correlated with the quantities gained from the numeric solutions obtained by finite element method. It is elucidated that the continuum fracture theory properly characterizes failure and the near notch tip fields even at tremendously limited distances of only few nanometers. The angular stress distributions found from atomic modeling are restored and correlated with the angular behaviours of the stresses obtained from continuum linear elastic fracture theory. The juxtaposition is shown to be in reasonable agreement between two approaches.

The carrier transport properties of a multilayer graphene with the turbostratic stacking structure are evaluated by transfer characteristics in a field‐effect transistor and Hall‐effect measurement with van der Pauw geometry. Herein, the multilayer graphene with the turbostratic stacking structure is synthesized by graphene overlayer growth on a monolayer graphene template using a chemical vapor deposition method. The sheet resistance of the inner layer in the grown multilayer graphene is lower than that of the monolayer graphene used as a growth template. This is caused by a screening effect due to the multistacking. Moreover, the value of carrier mobility in the grown multilayer graphene is higher than that of the monolayer graphene template. The enhancement of carrier mobility is caused by a turbostratic stacking effect where the band structure of the multilayer graphene is similar to that of the monolayer graphene. These results indicate that the synthesis technique of the multilayer graphene with the turbostratic stacking structure using the graphene template is effective to improve the carrier transport properties in the multilayer graphene sheet.

Optical interferometry plays an important role in the topographical surface measurement and characterization in precision/ultra-precision manufacturing. An appropriate surface reconstruction algorithm is essential in obtaining accurate topography information from the digitized interferograms. However, the performance of a surface reconstruction algorithm in interferometric measurements is influenced by environmental disturbances and system noise. This paper presents a comparative analysis of three algorithms commonly used for coherence envelope detection in vertical scanning interferometry, including the centroid method, fast Fourier transform (FFT), and Hilbert transform (HT). Numerical analysis and experimental studies were carried out to evaluate the performance of different envelope detection algorithms in terms of measurement accuracy, speed, and noise resistance. Step height standards were measured using a developed interferometer and the step profiles were reconstructed by different algorithms. The results show that the centroid method has a higher measurement speed than the FFT and HT methods, but it can only provide acceptable measurement accuracy at a low noise level. The FFT and HT methods outperform the centroid method in terms of noise immunity and measurement accuracy. Even if the FFT and HT methods provide similar measurement accuracy, the HT method has a superior measurement speed compared to the FFT method.

This paper explores the possibility of using a combination of the empirical mode decomposition (EMD) and the Hilbert transform (HT), termed the Hilbert-Huang transform (HHT) method, to identify the modal damping ratios of the structure with closely spaced modal frequencies. The principle of the HHT method and the procedure of using the HHT method for modal damping ratio identification are briefly introduced first. The dynamic response of a two-degrees-of-freedom (2DOF) system under an impact load is then computed for a wide range of dynamic properties from well-separated modal frequencies to very closely spaced modal frequencies. The natural frequencies and modal damping ratios identified by the HHT method are compared with the theoretical values and those identified using the fast Fourier transform (FFT) method. The results show that the HHT method is superior to the FFT method in the identification of modal damping ratios of the structure with closely spaced modes of vibration. Finally, a 36-storey shear building with a 4-storey light appendage, having closely spaced modal frequencies and subjected to an ambient ground motion, is analyzed. The modal damping ratios identified by the HHT method in conjunction with the random decrement technique (RDT) are much better than those obtained by the FFT method. The HHT method performing in the frequency-time domain seems to be a promising tool for system identification of civil engineering structures.

Based on an explicit formula used for describing the van der Waals (vdW) interaction between any two layers of multi-layered graphene sheets (MLGSs), the vibration properties of five- and eight-layered graphene sheets are analyzed with considering the influence of vdW interaction on the natural frequences. The present study shows that for a given combination n and m the lowest natural frequency (classical natural frequency) of a MLGSs is independent of vdW interaction, but that it is very significant for the influence of vdW interaction on the other higher frequencies (resonant frequencies). The different vibration modes, including in-phase and anti-phase ones, are given for exhibiting clearly the influence of vdW interaction.

In this present study, natural frequencies of the first two modes of bending vibration for the cracked simply supported Euler–Bernoulli beam is determined using finite element analysis (FEA). FEA natural frequencies for the cracked beam are used to investigate the behavior of the cracked beam and also used in the inverse problem of crack depth detection. Dynamic behavior of the cracked simply supported beam is observed, and it is found that normalized mode shape at crack location has great effect on amount of decreasing of natural frequencies. When normalized mode shape at crack location is increased, then natural frequencies decrease. In this study, pattern of mode shape played a vital role in decreasing or increasing natural frequencies. At the midpoint of the beam, there is largest bending moment in first bending mode and there is nodal point in second bending mode. Harmonic analysis for the cracked simply supported beam is carried out to find von Mises stress responses and appearance of peaks at frequency of first bending mode is noticed in graphs of von Mises stress response, expressing high values of von Mises stress at crack tip. Inverse problem of assessing the crack depth is performed using results of FEA first mode frequency ratio and published experimental results and the method showed good results in case of high crack depth ratios.