Element Mass Research Articles

Identification of structural element mass and stiffness changes using partial acceleration responses of chain-like systems under ambient excitations

It is important to conduct structural damage detection using only output time histories of structures under ambient excitations. Recently, an approach has been proposed for structural damage detection under ambient excitations using the synthesis of cross-correlation functions of partial structural responses and the extended Kalman filter (EKF). However, structural mass is assumed known in this approach. Although some methodologies have been presented for detecting damage due to relative structural mass and stiffness changes in chain-like systems, measurements of structural responses including acceleration, velocity, and displacement at each degree of freedom are required. This greatly limits the application of these methodologies. In this paper, without structural mass information, an algorithm is proposed to identify structural element mass and stiffness changes using only partial acceleration responses of chain-like systems under ambient excitations. First, based on the equations for cross-correlation functions of structural responses under ambient stationary excitations modeled as independent stationary white noise processes, EKF is utilized for identifying the structural element stiffness-mass coupled coefficients using only partial acceleration responses. Then, these coefficients are decoupled by cluster analysis and the least squares estimation to obtain structural element stiffness and mass changes. Furthermore, the proposed algorithm is extended for identifying chain-like structural element mass and stiffness changes under non-stationary ambient excitations assumed as time modulating white noises. The performances of the proposed algorithm are numerically investigated using the Phase I The American Society of Civil Engineers structural health monitoring benchmark building under stationary or non-stationary ambient excitations, respectively. Moreover, the experimental data with structural element mass and stiffness changes conducted at the Los Alamos National Laboratory are utilized to test the proposed algorithm.

Circulating trace elements: Comparison between early and late incubation in common eiders (Somateria mollissima) in the central Baltic Sea

We analyzed body mass and a panel of 64 trace elements in blood from incubating common eiders (Somateria mollissima) in the central Baltic Sea during the breeding seasons of 2017 (n = 27) and 2018 (n = 23). Using a non-invasive approach, the same incubating eiders nesting on Christiansø, Denmark were sampled once on day 4 and day 24 of incubation to provide a comparison between the early and late stages of incubation. Blood concentrations of chemical elements were quantified using high-resolution inductively coupled plasma mass spectrometry (HR-ICP-MS). Cadmium and lead significantly increased over the course of the incubation period while body mass, barium, calcium, cerium, cesium, iron, magnesium, manganese, molybdenum, phosphorus, selenium, strontium, sulfur, uranium, and zinc all significantly decreased. Excluding lead, all trace elements were within expected ranges. Lead blood concentrations had a 4.7-fold increase from 2017 to 2018 indicating a potential health threat. However, internal interactions between trace elements must be considered when making comparisons to toxicological thresholds. Body mass and many essential elements showed significantly higher levels in 2017 than 2018, which could be an indication of limitations in preferred food availability or harsher fasting conditions. Additional sampling years are needed to further investigate if these results reflect yearly fluctuations or decreasing health within the Christiansø eider colony. There was little overlap in element blood concentrations and body mass between days of incubation, indicating these parameters are affected by the physiological processes of reproduction and incubation. We recommend continued biomonitoring and use of complete trace element analysis for the Christiansø eiders to further understand year-to-year variations within colonies. Further investigation into the spatial ecology of the colony is also needed to provide a more robust understanding of exposure and source identification of trace elements.

Configuration effect and bandgap mechanism of quasi-one-dimensional periodic lattice structure

Considering the extensive application of periodic structure and bandgap feature of periodic elastic metamaterial, this paper presents the bandgap mechanism and characteristics of two types of complex periodic lattices for vibration attenuation. Specifically, the function of the spring and mass elements acting on the bandgap in periodic system is studied to understand the coupling mechanism of the lattice structure with complex configuration. The analytical expressions of the critical values for the mass, stiffness and configuration angle of the lattice to ensure the existence of the bandgap are obtained. The parameter effects on the bandgap width are studied as the bigger difference between the masses in the two chains, the larger the stiffness ratio, the smaller the angle α(α ≠ 0), the wider the bandgap. The bandgaps of the proposed Models 1 and 2 are 64.8% and 75.9% wider than that of the classical Model T.

The non-linear vibrations of simply supported column loaded by the mass element

The stability and free vibrations of slender support systems were the subject of many scientific and research works. This paper presents the boundary problem of column vibrations in which the longitudinal inertia of the mass element, which loads the slender system, is taken into account. The column was analysed as a simply supported structure. The formulation of boundary problem was carried out by using kinetic criterion of stability. Taking into consideration the load from longitudinal inertia of mass element in the mathematical model makes the system non-linear. The non-linear components of the mathematical model were expanded into a power series of a small parameter. Numerical calculations allowed determination of the influence of the column oscillations amplitude on the non-linear component of the natural frequency of the system. It has been shown that in supporting systems loaded by a mass element, the vibrations amplitude considerably affect natural frequency at appropriately selected parameters of the system. Also experimental verification of the adopted mathematical model was carried out, which showed good agreement between numerical and experimental studies.

Formulation for nonlinear dynamic analysis of steel frames considering the plastic zone method

A corotational Lagrangian formulation for nonlinear dynamic analysis of steel planar frames is addressed. This formulation employs the Plastic Zone Method and is capable of considering second-order effects, initial geometric imperfections and residual stresses. The element dynamic equilibrium is derived from the virtual power theorem, and local cubic shape functions are used to deduce the element tangent stiffness and mass matrices. The integration of stresses over the cross-section area is executed based on elastic–perfectly plastic stress-strain curve, which is applied for each slice of the cross-sections located at the Gauss points along the member length. In order to solve the system of dynamic nonlinear equations in time domain, the numerical analysis procedure makes use of the Newmark's implicit time integration method and the Newton-Raphson technique. The PPLANLEP computational program, which is based on the finite element method, is modified to perform the nonlinear time-history analyses. A good correspondence between the found numerical solutions and those reported by other researchers and obtained by OpenSees software is observed, indicating that the proposed method is efficient in predicting the nonlinear dynamic behavior of steel structures.

Elemental Abundances in Supernova Remnant W49B as Clues to Its Progenitor

Abstract We apply the Smoothed Particle Inference (SPI) technique to analyze the X-ray emission from SNR W49B. In X-rays, it is visible as a centrally filled supernova remnant, and was recently recognized as one of the first remnants to have plasma that is overionized. Using SPI we infer the density structure and derive the mass of individual elements in the plasma over the entire remnant. We have compared the abundances inferred with SPI to those obtained from a wide range of supernova explosion models, including both Type Ia and core-collapse, as well as energetic and off-center variants. Type Ia models that incorporate some form of detonation are found to be the most compatible, while pure deflagration models, and all core-collapse models, are found to be incompatible.

Influence of Longitudinal Inertia of Mass Element on Non-Linear Component of Beam Natural Frequency

Influence of Longitudinal Inertia of Mass Element on Non-Linear Component of Beam Natural Frequency

Determination of the Isotopic Composition of an Enriched Hafnium Spike by MC‐ICP‐MS Using a Regression Model

The isotope dilution (ID) method, owing to its high precision, is extensively used for the determination of element mass fractions in a wide range of natural samples. One of the prerequisites of the ID method is knowledge of the isotopic composition of an enriched spike, which is often challenging to accurately determine. In this study, we employ a regression mass bias correction model to accurately and precisely measure the isotopic composition of an enriched Hf spike (Lot No. 159293, Oak Ridge National Laboratory). A NIST SRM 3134 Re solution, whose isotopic composition was calibrated by an NRC IRIS‐1 Ir isotope standard, was used to calibrate the isotopic composition of the Hf spike. The obtained ratios of 176Hf/177Hf, 179Hf/177Hf and 180Hf/177Hf were 0.2406 ± 0.0005 (u, k = 1), 2.8620 ± 0.0005 (u, k = 1) and 384.65 ± 0.05 (u, k = 1), respectively, which meet the required precision levels for Hf isotopes in the application of the ID method. The combined uncertainties of the calibrated Re and Hf isotope ratios were evaluated using a Monte Carlo method, in which the uncertainty of the primary calibrator (IRIS‐1, 193Ir/191Ir = 1.6866 ± 0.0005, u, k = 1) was also taken into consideration. The precision of Hf spike was improved significantly compared with the SSB and C‐SSBIN methods. To the best of our knowledge, this is the first report of isotope ratio calibration in an enriched spike using the regression model. The precisely calibrated spike can lower the uncertainty of the Hf mass fraction significantly, thereby increasing the accuracy of the Lu‐Hf chronometer.

Free vibration analysis of nanotube based sensors including rotary inertia based on the Rayleigh beam and modified couple stress theories

In this study, a finite element formulation is presented to analyze the free vibration of carbon nanotube based sensor in conjunction with modified couple stress and Rayleigh beam theories. Rotary inertia effect and size dependency are considered for vibration problem of the cantilever single walled carbon nanotube. The aim of this paper is to examine the vibrational frequencies of single-walled carbon nanotube with these effects. Therefore, for the finite element solution, stiffness and mass matrices have been obtained that include these effects in the calculations. Numerical results are presented to show the variation of the frequencies with a variety of parameters such as the material length scale parameter, number of the finite elements, length of the nanotube and mode number.

Spectroscopic study of Nd3+ ion-doped Zn-Al-Ba borate glasses for NIR emitting device applications

Trivalent neodymium (Nd3+) -doped Zn-Al-Ba borate glasses of composition (60-x)B2O3+20BaO+10Al2O3+10ZnO + xNd2O3(x = 0.0, 0.5, 1.0, 1.5, 2.0 and 2.5 mol%) were prepared by a conventional melt-quenching technique and studied their physical, structural, optical and luminescence properties. The amorphous nature of the glasses has been confirmed by X-ray diffraction patterns. The EDAX data shows percent mass of elements of the glass system. FTIR spectra confirm the formation of BO3 and BO4 groups in the glass structure and compared them with Raman spectra. The Judd-Ofelt theory was adopted to analyze the radiative properties of Nd2O3 –doped glasses to derive oscillator strengths (f), JO parameters (Ωλ=2,4,6), stimulated emission cross-sections (σe), radiative transition probabilities (AR), and branching ratios (βR) of various transitions of Nd3+ ions. The lifetime of the 4F3/2 level of Nd3+ ions in the glasses decreases with the increase of Nd2O3 concentration due to the shortened distance between Nd3+ ion in the glass structure. The strongest emission intensity is found at 1056 nm (4F3/2 → 4I11/2 transition) when excited by 808 nm. The optimum concentration of Nd2O3 in the studied glasses is found to be 1.0 mol% based on luminescence intensity. All these results were compared with reported research of Nd3+:glasses to determine the lasing potentiality of studied glasses.

Levels and sources of hourly PM2.5-related elements during the control period of the COVID-19 pandemic at a rural site between Beijing and Tianjin

To control the spread of the novel coronavirus disease 2019 (COVID-19) in China, many anthropogenic activities were reduced and even closed on the national scale. To study the impact of this reduction and closing down, hourly concentrations of PM2.5-related elements were measured at a rural site before (12–25 January 2020), during (26 January–9 February 2020) and after (22 March–2 April 2020) the control period when all people remained socially isolated in their homes and could not return to economic zones for work. Nine major sources were identified by the positive matrix factorization model, including fireworks burning, coal combustion, vehicle emissions, dust, Cr industry, oil combustion, Se industry, Zn smelter, and iron and steel industry. Before the control period, K, Fe, Ca, Zn, Ba and Cu were the main elements, and fireworks burning, Zn smelter and vehicle emissions provided the highest contributions to the total element mass with 55%, 12.1% and 10.3%, respectively. During the control period, K, Fe, Ba, Cu and Zn were the dominating elements, and fireworks burning and vehicle emissions contributed 55% and 27% of the total element mass. After the control period, Fe, K, Ca, Zn and Ba were the main elements, and dust and iron and steel industry were responsible for 56% and 21% of the total element mass. The increased contribution from vehicle emissions during the control period could be attributed to our sampling site being near a town hospital and the fact that the vehicle activities were not restricted. The source apportionment results were also related to air mass backward trajectories. The largest reductions of dust, coal combustion, and the industrial sources (Cr industry, Zn smelter, Se industry, iron and steel industry) were distinctly seen for northwest transport (Ulanqab) and were least significant for northeast transport (Tangshan and Tianjin).

Integrated Shock Absorber With Both Tunable Inertance and Damping

Inerter is a two-terminal mass element and the applied force is proportional to the relative acceleration between the terminals. According to the second class of mechanical-electrical analogy, the inerter corresponds exactly to the capacitor in the electric network. Aiming at improving the limited vibration isolation performance using constant inertance of conventional inerter, a new semi-active inerter based on smart material, magnetorheological (MR) fluid, is proposed in this paper. Further, according to the design concept of “functional integration”, the MR inerter, an MR damper and a spiral spring are integrated to realize a new integrated inerter-spring-damper (IISD) with both adjustable inertance and damping characteristics. The MR inerter consists of a ball screw, an MR clutch, MR fluid, excitation coils, an excitation shell, a flywheel, a flywheel shell, a connector, upper and lower covers, bearings and seals. The tunable inertance is achieved by adjusting the excitation current in the excitation coils to change the operating state of the MR clutch. The MR damper and the spiral spring provide variable damping and constant stiffness, respectively. The mathematical model of the IISD is established. The adjustment principle of inertance is verified by numerical simulation, and the mechanical output characteristics of the IISD are analyzed. Besides, the 1/4 vehicle suspension model based on the proposed IISD is built by using MATLAB/SimMechanics. The frequency response and unit impulse response characteristics of the suspension are obtained via the comfort-oriented virtual experiment. The simulation results show that the suspension with the IISD has a 23.0% higher performance than the conventional suspension in vehicle body acceleration, and the suspension deflection and dynamic tire load are also improved.

Eruptive history and volcano-tectonic evolution of Paka volcanic complex in the northern Kenya rift: Insights into the geothermal heat source

In this paper, we provide insights into the eruptive history and volcano-tectonic evolution of the Paka volcanic complex in a revised stratigraphic framework. We integrate all available 40Ar/39Ar radiometric dates along with field observations, remote sensing data, and the analysis of surface and cutting samples from a 2552 m deep borehole (PK-01). Chemical analyses distinguish basalt, hawaiite, mugearite, benmorite, and trachyte rock type in Paka. It also indicates that the eruptive products are genetically related by fractional crystallization. Major element mass balance and Rhyolite-MELTS models are consistent with the trachyte being generated by 74–83% fractional crystallization of Paka basalt. Before the growth of the volcano, volcanic activity was characterised by plateau fissure eruptions at 582–405 ka. Eruptions directly related to the Paka edifice are divided into four different volcanic sequences. Sequences 1–4 span the periods 390–278 ka, 247–205 ka, 160–36 ka, and 36–8 ka. The Pre-Paka plateau eruption products outcrop at the base of the volcano flanks and are overlain by edifice-forming trachyte. Initial caldera-related subsidence is expressed by arcuate structures to the west and southeast parts of the volcano. These initial collapses are associated with tuff and pyroclastic eruptions estimated to have occurred at ~38 ka. Following these explosive eruptions, a ~1.5 by ~1.6 km main caldera developed. The lithological information from the drilled geothermal exploration borehole PK-01 indicates a minimum thickness of ~2200 m for the extrusive lava sequences, with the uppermost 1050 m of the strata being directly related to eruptions from the Paka volcano (Phases 1–4). We estimate a minimum total bulk volume of ~50 km3 for the volcanic material erupted from Paka during the last ~390 ka. This translates to an average eruption rate of ~1.2 × 10−4 km3/yr. The associated advected magmatic heat supported an ‘excess’ heat flux ranging between 110 and 138 mW/m2 or about twice present day average continental flux (57 mW/m2) and about 1.3 times the background values in geothermal areas (90 mW/m2). The apparent high heat flux implies a magma-driven geothermal system, where convection of the hydrothermal fluid is occurring above the heat source. Structural mapping revealed normal faults, strike-slip faults, lineaments, and an array of eruptive vents and domes as the main volcano-tectonic structures. We infer at least four faulting and fault reactivation events that have occurred during Paka geological history. The structural orientations in the area are dominated by NNE and NW with subordinate N-S and NNW striking structures. Evidence suggests that the intersection of NNE and NW trending structures may have had a major influence on the volcanism in the area.

Analysis of tectonic geochemical characteristics and leaching effects of typical pollutants in Kongyu gold mining area in Dadu River Basin, Kangding.

Kongyu Gold Mining Area is located in the northern margin of the Sichuan-Yunnan tectonic belt. This area has gone through two large tectonic cycles of Mesoproterozoic, Neoproterozoic and Phanerozoic. The strata are accompanied by a large number of tensile cracks, shear cracks and microfissures. The voidage, permeability and transitional effect of the rock are increased, and the transformation between surface water and groundwater is enhanced. On the other hand, tectonic movement controls the distributions and allocations of elements in the earth's crust, resulting in directional geochemical changes in crustal materials and rules. Driven by the tectonic force, the elements are reallocated. The ion content and ion compressibility of those elements increase and decrease inversely. The manifestations of rocks and minerals under directional pressure can be characterized by the flow and puncture of plastic minerals and the fragmentation of hard and brittle minerals. In the process of leaching, the pollutant elements precipitate from the deposits of different granular ores, and most are absorbed by the soil column; thus, the mass fraction of polluting elements in the soil column obviously increases. The variability is the largest when the leachate passes through the fine ore. The rate of change of the element mass fraction from high to low is Ni, Zn, Cu, Cd, Pb, As and Cr. A small part migrated from the soil column to the collection fluid, and the leaching effect is related to the rate of change of soil mass fraction, the ion radius of elements and the compressibility.

Understanding Saturn’s interior from theCassiniGrand Finale gravity measurements

Context.Measurements of Saturn’s gravity field byCassiniGrand Finale have been acquired with high precision. It has been demonstrated that the even gravitational harmonicsJ6–J10have larger absolute values than the predictions by typical rigid-body interior models. A four-layer structure model, proposed to interpret Juno’s gravity measurements for Jupiter, has been applied to Saturn, but great attention was paid to the depth of zonal flows in order to interpret the large absolute values ofJ6–J10.Aims.We aim to understand the internal structure and interior composition of Saturn with a similar model for Jupiter. The additional uncertainties in Saturn’s structure and composition are investigated in detail, such as rotation periods, atmospheric helium mass fractions, and flow-induced gravity corrections. Also, we investigate the effect of equations of state for hydrogen and helium on the predictions of the core mass and heavy element abundance.Methods.In the four-layer structure model, we adjusted the heavy element abundances in the outer two envelopes and the mass of the compact core in order to reproduce Saturn’s equatorial radius as well as theCassiniGrand Finale gravity measurements corrected by the flow-induced gravity signals. Different four-layer interior models are specified in terms of the rotation period, the atmospheric helium mass fraction, and the flow-induced gravity corrections. Two different ab initio equations of state for hydrogen and helium were used in interior structure calculations. Optimized calculations were then performed to explore Saturn’s internal structure and composition.Results.It is found that the absolute values ofJ6–J10tend to increase with increasing deep rotation rate and depend on the equations of state adopted in interior calculations. Saturn’s deep rotation rate and atmospheric helium mass fraction are important to determine the distribution of helium and heavy elements in the outer envelopes. We also show that the core mass and heavy element abundance in Saturn are dependent upon the deep rotation rate, the atmospheric helium mass fraction, the flow-induced gravity corrections, and the equations of state for hydrogen and helium.

Geochemical insights into the relationship of rock varnish and adjacent mineral dust fractions

Rock varnishes are μm-thin, dark, manganese(Mn)-rich crusts that accrete in the order of few μm/ka on weathering-resistant lithologies. Although these crusts can form in all climates, they are best known in arid to semi-arid settings. Aeolian dust is understood as a major contributor to the distinct trace metal and REE enrichments in rock varnish. However, the exact proportions of abiotic and biotic formation mechanisms that may explain the oxidation-reactions of Mn2+ to Mn4+, present as Mn oxyhydroxides in the varnish, are still a matter of ongoing debate.We present here the first systematic study of trace element enrichment processes between the uppermost layer of the varnish sequence and their adjacent <50 μm and >50 μm dust fractions across a selection of 41 major and trace elements. This approach is used to investigate samples from three fully arid deserts: the An Nafud in Saudi Arabia, the Negev in Israel, and the Mojave in the USA, which are compared to the significantly different environment of the semi-arid Knersvlakte in South Africa. A new in situ trace element analysis protocol was developed to perform femto- and nanosecond sector-field LA-ICP-MS microanalyses at high-spatial resolution, which allows us to measure the most recent varnish layers for their comparison with recent dust. In agreement with previous studies, all varnishes are enriched in Mn, Pb, Ce, Co, Ba, Zn, Ni, and the Rare-Earth Elements (REE). Here we demonstrate that fine (<50 μm) dust is characterized by similar trace element trends as the varnishes, at overall lower mass fractions. Dust >50 μm has low trace element mass fractions, and enrichment patterns plotting distinctly away from varnish and fine dust. Based on these geochemical patterns, our results indicate a general enrichment mechanism from fine dust to varnish. Previous studies suggested dust to play an integral role in providing the trace elements that are incorporated into the varnish by pH-Eh fluctuations in short-term rain and fog events. We amalgamate and refine previous growth models by providing direct evidence that leaching of about 10% of the Mn and other trace elements from clay minerals in rain or fog droplets at pH ~5 and subsequent scavenging on varnish surfaces at pH ~8 leads integrated over time to the distinct enrichment patterns of the varnish, while initial Mn oxyhydroxide formation is suggested to follow pathways of metal oxide mediated photo-catalysis.For the semi-arid occurrence in the Knersvlakte we present a distinct growth model as both environment, varnish, and dust composition differ significantly from the arid settings. Here, thick, metallic-looking varnish occurs mainly on the rim of quartz pebbles, lacks microlamination, and likely has upscaled growth processes. Among other aspects, we suggest a more complex interplay between photo-catalysis, nocturnal condensation events on quartz pebbles with subsequent water trapping at the rock-soil-atmosphere interface, due to a salic top-soil layer, to mainly account for these differences.

Supporting dataset and methods for body sizes and concentrations of chemical elements measured in elytra and abdomens of Stag Beetles Lucanus cervus.

The dataset presented in this data paper supports “Breaking down insect stoichiometry into chitin-based and internal elemental traits: Patterns and correlates of continent-wide intraspecific variation in the largest European saproxylic beetle” (Orłowski et al. 2020). Here we present the supplementary data and description of methods on the following: (1) mass of elytra and abdomens across 28 local Stag Beetle Lucanus cervus populations in Europe. (2) Population origin and coverage of six major land-cover types, including transport infrastructure, measured in three radii (500 m, 1000 m and 5000 m) around the sampling sites of these populations. (3) The relationship between the mass and concentrations of elements measured in abdomens and elytra in 28 Stag Beetle populations and major land-cover types around the sampling sites.

A crustal scarcity indicator for long-term global elemental resource assessment in LCA

PurposeHow to assess impacts of mineral resources is much discussed in life cycle assessment (LCA). We see a need for, and a lack of, a mineral resource impact assessment method that captures the perspective of long-term global scarcity of elements.MethodA midpoint-level mineral resource impact assessment method matching this perspective is proposed, called the crustal scarcity indicator (CSI), with characterization factors called crustal scarcity potentials (CSPs) measured as kg silicon equivalents per kg element. They are based on crustal concentrations, which have been suggested to correlate with several important resource metrics (reserves, reserve base, reserves plus cumulative production, and ore deposits), thereby constituting proxies for long-term global elemental scarcity.Results and discussionReady-to-use CSPs are provided for 76 elements, through which the CSI can be calculated by multiplying with the respective masses of elements extracted from Earth’s crust for a certain product. As follows from their crustal concentrations, the three platinum-group metals iridium, osmium, and rhodium have the highest CSPs, whereas silicon, aluminum, and iron have the lowest CSPs.ConclusionAn evaluation of the CSPs and the characterization factors of four other mineral resource impact assessment methods in LCA (the abiotic depletion, the surplus ore, the cumulative exergy demand, and the EPS methods) were conducted. It showed that the CSPs are temporally reliable, calculated in a consistent way, and have a high coverage of elements in comparison. Furthermore, a quantitative comparison with the characterization factors of the four other methods showed that the CSPs reflect long-term global elemental scarcity comparatively well while requiring a minimum of assumptions and input parameters.RecommendationsWe recommend using the CSI for assessments of long-term global elemental scarcity in LCA. Since the CSI is at the midpoint level, it can be complemented by other mineral resource impact assessment methods (both existing and to be developed) to provide a more comprehensive view of mineral resource impacts in an LCA.

Experimental and multiscale quantum mechanics modeling of the mechanical properties of PVC/graphene nanocomposite

In current work, we developed mechanical properties of PVC (polyvinyl chloride)/graphene nanocomposite theoretically and experimentally. In our theoretical model, a multi-scale finite element model was used to predict Young’s modulus of the stated nanocomposite. The molecular structure of pristine graphene was treated using the density functional theory (DFT) method. By assuming graphene as a space-frame structure that preserves the discrete nature of graphene, they were modeled by the use of three-dimensional elastic beam elements for the Carbon-Carbon covalent bonds and point mass elements for the atoms. Then interfacial van der Waals interaction that exists between PVC and graphene was modeled using the general form of Lennard–Jones potential and simulated by a nonlinear truss rod model. The Lennard–Jones parameters and van der Waals forces were determined versus separation distance for the stated nonlinear truss rod via the DFT method. Finally, we prepared PVC/graphene samples with different weight percentages of graphene nanoplatelets experimentally using the melt-mixing procedure. Our computational modeling demonstrated that the magnitudes of Young’s modulus PVC/graphene were close to the experimentally obtained results until 1 wt% with an average difference of about 25%. Finally, we justified the obtained mechanical results by investigating the morphology of experimental samples using Transmission electron microscopy (TEM) and Scanning Electron Microscopy (SEM) images.

Performance of non-uniform functionally graded piezoelectric energy harvester beams

The appearance of functionally graded piezoelectric materials has solved the lamination problem of the conventional piezoelectric structures. Functionally graded piezoelectric materials are the new materials with unexplored capabilities. This article theoretically investigates the effects of non-uniformity on the performance of the functionally graded piezoelectric material cantilever beams subjected to harmonic excitation. The governing equations are derived based on Timoshenko and Euler–Bernoulli beam theories. The finite element method with the application of superconvergent element is employed here for the discretization and the vibration analysis of the system. This model is validated by comparing the numerical results with the experimental results of piezoelectric energy harvesters of conventional shapes available in the open literature. Parametric studies are carried out with respect to the effects of tapering ratios, the degree of non-uniformity, load resistance, and the volume fraction parameter on the electrical output power and the fundamental resonance frequency. It was observed that the application of diverging beams noticeably enhances the power output per mass of piezoelectric element extracted while decreases the natural frequency which is advantageous for scavenging energy from ambient surroundings. The results reveal that there is an optimal value for the non-homogeneous parameter leading to the maximized harvested energy under different operating conditions.