Suitable Grade Research Articles

Statistical-empirical pavement temperature prediction models based on data from road weather stations in Estonia

Asphalt pavement properties are greatly affected by seasonal temperature variation. Binder grade selection needs to be aligned with forecasted operational pavement temperatures to maximise pavement longevity. Different widely adopted models for determining binder Superpave Performance Grading have been shown to provide inaccurate results for the Nordic-Baltic region, leading to under- or overestimation of operational pavement temperatures and erroneous selection of a suitable binder grade. This study proposes empirically formulated pavement temperature prediction models for Estonia based on temperature data collected from six different road weather stations in Estonia from 2019 to 2023. Models were derived using measurements from daily maximum and minimum air temperatures combined with pavement temperature profiles with depth.

Evaluation and Promotion of Alluvial Fan Land Suitability for Agriculture in the Lhasa River Basin, Qinghai–Tibet Plateau

Alluvial fans have been proven to have great utilisation potential in QTP, but to what extent they are suitable for agricultural development is unknown. Therefore, using the alluvial fan in the Lhasa River Basin (LRB) as a case study, this paper established an evaluation system of land suitability for agriculture (LSA). Principal component analysis (PCA) and the exhaustive method (EM) were used to define the minimum dataset (MDS) and then the LSA of the alluvial fan in the LRB was evaluated using a comprehensive index of LSA. Two scientific approaches were implemented to improve the LSA using a scenario simulation. The results showed that the MDS assessed by the EA was more representative compared to the PCA. Alluvial fans with suitable grades are mainly distributed in the Lhasa River’s middle and lower reaches. Developing facility agriculture and repairing roads accessing the alluvial fans are effective approaches to improve the LSA, which can increase the suitable-grade area from 58.62% to 97.82% and 63.85%, respectively. Therefore, most alluvial fans in the LRB are suitable for developing agriculture, and under the influence of human activities, there will be more alluvial fans suitable for developing agriculture. Our research provides scientific methods for the sustainable development of land in alpine regions.

Standardization of Optimum Grading Sieve Size for Seed Processing in Black Gram [Vigna mungo (L.) Hepper] Varieties

Background: The seeds harvested from the field may not be homogenous in seed size, physical purity and viability in Black gram. Seeds are to be cleaned and graded using seed processing machineries to maintain uniformity of a seed lot. Every variety is having its individuality in seed size. Hence, the common recommendation of 2.8 mm sieve size recommended by Indian Minimum Seed Certification Standards (IMSCS) for grading black gram seeds may not be suitable to recover a maximum quality seeds in all varieties while processing. The present study was carried out to identify a suitable grading sieve size for newly released black gram varieties for getting good quality seeds with better seed recovery during processing. Methods: The study was conducted at Seed Technology Research Unit, Pandit Jawaharlal Nehru College of Agriculture and Research Institute, Karaikal during the year 2020-2023. The experiment was laid out in completely randomized design with four replications. Four newly released black gram varieties viz., ADT 6, VBN 8, VBN 10 and VBN 11 were taken for the study. Specified quantities of unprocessed seeds have been sieved using slotted sieves of three sizes above (3.4 mm, 3.2 mm and 3.0 mm) and two sizes below (2.7 mm and 2.5 mm) the recommended sieve size of 2.8 mm for black gram varieties as per the IMSCS. The seeds retained over each sieves were collected separately and tested for seed quality parameters. Result: The results revealed that the seed recovery percent increased with decrease in sieve size while the seed quality parameters found higher with increase in sieve size.The sieve size of 2.7 mm (slotted) registered the maximum cumulative seed recovery of 87% and 89.9%, respectively in Black gram seeds of cv. ADT 6 and VBN 10 along with required seed standards. However, seeds retained from the sieve size of 3.0 mm (slotted) registered the maximum cumulative seed recovery of 91.2% and 87.5%, respectively in VBN 8 and VBN 11 with requisite seed germination and physical purity as per the IMSCS (75% and 98%). Hence, it is suggested that the sieve size of 2.7 mm may be considered as grading sieve size for seed processing in Black gram seeds of cv. ADT 6 and VBN 10 and 3.0 mm may be used as grading screen (Bottom screen) for VBN 8 and VBN 11 for getting good quality seeds with higher seed germination, physical purity and pure live seeds.

Optimal Design of Voltage Equalization Ring for the 1100 kV DC Voltage Proportional Standard Device Based on the Nation Standard Device Neural Network and Grey Wolf Optimization Algorithm

The DC voltage ratio standard device is an important tool for calibrating DC voltage transformers. At the 1100 kV voltage level, an increase in electric field intensity will increase the local heat generated inside the device, affecting the accuracy of its measurement. Using a suitable grading ring can even out the electric field intensity and reduce the maximum field strength to improve its measurement accuracy. This article mainly optimizes the design of the grading-ring structure of the 1100 kV DC voltage ratio standard device. First, a finite-element model of the 1100 kV DC voltage ratio standard device was built based on ANSYS; the electric field distribution around the voltage divider was calculated and analyzed, and a data set was constructed based on the calculation results. Secondly, for the optimization of electric field strength, this article presents the design of the nation standard device neural network, which learns the relationship between the structural parameters of the toroidal core and the field strength under the PyTorch 1.8 deep learning framework. Due to the strong convergence performance, few parameters, and ease of implementation of the grey wolf optimization algorithm, this study selected this algorithm to optimize the structural parameters of the grading ring. Finally, simulation examples are established in Python for validation. The experimental results indicate that the maximum field strength of the grading ring decreased from 12,161.1348 V/cm to 10,009.2881 V/cm, a reduction of 17.69%. The optimized structural parameters of the grading ring effectively reduced the electric field intensity around the 1100 kV DC voltage proportional standard device, providing a reliable and practical design approach for the selection of the DC voltage ratio standard device.

Multi-steps integrated mathematical MCDM model for construction material selection of Addis Ababa high-rise building infrastructure

ABSTRACT The construction industry is confronted by resource constraints. It affects the initial costs and environment that requires resource and method optimization. The objective of the research is to design a mathematical MCDM model that would enable to select economically and ecologically suitable building material. To achieve this, the researcher designed, evaluated, and selected the suitable concrete grade using a combined mathematical MCDM. The objective sampling technique is used in Addis Ababa to collect samples of high-rise structures and materials. The study used objective-weighed MCDM and fuzzy-AHP to create specific concrete grades. The amount of the objective was fitted by 95% sensitivity analysis cost and quantity of concrete using a combination of MCDM, linear programming, and Monte Carlo simulation. The result demonstrates that, although the unit cost of concrete increased as strength grew, the project’s overall cost was reduced by reducing the project quantities. It will also add more space with environmentally friendly, sustainable structures. In conclusion, the integrated mathematical MCDM model is a helpful tool for selecting urban structure cost-effective materials

Exploring STEM Education for Real-World Climate Change Concerns to Empower Students as Change Agents

This article explores the application of STEM (Science, Technology, Engineering, and Mathematics) curriculum to real-world problems, with a focus on increasing the relevance and community involvement in climate change projects. Students are empowered to actively contribute to the resolution of problems in their communities when they are involved in community-based activities. This method encourages student involvement, critical thinking, and a sense of social responsibility. STEM projects must be aligned with suitable grade levels and selected major real-world problems to be successful and appropriate. Climate change was chosen as a real-world topic because of its urgency and far-reaching repercussions, which necessitate multidisciplinary approaches and innovative solutions. Students gain critical thinking skills, problem-solving ability, and a sense of environmental stewardship by immersing them in the subject of climate change. The article outlines a qualitative approach that involves literature review, group discussions, and educator observations to lay a solid theoretical foundation and ensure the strategy's success. The debate focuses on the significance of meaningful educational experiences, ways for preparing educators for community involvement, and the need to recognize and celebrate accomplishments. Students get a deeper knowledge of scientific principles while developing the skills and mindset to address global concerns as responsible global citizens by integrating STEM education, community involvement, and climate change.

Evaluation method for the availability of solar energy resources in road areas before route corridor planning

The full utilization of solar energy resources along the road is an effective method to solve the energy shortage in transportation. The key to this is an accurate evaluation of solar energy resources, which provides the rationale for the optimal location of road photovoltaic (PV) projects. However, determining the availability of solar energy resources in road areas before route corridor planning remains difficult. To address the issue, this paper developed a standardized method. Firstly, this paper analyzed the critical factors affecting the availability of solar energy resources. They were meteorology, topography, land use type, geology, and location. On that basis, we developed a four-level evaluation indicator system. Then, it proposed a multi-indicator evaluation method based on the Analytic Hierarchy Process (AHP) and the Geographic Information System (GIS). It used AHP to calculate the weights of each indicator, with solar radiation being the most important. It used GIS to analyze and overlay the spatial distribution of multiple indicators to obtain the map of suitability grades, which could be used to route corridor selection for road PV projects. It also used a case study to demonstrate how the method is applied. The findings show that the method can accurately evaluate the availability of solar energy resources. Furthermore, it studied the appropriate division of evaluation units and it is advised that they shouldn't be larger than 30 m × 30 m. These results provide guidance as a reference for the application of road PV projects and site selection for route corridors worldwide. That will promote the integration of transportation and energy in the future.

Modeling soybean cultivation suitability in China and its future trends in climate change scenarios

Soybean is an important source of oil and vegetable protein and plays a key role in agricultural production and economy. A suitability evaluation of soybean cultivation is important for identifying potential soybean planting areas. Based on the raster data of soybean harvest ratio (FSHA) and climate-soil-topography-socio-economy environmental factors, we used MaxEnt to simulate the soybean planting suitability and potential distribution in China and the future trends of soybean cultivation under climate change. Three shared socio-economic paths (SSPs) that set up in the future climate section were considered, including SSP126 (sustainable path), SSP245 (intermediate path), and SSP585 (fossil fuel dominated development path). The result shows that the suitability of soybean cultivation was primarily influenced by elevation, precipitation of warmest quarter, capacity of the clay fraction, slope, portion of primary industry, topsoil gravel content, mean diurnal temperature range and accumulated temperature ≥10 °C. High-suitability and moderate-suitability area are respectively 26.51 Mha and 41.93 Mha in China. High-suitability areas for soybean are mainly concentrated in the Northeast Plain, the North China Plain and the northern parts of the middle and lower Yangtze River plain. There were many provinces with high soybean planting potential but low development degrees, including Hebei, Henan, Shandong, Tianjin, Jilin, Liaoning, Jiangsu, Hubei and Shaanxi. From 2021 to 2060, the total area highly and moderately suitable for soybean cultivation is projected to increase first and then decrease under both SSP126 and SSP245 scenarios. However, it shows a continued upward trend under SSP585, the rising part accounting for more than 10% in the base of historical data. Specifically, under SSP585, the suitability grade in most parts of Northeast China (eastern Inner Mongolia, northern Heilongjiang and western Jilin and Liaoning) will have a general promotion, opposite to the result under SSP126. Moreover, parts of southwest China (Yunnan, Chongqing, northern Guizhou and eastern Sichuan) may be more suitable for soybean cultivation in both scenarios. This study provides a practical reference for current and future soybean planting layout and relative countermeasures.

Grading bamboo through four-point bending tests. A report on six species of Italian bamboo

The adoption of natural construction materials can help mitigate the environmental impact of the construction industry by reducing the amount of energy required and emissions. Among the natural materials, bamboo is a remarkable option, combining high mechanical resistance with a low specific weight and a very high growth speed; however, its application is limited by the absence of a suitable grading method. This paper aims at filling this lack by providing a strength-based grading methodology relying on a four-point bending test. Experimental results were processed considering bamboo both as a homogeneous material and as a non-homogeneous material and using the ANOVA test. Results show that statistical groups can be defined which are not based on the bamboo species, but on the values of the mechanical properties, hence supporting the appropriateness of strength classes. The bending tests used in this paper could be a crucial test for bamboo grading: it is easier to perform than a tensile test and it gives complete information on the change of material properties along the culm wall thickness. The study focuses on six different species of bamboo grown in Italy, for which little data is present in the literature.

Evaluation of Urban Resource Environmental Carrying Capacity and Land Spatial Development Suitability in a Semiarid Area of the Yellow River Basin

At present, the carrying capacity of resources and the environment in some areas has reached an upper limit, and the problems of ecological destruction and environmental pollution have become increasingly prominent. The overexploitation and disorderly development of land space, resulting in the spatial imbalance between the population economy and the resource environment, is one of the root causes of excessive resource consumption, ecological degradation, and environmental pollution. Resource and environmental carrying capacity and suitability evaluation of land space development is the basis of land space planning. It provides conditions for the modernization of land space governance. The framework provided by the “ Double Evaluation Guide (Trial) “ is universal. It is necessary to adapt it to local conditions and to achieve the ” Double Evalution” results, according to the characteristics of regional development. Taking Hohhot as the research area, which is based on the “Guide”, involves selecting convincing and credible evaluation factors and using the single factor integration method and the discriminant matrix method. The “double evaluation” of Hohhot was also analyzed. This provides basic data for regional high-quality development and land space planning. The results show the following: (1) The ecological function of Hohhot is good. The areas with low importance for ecological protection accounted for about 18%, the areas with medium ecological protection accounted for about 62%, and the areas with high ecological protection accounted for about 21%. (2) The carrying capacity of agricultural function in Hohhot is medium. The carrying capacity of the low polar region accounted for about 23%, the medium polar region’s carrying capacity accounted for about 71%, and the high polar region’s carrying capacity accounted for about 6%. (3) The urban function carrying capacity of Hohhot is medium. The carrying capacity of the low-grade area accounted for about 25%, the medium-grade area’s carrying capacity accounted for about 55%, and the high-grade area’s carrying capacity accounted for about 21%. (4) The overall agricultural production suitability grade of Hohhot is not suitable. (5) The suitability of urban construction in Hohhot is general. The unsuitable area accounts for about 40%, the more suitable area accounts for about 45%, and the most suitable area accounts for about 15%.

Suitability Evaluation of Old Industrial Buildings Transformed into Stadiums

The regeneration and utilization of idle, old industrial buildings in urban areas has become a focus of urban development, owing to urban renewal and industrial structural adjustment. At the same time, the increasing demand for sports space has highlighted the insufficient supply of sports facilities in cities. To solve this dilemma, the transformation of old industrial buildings into sports venues has become another mode of recycling and reuse in recent years. Due to the many specialties, complex contents, and numerous influencing factors involved in the transformation process, the suitability of these buildings is uncertain. To ensure the suitability of the transformation project, the theory of old industrial buildings recycling and sports building design specifications was used. An index system was established for the evaluating the suitability of transforming old industrial buildings into stadiums, which included five first-level and twenty second-level indices. Based on the matter–element extension theory, a suitability evaluation model was constructed to transform old industrial buildings into sports venues. The correlation function of each evaluation index was calculated, and the index weight was determined using the entropy weight method to obtain the suitability grade of the renovation project, which was verified by the renovation project case. The research shows that the suitability level of the renovation project is level II, which is consistent with the actual situation, indicating that the evaluation model—based on entropy weight method and matter–element extension method—for the transformation of old industrial buildings and stadiums has high reliability.

Logic reasoning under data veracity concerns

Logic reasoning involving big data often requires the proper handling of data veracity. Indeed with data that cannot be trusted to the same extent, users should at least be aware on the trust they can have in the obtained reasoning. In this paper, we propose a novel logic framework that is based on so-called L-grades. L-grades are a special case of Zadeh's Z-numbers, consisting of a pair (s,c)∈[0,1]2 in which s is a suitability grade (or satisfaction grade) and c is a confidence grade denoting how confident we can be on s. Both grades are further processed using fuzzy logic. A novel negation operator and novel conjunction and disjunction operators satisfying commutativity, associativity, but not distributivity properties are proposed. Furthermore, so-called sibling aggregators for L-grades are introduced and studied. With this framework we aim to contribute to explainable computational intelligence. The practical applicability of L-grades is discussed based on the demand for more informative, explainable results in the TILES decision support system for sand extraction from the North Sea seabed.

Comparing outcomes of laser hemorrhoidoplasty and LigaSure hemorrhoidectomy in grade II-III hemorrhoidal disease: a retrospective analysis.

Hemorrhoidal disease is a common ailment that presents a challenge in terms of standard treatment methods. Although surgical hemorrhoidectomy is often considered the gold standard, new surgical techniques have emerged, such as laser hemorrhoidoplasty and LigaSure hemorrhoidectomy, to address postoperative pain, bleeding, and extended return-to-work times. This study aims to compare the outcomes of laser hemorrhoidoplasty and LigaSure hemorrhoidectomy in patients with grade II-III hemorrhoidal disease. A retrospective analysis was conducted on a cohort of patients who underwent laser hemorrhoidoplasty or LigaSure hemorrhoidectomy. Data were collected on postoperative pain, complications, recurrence rates, and return-to-work times. The primary outcome was the difference in postoperative pain between the two groups, as assessed using the Visual Analog Scale (VAS). Patients in the laser hemorrhoidoplasty group experienced significantly lower postoperative pain compared to those in the LigaSure hemorrhoidectomy group. Bleeding amounts during the operation were also significantly lower in the laser group. However, the recurrence rate was higher in the laser group compared to the LigaSure group (9.4% versus 2.5%). Return to work and normal activities time after laser hemorrhoidoplasty was shorter than after LigaSure hemorrhoidectomy. Laser hemorrhoidoplasty is a minimally invasive technique that can be safely applied in suitable grade II-III patients, offering lower postoperative pain rates, fewer complications, and shorter return to work and normal activity times compared to LigaSure hemorrhoidectomy. However, recurrence rates are still higher for laser hemorrhoidoplasty. Future studies should explore the potential of combining laser hemorrhoidoplasty with other surgical treatments.

Optimizing concrete performance: An investigation into the impact of supplementary cementitious materials and sand particle sizes

The significance of employing suitable grades of aggregates and binders combined with waste materials in optimizing the performance of concrete cannot be overstated. It is evidenced from research that supplementary cementitious materials (SCM) sourced from construction waste can enhance the properties of cured concrete with less environmental impact and substantial economic savings. This study investigates the effect of SCM modified with customized sand particle sizes as fine aggregates on concrete’s compressive strength and durability properties. The SCMs comprised silica fume (SF), glass powder (GP), and marble dust (MD) in different percentages (0%, 15%, and 20%). The results indicated higher compressive strength at 28-d could be obtained by adding SCM and finer sand particle size distribution than natural sand grain sizes. The study suggests an effective approach for the recyclability of locally available industrial by-products as ingredient modifiers, which possess great potential for cement production for improved performance and to benefit localities with the predominance of finer sand and soil varieties for usage as a substitute to the traditional grain size of fine aggregates.

Establishment of Soil Suitability for Growing Bracken (Pteridium aquilinum L.) Using the Quantification Theory I

The soil suitability grades are classifying as soil series by judging the potential productivity of the soil based on the yield of crops. The soil suitability grade is divided into four grades, which are very suitable, suitable, possible, and not suitable areas. The reason for classifying the grades is to help farmers in selecting crops to grow in consideration of the characteristics of the soil. Among the soil characteristics used previously to set the soil suitability grade of 66 crops, the five most common characteristics selected. As for the crop it applied as the determinant, the bracken with the largest number of plots selected among the crops excluding the crops with the crop exclusion criteria registered with the agricultural business. The relationship between yield and soil characteristics confirmed by examining the cultivated yield of local bracken and the soil characteristics of the plots. For subsoil, the highest yield was shown when the sub-soil texture were loam and silty loam with a clay content of 15 - 35%, the drainage grade was slightly poor, the available soil depth was >100 cm, the gravel content was 15 - 35%, and the slope was >30%. Based on this, the partial correlation coefficient was calculated. As a result, the drainage grade was the highest at 0.22, indicating the greatest influence. The corresponding soil suitability grade was applied to the soil characteristics of 1,361 phases in Korea to obtain the predicted value for the soil specific factors. The predicted values ​​ranged from 35 - 73 kg ha-1, with 92 very suitable areas, 487 suitable areas, 421 possible areas, and 361 not suitable areas.The soil suitability grades map of bracken in Korea. Based on the relationship value between the detailed soil characteristics and yield of bracken through a soil survey on the yield and the bracken cultivation fields.

Estimating the dimensional change behavior of nuclear graphite with heavy-ion irradiation-induced bending

Two promising reactor Generation IV designs employ nuclear graphite as their moderator and reflector. To this end, new graphite grades are being developed, which will require their suitability for reactor design to be established. Understanding graphite irradiation behavior, especially dimensional change, is critical when selecting a particular nuclear graphite grade. This is usually established by fast neutron irradiation experiments in a material test reactor (MTR). However, due to the limited accessibility to the MTR irradiation facility, cost, and the time required for such experiments to be carried out, the development of new nuclear graphite grades is restrictive. Here, a novel approach is proposed to enable suitable grades to be selected from a number of candidates before an MTR program is implemented by estimating the irradiation-induced dimensional change behaviors of several nuclear graphite grades based on the bending of graphite foils under ion irradiation. The method is capable of efficiently distinguishing the most dimensionally stable graphite grades in the laboratory without the need to irradiate many samples in an MTR program.

Feature Selection: Binary Harris Hawk Optimizer Based Biomedical Datasets

Feature selection (FS) is an essential preprocessing step in utmost solutions for the high-dimensional problem to reduce the number of features by deleting irrelevant and redundant data that preserve a suitable grade of classification accuracy. Feature selection can be treated as an optimization problem. Heuristic optimization algorithms are hopeful approaches to solve feature selection problems because of their difficulty, especially in high-dimensional data. Binary Harris hawk optimization (BHHO) is one of the lately suggested metaheuristic algorithms that has been demonstrated to be used more efficiently in facing some optimization problems. Support vector machines (SVMs) are a vital technique that are employed competently to resolve classification issues. We modified the BHHO algorithm with SVM classifier to solve the feature selection issue. This study suggests BHHO-FS to fix the feature selection problem in biomedical datasets. We ran the proposed approach BHHO-FS on real biomedical datasets with 17 types of cancer for Iraqi patients in 2010-2012. The experimental results demonstrate the supremacy of the proposed BHHO-FS in terms of three performance metrics: feature selection accuracy, runtime and number of selected features compared to four other state-of-art algorithms: Fire Fly (FF) algorithm, Genetic Algorithm (GA), Grasshopper Optimization Algorithm (GOA) and Particle Swarm Algorithm (PSO). Comparative experiments designate the importance of the proposed approach in comparison with the other four mentioned algorithms. The implementation of the proposed BHHO-FS approach on 17 datasets for different types of cancers reveals 99.967% average accuracy.

Spatiotemporal Changes in Waterfowl Habitat Suitability in the Caohai Lake Wetland and Responses to Human Activities

The Caohai Lake wetland is one of the most important wetlands in China and is also one of the most important overwintering areas for waterfowl. However, the spatiotemporal changes in the waterfowl habitat’s suitability and its response patterns to human activities are still unclear. Understanding these patterns is key to plateau wetland biodiversity conservation. In this study, remote sensing, the geographic information system, and global positioning system (3S) technology were employed, and the water source status, disturbance, shelter, and food availability were used as evaluation factors for waterfowl habitat selection. A suitability evaluation model was constructed to evaluate the spatiotemporal characteristics of the Caohai Lake wetland habitat’s suitability in 2000, 2010, and 2022, and to evaluate the response mechanisms of the waterfowl toward human activities. The results show the following: (1) there were frequent changes in the suitability grade of the study area from 2000 to 2022, and there was an overall trend toward improvement as the areas of suitable regions continuously increased. This was due to the continuous improvements in water source status, food availability, and shelter. (2) Human disturbances gradually increased from 2000 to 2022, and the human disturbance index was negatively correlated with the waterfowl habitat suitability. (3) There were significant spatial differences in the suitable waterfowl habitats. The marshlands near the banks of the lake were the regions with optimum and good suitability, while the areas of poor suitability and unsuitable regions were the deep-water areas, roads, and residential areas with high human disturbance, along with the regions near these areas. It is vital to further decrease human disturbances, in order to increase the habitat suitability of the study area.

Viscoelastic free vibration analysis of in-plane functionally graded orthotropic plates integrated with piezoelectric sensors: Time-dependent 3D analytical solutions

This paper proposes an accurate three-dimensional framework for elastic and viscoelastic free vibration investigation of in-plane functionally graded (IPFG) orthotropic rectangular plates integrated with piezoelectric sensory layers. The developed analytical framework is capable of considering layer-wise unidirectional linear functional gradation in both stiffness and density of the orthotropic composite layers. 3D piezoelasticity-based governing equations of motion are formulated in mixed form by employing Hamilton’s principle, and further solved analytically for Levy-type support conditions using the power-series-based extended Kantorovich method (EKM) jointly with Fourier series. The displacements, stresses, and electrical variables (electric field and electric potential) are solved as the primary variables that ensure the point-wise interlayer continuity and electro-mechanical support conditions. The viscoelastic property of the orthotropic interlayer is defined by employing Biot model, which is similar to the standard linear viscoelastic model. The correctness and efficacy of the present mathematical model are established by comparing the present numerical results with published literature and 3D finite element results, obtained by utilizing user material subroutine in the commercial FE software ABAQUS. An extensive numerical study is performed for various configurations and thickness ratios to investigate the influences of in-plane gradation, viscoelasticity and their coupled effects on the free-vibration response of hybrid laminated plates. It is found that in-plane gradation of stiffness and density remarkably alters the flexural frequencies and corresponding mode shapes of the hybrid intelligent rectangular plates. The flexural frequencies and stresses in the plate can be modified by selecting suitable grading indexes. Another interesting observation is that the in-plane gradation shows a considerably less effect on the electrical response of piezoelectric layers, which can play a vital role in the design of sensors and actuators for dynamic applications. Further, the numerical study demonstrates a potential time-dependent structural behaviour based on the present viscoelastic modelling. The consideration of viscoelasticity could be crucial for analysing the mechanical behaviour of a wide range of polymer composites more realistically and for prospective temporal programming in smart structural systems by exploiting the viscoelastic effect. Although the present analytical solution has been proposed for the free-vibration investigation of smart in-plane functionally graded (IPFG) viscoelastic plates, it can also be utilized directly to analyze the symmetric and asymmetric laminated piezoelectric smart plates with constant properties.

On rationality of C-graded vertex algebras and applications to Weyl vertex algebras under conformal flow

Using the Zhu algebra for a certain category of C-graded vertex algebras V, we prove that if V is finitely Ω-generated and satisfies suitable grading conditions, then V is rational, i.e., it has semi-simple representation theory, with a one-dimensional level zero Zhu algebra. Here, Ω denotes the vectors in V that are annihilated by lowering the real part of the grading. We apply our result to the family of rank one Weyl vertex algebras with conformal element ωμ parameterized by μ∈C and prove that for certain non-integer values of μ, these vertex algebras, which are non-integer graded, are rational, with a one-dimensional level zero Zhu algebra. In addition, we generalize this result to appropriate C-graded Weyl vertex algebras of arbitrary ranks.