Search results for: Free frequencies

Authors: Hasan Hassoun, Jaafar Hallal, Denis Duhamel, Mohammad Hammoud, Ali Hage Diab

Abstract:

This paper aims to prove the accuracy of an inexpensive smartphone camera as a non-contact vibration sensor to recover the vibration modes of a vibrating structure such as a cantilever beam. A video of a vibrating beam is filmed using a smartphone camera and then processed by the motion magnification technique. Based on this method, the first two natural frequencies and their associated mode shapes are estimated experimentally and compared to the analytical ones. Results show a relative error of less than 4% between the experimental and analytical approaches for the first two natural frequencies of the beam. Also, for the first two-mode shapes, a Modal Assurance Criterion (MAC) value of above 0.9 between the two approaches is obtained. This slight error between the different techniques ensures the viability of a cheap smartphone camera as a non-contact vibration sensor, particularly for structures vibrating at relatively low natural frequencies.

Keywords: Modal Analysis, motion magnification, smartphone camera, structural vibration, vibration modes.

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Authors: Giho Jeong, Sooin Jeong, Kuisoon Kim

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It is very important to determine reference temperature when convective temperature because it should be used to calculate the temperature potential. This paper deals with the development of a new method that can determine heat transfer coefficient and reference free stream temperature simultaneously, based on transient heat transfer experiments with using two narrow band thermo-tropic liquid crystals (TLC's). The method is validated through error analysis in terms of the random uncertainties in the measured temperatures. It is shown how the uncertainties in heat transfer coefficient and free stream temperature can be reduced. The general method described in this paper is applicable to many heat transfer models with unknown free stream temperature.

Keywords: Heat transfer coefficient, Thermo-tropic LiquidCrystal (TLC), Free stream temperature.

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Authors: Elia Favarelli, Enrico Testi, Andrea Giorgetti

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Autonomous structural health monitoring (SHM) of many structures and bridges became a topic of paramount importance for maintenance purposes and safety reasons. This paper proposes a set of machine learning (ML) tools to perform automatic feature selection and detection of anomalies in a bridge from vibrational data and compare different feature extraction schemes to increase the accuracy and reduce the amount of data collected. As a case study, the Z-24 bridge is considered because of the extensive database of accelerometric data in both standard and damaged conditions. The proposed framework starts from the first four fundamental frequencies extracted through operational modal analysis (OMA) and clustering, followed by time-domain filtering (tracking). The fundamental frequencies extracted are then fed to a dimensionality reduction block implemented through two different approaches: feature selection (intelligent multiplexer) that tries to estimate the most reliable frequencies based on the evaluation of some statistical features (i.e., entropy, variance, kurtosis), and feature extraction (auto-associative neural network (ANN)) that combine the fundamental frequencies to extract new damage sensitive features in a low dimensional feature space. Finally, one-class classification (OCC) algorithms perform anomaly detection, trained with standard condition points, and tested with normal and anomaly ones. In particular, principal component analysis (PCA), kernel principal component analysis (KPCA), and autoassociative neural network (ANN) are presented and their performance are compared. It is also shown that, by evaluating the correct features, the anomaly can be detected with accuracy and an F1 score greater than 95%.

Keywords: Anomaly detection, dimensionality reduction, frequencies selection, modal analysis, neural network, structural health monitoring, vibration measurement.

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Authors: Ferhat Kadioglu, Ahmet Reha Gunay

Abstract:

Correct measurement of a structural damping value is an important issue for the reliable design of the components exposed to vibratory and noise conditions. As far as a vibrating beam technique is concerned, the specimens under the test somehow are interacted with measuring and exciting devices and also with boundary conditions of the test set-up. The aim of this study is to propose a vibrating beam method that offers a non-contact dynamic measurement of solid beam specimens. To evaluate possible effects of the clamped portion of the specimens with clamped-free ends on the dynamic values (damping and the elastic modulus), the same measuring devices were used, and the results were compared to those with the free-free ends. To get clear idea about the sensitivity of the boundary conditions to the damping values at low, medium and high levels, representative materials were subjected to the tests. The results show that the specimens with low damping values are especially sensitive to the boundary conditions and the most reliable structural damping values are obtained for the specimens with free-free ends. For the damping values at the low levels, a deviation of about 368% was obtained between the specimens with free-free and clamped-free ends, yet, for those having high inherent damping values, comparable results were obtained.

Keywords: Vibrating beam technique, dynamic values, damping, boundary conditions, non-contact measuring systems.

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Authors: Askar Sabet, Abdolrasoul Fakhraee, Motahahre Ramezanpour, Noorallah Alipour

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An efficient and green method for oxidation of thiols to the corresponding disulfides is reported using ionic liquid [HSO3N(C2H4OSO3H)3] in the presence of free nano-Fe2O3 at 60°C. Ionic liquid is selective oxidant for S-S Coupling variety aliphatic and aromatic of thiols to corresponding disulfide in the presence of free nano-Fe2O3 as recoverable catalyst. Reaction has been performed in methanol as an inexpensive solvent. This reaction is clean and easy work-up with no side reaction.

Keywords: Thiol, Disulfide, Ionic liquid, Free Nano-Fe2O3, Oxidation, Coupling.

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Authors: Negar Riazifar, Nigel G. Stocks

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This paper proposes strategies in level crossing (LC) sampling and reconstruction that provide alias-free high-fidelity signal reconstruction for speech signals without exponentially increasing sample number with increasing bit-depth. We introduce methods in LC sampling that reduce the sampling rate close to the Nyquist frequency even for large bit-depth. The results indicate that larger variation in the sampling intervals leads to alias-free sampling scheme; this is achieved by either reducing the bit-depth or adding a jitter to the system for high bit-depths. In conjunction with windowing, the signal is reconstructed from the LC samples using an efficient Toeplitz reconstruction algorithm.

Keywords: Alias-free, level crossing sampling, spectrum, trigonometric polynomial.

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Authors: S. Y. Choi, Y. H. Na, J. H. Kim

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In this work, thermoelastic damping effect on the hemi- spherical shells is investigated. The material is selected silicon, and heat conduction equation for thermal flow is solved to obtain the temperature profile in which bending approximation with inextensional assumption of the model. Using the temperature profile, eigen-value analysis is performed to get the natural frequencies of hemispherical shells. Effects of mode numbers, radii and radial thicknesses of the model on the natural frequencies are analyzed in detail. Furthermore, the quality factor (Q-factor) is defined, and discussed for the ring and hemispherical shell.

Keywords: Thermoelastic damping, hemispherical shell, quality factor

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Authors: Tamal Bose, Zhurun Zhang, Miloje Radenkovic, Ojas Chauhan

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In this paper, a novel approach is presented for designing multiplier-free state-space digital filters. The multiplier-free design is obtained by finding power-of-2 coefficients and also quantizing the state variables to power-of-2 numbers. Expressions for the noise variance are derived for the quantized state vector and the output of the filter. A “structuretransformation matrix" is incorporated in these expressions. It is shown that quantization effects can be minimized by properly designing the structure-transformation matrix. Simulation results are very promising and illustrate the design algorithm.

Keywords: Digital filters, minimum noise, multiplier-free, quantization, state-space.

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Authors: A. Meftah, D. Zarga, M. Yahiaoui

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In this paper, we have used an analytical method to analyze the vibratory behavior of plates in materials with gradient of properties, simply supported, proposing a refined non polynomial theory. The number of unknown functions involved in this theory is only four, as compared to five in the case of other higher shear deformation theories. The transverse shearing effects are studied according to the thickness of the plate. The motion equations for the FGM plates are obtained by the Hamilton principle application, the solutions are obtained using the Navier method, and then the fundamental frequencies are found, solving an eigenvalue equation system, the results of this analysis are presented and compared to those available in the literature.

Keywords: FGM plates, Navier method, vibratory behavior.

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Authors: M. S. Ahmed, F. A. Mohammad

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The aim of this paper is to perform experimental modal analysis (EMA) of reinforced concrete (RC) square slabs. EMA is the process of determining the modal parameters (Natural Frequencies, damping factors, modal vectors) of a structure from a set of frequency response functions FRFs (curve fitting). Although, experimental modal analysis (or modal testing) has grown steadily in popularity since the advent of the digital FFT spectrum analyzer in the early 1970’s, studying all types of members and materials using such method have not yet been well documented. Therefore, in this work, experimental tests were conducted on RC square slab specimens of dimensions 600mm x 600mmx 40mm. Experimental analysis was based on freely supported boundary condition. Moreover, impact testing as a fast and economical means of finding the modes of vibration of a structure was used during the experiments. In addition, Pico Scope 6 device and MATLAB software were used to acquire data, analyze and plot Frequency Response Function (FRF). The experimental natural frequencies which were extracted from measurements exhibit good agreement with analytical predictions. It is showed that EMA method can be usefully employed to investigate the dynamic behavior of RC slabs.

Keywords: Natural frequencies, Mode shapes, Modal analysis, RC slabs.

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Authors: Minghui Wang, Juntao Zhang

Abstract:

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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Authors: Bahadur Singh Hathan, B. L. Prassana

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Most of the commercial gluten free products are nutritionally inferior when compared to gluten containing counterparts as manufacturers most often use the refined flours and starches. So it is possible that people on gluten free diet have low intake of fibre content. The foxtail millet flour and copra meal are gluten free and have high fibre and protein contents. The formulation of fibre rich gluten free cookies was optimized by response surface methodology considering independent process variables as proportion of Foxtail millet (Setaria italica) flour in mixed flour, fat content and guar gum. The sugar, sodium chloride, sodium bicarbonates and water were added in fixed proportion as 60, 1.0, 0.4 and 20% of mixed flour weight, respectively. Optimum formulation obtained for maximum spread ratio, fibre content, surface L-value, overall acceptability and minimum breaking strength were 80% foxtail millet flour in mixed flour, 42.8 % fat content and 0.05% guar gum.

Keywords: Copra meal flour, Fiber rich gluten-free cookies, Foxtail millet flour, Optimization

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: Stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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Authors: F. Soleymani, M. Sharifi

Abstract:

Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

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Authors: A. Izadbakhsh, M. M. Fateh

Abstract:

A model-free robust control (MFRC) approach is proposed for position control of robot manipulators in the state space. The control approach is verified analytically to be robust subject to uncertainties including external disturbances, unmodeled dynamics, and parametric uncertainties. There is a high flexibility to work on different systems including actuators by the use of the proposed control approach. The proposed control approach can guarantee the robustness of control system. A PUMA 560 robot driven by geared permanent magnet dc motors is simulated. The simulation results show a satisfactory performance for control system under technical specifications. KeywordsModel-free, robust control, position control, PUMA 560.

Keywords: Model-free, robust control, position control, PUMA 560.

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Authors: Basavaraj Vadavadagi, Satishkumar Shekhawat

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Interstitial free steels possess better formability and have many applications in automotive industries. Forming limit diagrams (FLDs) indicate the formability of materials which can be determined by experimental and finite element (FE) simulations. FLDs were determined experimentally by LDH test, utilizing optical strain measurement system for measuring the strains in different width specimens and by FE simulations in Interstitial Free (IF) and Interstitial Free High Strength (IFHS) steels. In this study, the experimental and FE simulated FLDs are compared and also the stress based FLDs were investigated.

Keywords: Forming limit diagram, Limiting Dome Height, optical strain measurement, interstitial

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Authors: Andres G. Victorio, Montita Rungswang

Abstract:

A free-trade agreement is found to increase Thailand-s agricultural imports from New Zealand, despite the short span of time for which the agreement has been operational. The finding is described by autoregressive estimates that correct for possible unit roots in the data. The agreement-s effect upon imports is also estimated while considering an error-correction model of imports against gross domestic product.

Keywords: Agricultural imports, free trade, unit roots, cointegration, error correction.

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Authors: V. K. Nelson, S. Karthikeyan

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Axisymmetric vibration of an infinite Pyrocomposite circular hollow cylinder made of inner and outer pyroelectric layer of 6mm-class bonded together by a Linear Elastic Material with Voids (LEMV) layer is studied. The exact frequency equation is obtained for the traction free surfaces with continuity condition at the interfaces. Numerical results in the form of data and dispersion curves for the first and second mode of the axisymmetric vibration of the cylinder BaTio3 / Adhesive / BaTio3 by taking the Adhesive layer as an existing Carbon Fibre Reinforced Polymer (CFRP) are compared with a hypothetical LEMV layer with and without voids and as well with a pyroelectric hollow cylinder. The damping is analyzed through the imaginary parts of the complex frequencies.

Keywords: Axisymmetric vibration, CFRP, hollow cylinders, LEMV, pyrocomposite

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Authors: R. Khadim, M. Erritali, A. Maaden

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Localization of nodes is one of the key issues of Wireless Sensor Network (WSN) that gained a wide attention in recent years. The existing localization techniques can be generally categorized into two types: range-based and range-free. Compared with rang-based schemes, the range-free schemes are more costeffective, because no additional ranging devices are needed. As a result, we focus our research on the range-free schemes. In this paper we study three types of range-free location algorithms to compare the localization error and energy consumption of each one. Centroid algorithm requires a normal node has at least three neighbor anchors, while DV-hop algorithm doesn’t have this requirement. The third studied algorithm is the amorphous algorithm similar to DV-Hop algorithm, and the idea is to calculate the hop distance between two nodes instead of the linear distance between them. The simulation results show that the localization accuracy of the amorphous algorithm is higher than that of other algorithms and the energy consumption does not increase too much.

Keywords: Wireless Sensor Networks, Node Localization, Centroid Algorithm, DV–Hop Algorithm, Amorphous Algorithm.

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Authors: S. Lecheb, A. Nour, A. Chellil, A. Basta, D. Belmiloud, H. Kebi

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In recent years, a new numerical method has been developed, the extended finite element method (X-FEM). The objective of this work is to exploit the (X-FEM) for the treatment of the fracture mechanics problems on 3D geometries, where we showed the ability of this method to simulate the fatigue crack growth into two cases: edge and central crack. In the results we compared the six first natural frequencies of mode shapes uncracking with the cracking initiation in the structure, and showed the stress intensity factor (SIF) evolution function as crack size propagation into structure, the analytical validation of (SIF) is presented. For to evidence the aspects of this method, all result is compared between FEA and X-FEM.

Keywords: 3D fatigue crack growth, FEA, natural frequencies, stress intensity factor (SIF), X-FEM.

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Authors: Nilson Barbieri, Renato Barbieri

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–In this paper the damage in clamped-free, clampedclamped and free-free beam are analyzed considering samples without and with structural modifications. The damage location is investigated by the use of the bispectrum and wavelet analysis. The mathematical models are obtained using 2D elasticity theory and the Finite Element Method (FEM). The numerical and experimental data are approximated using the Particle Swarm Optimizer (PSO) method and this way is possible to adjust the localization and the severity of the damage. The experimental data are obtained through accelerometers placed along the sample. The system is excited using impact hammer.

Keywords: Damage, beam, PSO, bispectrum, wavelet transform

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Authors: Maja Benkovic, Ingrid Bauman

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The objective of this work was to investigate flow properties of powdered infant formula samples. Samples were purchased at a local pharmacy and differed in composition. Lactose free infant formula, gluten free infant formula and infant formulas containing dietary fibers and probiotics were tested and compared with a regular infant formula sample which did not contain any of these supplements. Particle size and bulk density were determined and their influence on flow properties was discussed. There were no significant differences in bulk densities of the samples, therefore the connection between flow properties and bulk density could not be determined. Lactose free infant formula showed flow properties different to standard supplement-free sample. Gluten free infant formula with addition of probiotic microorganisms and dietary fiber had the narrowest particle size distribution range and exhibited the best flow properties. All the other samples exhibited the same tendency of decreasing compaction coefficient with increasing flow speed, which means they all become freer flowing with higher flow speeds.

Keywords: flow properties, infant formula, powderedmaterial

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Authors: Khairul Jauhari, Achmad Widodo, Ismoyo Haryanto

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In this article, the radial displacement error correction capability of a high precision spindle grinding caused by unbalance force was investigated. The spindle shaft is considered as a flexible rotor mounted on two sets of angular contact ball bearing. Finite element methods (FEM) have been adopted for obtaining the equation of motion of the spindle. In this paper, firstly, natural frequencies, critical frequencies, and amplitude of the unbalance response caused by residual unbalance are determined in order to investigate the spindle behaviors. Furthermore, an optimization design algorithm is employed to minimize radial displacement of the spindle which considers dimension of the spindle shaft, the dynamic characteristics of the bearings, critical frequencies and amplitude of the unbalance response, and computes optimum spindle diameters and stiffness and damping of the bearings. Numerical simulation results show that by optimizing the spindle diameters, and stiffness and damping in the bearings, radial displacement of the spindle can be reduced. A spindle about 4 μm radial displacement error can be compensated with 2 μm accuracy. This certainly can improve the accuracy of the product of machining.

Keywords: Error correction, High precision grinding, Optimization, Radial displacement, Spindle.

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Authors: S.Aranganayagi, K.Thangavel

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Clustering categorical data is more complicated than the numerical clustering because of its special properties. Scalability and memory constraint is the challenging problem in clustering large data set. This paper presents an incremental algorithm to cluster the categorical data. Frequencies of attribute values contribute much in clustering similar categorical objects. In this paper we propose new similarity measures based on the frequencies of attribute values and its cardinalities. The proposed measures and the algorithm are experimented with the data sets from UCI data repository. Results prove that the proposed method generates better clusters than the existing one.

Keywords: Clustering, Categorical, Incremental, Frequency, Domain

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Authors: Dong Ming, Su Caihong

Abstract:

The scenario of bypass transition is generally described as follows: the low-frequency disturbances in the free-stream may generate long stream-wise streaks in the boundary layer, which later may trigger secondary instability, leading to rapid increase of high-frequency disturbances. Then possibly turbulent spots emerge, and through their merging, lead to fully developed turbulence. This description, however, is insufficient in the sense that it does not provide the inherent mechanism of transition that during the transition, a large number of waves with different frequencies and wave numbers appear almost simultaneously, producing sufficiently large Reynolds stress, so the mean flow profile can change rapidly from laminar to turbulent. In this paper, such a mechanism will be figured out from analyzing DNS data of transition.

Keywords: boundary layer, breakdown, bypass transition, stability, streak.

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Authors: A. Norezzine, N. Y. Rebouh, M. Souadkia, D. Parpura, A. Gadzhikurbanov, E. A. Gladyr, P. M. Klenovitsky, A. A. Nikishov, A. Dranidis

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This article deals with the genetic characteristics of samples Schwyz-zebu cattle from three farms of the Republic of Tajikistan on 10 microsatellite markers (STS). Hence, the present study was carried out to evaluate the heterozygosity in the population and to characterize this breed by identifying DNA markers using microstatellites. Microsatellites often have multiple alleles and may have heterozygosity frequencies of 70% or more. This makes them highly informative for genetic analysis. A total of ten microsatellite primers were used for microsatellite analysis in genomic DNA of Zebu cattle. The amplified products were analysed for polymorphic alleles and their frequencies. The resulting information can be used in dealing with the conservation and sustainable use of genetic resources of the Tajik Schwyz-zebu cattle.

Keywords: DNA, gene pool, Schwyz-zebu cattle, microsatellite loci.

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Authors: E. Marei, A. Hammad, S. Ismail, A. El-Gindy

Abstract:

This study aims to investigate the ability of different formula of mixed bacteria as a biological treatments of wastewater after primary treatment as a bio-treatment and bio-removal and bio-adsorbent of different heavy metals in natural circumstances. The wastewater was collected from Sarpium forest site-Ismailia Governorate, Egypt. These treatments were mixture of free cells and mixture of immobilized cells of different bacteria. These different formulas of mixed bacteria were prepared under Lab. condition. The obtained data indicated that, as a result of wastewater bio-treatment, the removal rate was found to be 76.92 and 76.70% for biological oxygen demand, 79.78 and 71.07% for chemical oxygen demand, 32.45 and 36.84 % for ammonia nitrogen as well as 91.67 and 50.0% for phosphate after 24 and 28 hrs with mixed free cells and mixed immobilized cells, respectively. Moreover, the bio-removals of different heavy metals were found to reach 90.0 and 50. 0% for Cu ion, 98.0 and 98.5% for Fe ion, 97.0 and 99.3% for Mn ion, 90.0 and 90.0% Pb, 80.0% and 75.0% for Zn ion after 24 and 28 hrs with mixed free cells and mixed immobilized cells, respectively. The results indicated that 13.86 and 17.43% of removal efficiency and reduction of total dissolved solids were achieved after 24 and 28 hrs with mixed free cells and mixed immobilized cells, respectively.

Keywords: Biological desalination, bio-sorption heavy metals, free cell bacteria, immobilized bacteria, wastewater bio-treatment.

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Authors: Ivanova B. Natalia, Djambova Т. Svetlana, Hristev S. Ivailo

Abstract:

The acoustic properties of recycled felt panels have been investigated using various methods. Experimentally, the sound insulation of the panels has been evaluated for frequencies in the range of 600 Hz to 4000 Hz, utilizing a small-sized acoustic chamber. Additionally, the sound absorption coefficient for the frequency range of 63 Hz to 4000 Hz was measured according to the EN ISO 354 standard in a laboratory reverberation room. This research was deemed necessary after conducting reverberation time measurements of a university classroom following the EN ISO 3382-2 standard. The measurements indicated values of 2.86 s at 500 Hz, 3.23 s at 1000 Hz, and 2.53 s at 2000 Hz, which significantly exceeded the requirements set by the national regulatory framework (0.6 s) for such premises. For this reason, recycled felt panels have been investigated in the laboratory, showing very good acoustic properties at high frequencies. To enhance performance in the low frequencies, the influence of the distance of the panel spacing was examined. Furthermore, the sound insulation of the panels was studied to expand the possibilities of their application, both for the acoustic treatment of educational and multifunctional halls and for sound insulation purposes (e.g., a suspended ceiling with an air gap passing from room to room). As a conclusion, a theoretical acoustic design of the classroom has been carried out with suggestions for improvements to achieve the necessary acoustic and aesthetic parameters for such rooms.

Keywords: Acoustic panels, recycled felt, sound absorption, sound insulation, classroom acoustics.

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Authors: Indunil Jayatilake, Warna Karunasena, Weena Lokuge

Abstract:

An Australian manufacturer has fabricated an innovative GFRP sandwich panel made from E-glass fiber skin and a modified phenolic core for structural applications. Debonding, which refers to separation of skin from the core material in composite sandwiches, is one of the most common types of damage in composites. The presence of debonding is of great concern because it not only severely affects the stiffness but also modifies the dynamic behaviour of the structure. Generally it is seen that the majority of research carried out has been concerned about the delamination of laminated structures whereas skin-core debonding has received relatively minor attention. Furthermore it is observed that research done on composite slabs having multiple skin-core debonding is very limited. To address this gap, a comprehensive research investigating dynamic behaviour of composite panels with single and multiple debonding is presented. The study uses finite-element modelling and analyses for investigating the influence of debonding on free vibration behaviour of single and multilayer composite sandwich panels. A broad parametric investigation has been carried out by varying debonding locations, debonding sizes and support conditions of the panels in view of both single and multiple debonding. Numerical models were developed with Strand7 finite element package by innovatively selecting the suitable elements to diligently represent their actual behavior. Three-dimensional finite element models were employed to simulate the physically real situation as close as possible, with the use of an experimentally and numerically validated finite element model. Comparative results and conclusions based on the analyses are presented. For similar extents and locations of debonding, the effect of debonding on natural frequencies appears greatly dependent on the end conditions of the panel, giving greater decrease in natural frequency when the panels are more restrained. Some modes are more sensitive to debonding and this sensitivity seems to be related to their vibration mode shapes. The fundamental mode seems generally the least sensitive mode to debonding with respect to the variation in free vibration characteristics. The results indicate the effectiveness of the developed three dimensional finite element models in assessing debonding damage in composite sandwich panels.

Keywords: Debonding, free vibration behaviour, GFRP sandwich panels, three dimensional finite element modelling.

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Authors: Z. Altawallbeh

Abstract:

In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

Keywords: Exterior algebra, free resolution, free and projective modules, Hochschild homology, homotopic function, symmetric algebra.

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