Search results for: consistent and concentrated mass matrices

Authors: Alfredo Reyes-Salazar, Mario D. Llanes-Tizoc, Eden Bojorquez, Federico Valenzuela-Beltran, Juan Bojorquez, Jose R. Gaxiola-Camacho, Achintya Haldar

Abstract:

Seismic analysis of steel buildings is usually based on the use of the concentrated mass (ML) matrix and the Rayleigh damping matrix (C). Similarly, the initial stiffness matrix (KO) and the first two modes associated with lateral vibrations are commonly used to develop matrix C. The evaluation of the accuracy of these practices for the particular case of steel buildings with moment-resisting steel frames constitutes the main objective of this research. For this, the non-linear seismic responses of three models of steel frames, representing low-, medium- and high-rise steel buildings, are considered. Results indicate that if the ML matrix is used, shears and bending moments in columns are underestimated by up to 30% and 65%, respectively when compared to the corresponding results obtained with the consistent mass matrix (MC). It is also shown that if KO is used in C instead of the tangent stiffness matrix (Kt), axial loads in columns are underestimated by up to 80%. It is concluded that the consistent mass matrix should be used in the structural modelling of moment-resisting steel frames and that the tangent stiffness matrix should be used to develop the Rayleigh damping matrix.

Keywords: moment-resisting steel frames, consistent and concentrated mass matrices, non-linear seismic response, Rayleigh damping

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Authors: Aref Aasi, Sadegh Mehdi Aghaei, Balaji Panchapakesan

Abstract:

This work aims to evaluate the free and forced vibration of a beam with two end joints subjected to a concentrated moving mass and a load using the Euler-Bernoulli method. The natural frequency is calculated for different locations of the concentrated mass and load on the beam. The analytical results are verified by the experimental data. The variations of natural frequency as a function of the location of the mass, the effect of the forced frequency on the vibrational amplitude, and the displacement amplitude versus time are investigated. It is discovered that as the concentrated mass moves toward the center of the beam, the natural frequency of the beam and the relative error between experimental and analytical data decreases. There is a close resemblance between analytical data and experimental observations.

Keywords: Euler-Bernoulli beam, natural frequency, forced vibration, experimental setup

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Authors: Houari Boumediene University of Science, Technology.

Abstract:

"Various methods are typically used in the dynamic analysis of transversely vibrating beams. To achieve this, numerical methods are used to solve the general eigenvalue problem. The equations of equilibrium, which describe the motion, are derived from a fourth-order differential equation. Our study is based on the finite element method, and the results of the investigation are the vibration frequencies obtained using the Jacobi method. Two types of elementary mass matrices are considered: one representing a uniform distribution of mass along the element and the other consisting of concentrated masses located at fixed points whose number increases progressively with equal distances at each evaluation stage. The beams studied have different boundary constraints, representing several classical situations. Comparisons are made for beams where the distributed mass is replaced by n concentrated masses. As expected, the first calculation stage involves determining the lowest number of beam parts that gives a frequency comparable to that obtained from the Rayleigh formula. The obtained values are then compared to theoretical results based on the assumptions of the Bernoulli-Euler theory. These steps are repeated for the second type of mass representation in the same manner."

Keywords: finite element method, bernouilli eulertheory, structural analysis, vibration analysis, rayleigh quotient

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Authors: Brando Vagenende, Marie-Anne Guerry

Abstract:

For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: Manideepa Saha, Jahnavi Chakrabarty

Abstract:

Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.

Keywords: convergence, Gauss-Seidel, iterative method, Jacobi, SOR

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

Abstract:

A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An in-compressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping

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Authors: Qinyi Mei, Li-Ping Wang

Abstract:

MDS matrices are of great significance in the design of block ciphers and hash functions. In the present paper, we investigate the problem of constructing MDS matrices which are both lightweight and low-latency. We propose a new method of constructing lightweight MDS matrices using circulant matrices which can be implemented efficiently in hardware. Furthermore, we provide circulant MDS matrices with as few bit XOR operations as possible for the classical dimensions 4 × 4, 8 × 8 over the space of linear transformations over finite field F42 . In contrast to previous constructions of MDS matrices, our constructions have achieved fewer XORs.

Keywords: linear diffusion layer, circulant matrix, lightweight, maximum distance separable (MDS) matrix

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Authors: A. M. Metak, T. T. Ajaal, Amal Metak, Tawfik Ajaal

Abstract:

Commercial nanocomposite food packaging type nano-silver containers were characterised using scanning electron microscopy (SEM) and energy-dispersive X-Ray spectroscopy (EDX). The presence of nanoparticles consistent with the incorporation of 1% nano-silver (Ag) and 0.1% titanium dioxide (TiO2) nanoparticle into polymeric materials formed into food containers was confirmed. Both nanomaterials used in this type of packaging appear to be embedded in a layered configuration within the bulk polymer. The dimensions of the incorporated nanoparticles were investigated using X-Ray diffraction (XRD) and determined by calculation using the Scherrer Formula; these were consistent with Ag and TiO2 nanoparticles in the size range 20-70nm both were spherical shape nanoparticles. Antimicrobial assessment of the nanocomposite container has also been performed and the results confirm the antimicrobial activity of Ag and TiO2 nanoparticles in food packaging containers. Migration assessments were performed in a wide range of food matrices to determine the migration of nanoparticles from the packages. The analysis was based on the relevant European safety directives and involved the application of inductively coupled plasma mass spectrometry (ICP-MS) to identify the range of migration risk. The data pertain to insignificance levels of migration of Ag and TiO2 nanoparticles into the selected food matrices.

Keywords: nano-silver, antimicrobial food packaging, migration, titanium dioxide

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Authors: Jaroslav Krutil, Simona Fialová, , František Pochylý

Abstract:

A nonlinear mathematical model of mutual fluid-structure interaction is presented in the work. The model is applicable to the general shape of sealing gaps. An in compressible fluid and turbulent flow is assumed. The shaft carries a rotational and procession motion, the gap is axially flowed through. The achieved results of the additional mass, damping and stiffness matrices may be used in the solution of the rotor dynamics. The usage of this mathematical model is expected particularly in hydraulic machines. The method of control volumes in the ANSYS Fluent was used for the simulation. The obtained results of the pressure and velocity fields are used in the mathematical model of additional effects.

Keywords: nonlinear mathematical model, CFD modeling, hydrodynamic sealing gap, matrices of mass, stiffness, damping

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Authors: Ric Joseph R. Murillo, Edna N. Gueco, Dennis I. Merino

Abstract:

Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined

Keywords: α-involutory Matrices, sum of α-involutory Matrices, Trace, Matrix Theory

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Authors: Divyesh Patel, Tanuja Srivastava

Abstract:

This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: discrete tomography, exactly-1-4-adjacency, simulated annealing, binary matrices

Procedia PDF Downloads 371

Authors: Falek Kamel

Abstract:

Various approaches are usually used in the dynamic analysis of beams vibrating transversally. For this, numerical methods allowing the solving of the general eigenvalue problem are utilized. The equilibrium equations describe the movement resulting from the solution of a fourth-order differential equation. Our investigation is based on the finite element method. The findings of these investigations are the vibration frequencies obtained by the Jacobi method. Two types of the elementary mass matrix are considered, representing a uniform distribution of the mass along with the element and concentrated ones located at fixed points whose number is increased progressively separated by equal distances at each evaluation stage. The studied beams have different boundary constraints representing several classical situations. Comparisons are made for beams where the distributed mass is replaced by n concentrated masses. As expected, the first calculus stage is to obtain the lowest number of beam parts that gives a frequency comparable to that issued from the Rayleigh formula. The obtained values are then compared to theoretical results based on the assumptions of the Bernoulli-Euler theory. These steps are used for the second type of mass representation in the same manner.

Keywords: structural elements, beams vibrating, dynamic analysis, finite element method, Jacobi method

Procedia PDF Downloads 135

Authors: K. Meera Saheb, K. Krishna Bhaskar

Abstract:

Complex structures used in many fields of engineering are made up of simple structural elements like beams, plates etc. These structural elements, sometimes carry concentrated masses at discrete points, and when subjected to severe dynamic environment tend to vibrate with large amplitudes. The frequency amplitude relationship is very much essential in determining the response of these structural elements subjected to the dynamic loads. For Timoshenko beams, the effects of shear deformation and rotary inertia are to be considered to evaluate the fundamental linear and nonlinear frequencies. A commonly used method for solving vibration problem is energy method, or a finite element analogue of the same. In the present Coupled Displacement Field method the number of undetermined coefficients is reduced to half when compared to the famous Rayleigh Ritz method, which significantly simplifies the procedure to solve the vibration problem. This is accomplished by using a coupling equation derived from the static equilibrium of the shear flexible structural element. The prime objective of the present paper here is to study, in detail, the effect of a central concentrated mass on the large amplitude free vibrations of uniform shear flexible beams. Accurate closed form expressions for linear frequency parameter for uniform shear flexible beams with a central concentrated mass was developed and the results are presented in digital form.

Keywords: coupled displacement field, coupling equation, large amplitude vibrations, moderately thick plates

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Authors: Ivan Baravy

Abstract:

Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Dariusz Jacek Jakóbczak

Abstract:

Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: K. M. Aldossari, W. A. Elsaigh, M. J. Shannag

Abstract:

An experimental study was conducted to investigate the effect of hooked-end steel fibers on the flexural behavior of normal and high strength concrete matrices. The fiber content appropriate for the concrete matrices investigated was also determined based on flexural tests on standard prisms. Parameters investigated include: Matrix compressive strength ranging from 45 MPa to 70 MPa, corresponding to normal and high strength concrete matrices respectively; Fiber volume fraction including 0, 0.5%, 0.76%, and 1%, equivalent to 0, 40, 60, and 80 kg/m3 of hooked-end steel fibers respectively. Test results indicated that flexural strength and toughness of normal and high strength concrete matrices were significantly improved with the increase in the fiber content added; Whereas a slight improvement in compressive strength was observed for the same matrices. Furthermore, the test results indicated that the effect of increasing the fiber content was more pronounced on increasing the flexural strength of high strength concrete than that of normal concrete.

Keywords: concrete, flexural strength, toughness, steel fibers

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Authors: Mohammad Saleem, Mujahid Kamran

Abstract:

It is shown that causality, the principle that cause must precede effect, leads inter alia, to highly significant result that the velocity of a material particle cannot be even equal to that of light. Consequently, combined with special relativity, it leads to the conclusion that material particles of zero rest mass cannot exist in nature. Thus, causality, a principle without which nature would be incomprehensible, combined with special relativity, forbids the existence of material particles of zero rest mass. For instance, the neutrinos, as is now known, are material particles of non-zero rest mass. The situation changes when we consider the gauge particles. In fact, when the principle of causality was proposed, the concept of gauge particles had not yet been introduced. Now we know that photon, a gauge particle with zero rest mass does exist in nature. Therefore, principle of causality, as generally stated, is valid only for material particles. For gauge particles, in order to make the statement of causality consistent with experiment, it has to be modified: The cause should either precede or be simultaneous with the effect. Combined with special relativity, it allows gauge particles of zero rest mass.

Keywords: causality, gauge particles, material particles, special relativity

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Authors: Haiyang Su, Kun Qian

Abstract:

We developed a novel plasmonic matrix assisted laser desorption/ionization mass spectrometry (MALDI MS) approach to detect small nutrients and toxin in complex biological emulsion samples. We used silver nanoshells (SiO₂@Ag) with optimized structures as matrices and achieved direct analysis of ~6 nL of human breast milk without any enrichment or separation. We performed identification and quantitation of small nutrients and toxins with limit-of-detection down to 0.4 pmol (for melamine) and reaction time shortened to minutes, superior to the conventional biochemical methods currently in use. Our approach contributed to the near-future application of MALDI MS in a broad field and personalized design of plasmonic materials for real case bio-analysis.

Keywords: plasmonic materials, laser desorption/ionization, mass spectrometry, small nutrients, toxins

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Authors: Emine Tuğba Akyüz

Abstract:

In this study, the analysis of Hadamard matrices, which is a special type of matrix, was made under three headings: norms, singular values, condition number. Six norm types was applied to Hadamard matrices and the relationship between the results and the size of the matrix has been studied. As a result of the investigation when 2-norm was used on the problem Hx =f, the equation ‖x‖_2= ‖f‖_2/√n was shown (H is n-dimensional Hadamard matrix). Related with this, the relationship between the the singular value of H and 2-norm and eigenvalues was shown. Then, the evaluation of condition number for Hx =f was made.

Keywords: condition number, Hadamard matrix, norm, singular value

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Authors: E. V. Kuzmicheva

Abstract:

An attention is concentrated on a service quality estimation of sport services. A typical mathematical model was developed at the base of the «general economic theory of mass service» accounting pedagogical requirements of fitness services. Also it took into account a dependence of the club member number versus on a value of square of sport facilities. Final recommendations were applied to the fitness club resulted in some improvement of the quality sport service, an increasing of the revenue from club members and profit of clubs.

Keywords: fitness club, efficiency of operation, facilities, service quality, mass service

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Authors: Malika Yaici, Kamel Hariche

Abstract:

In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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Authors: Gulgassyl Nugmanova, Zhanat Zhunussova, Kuralay Yesmakhanova, Galya Mamyrbekova, Ratbay Myrzakulov

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In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields.

Keywords: Heisenberg Ferromagnet equations, soliton equations, equivalence, Lax representation

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Authors: Moses C. Siame, Kazutoshi Haga, Atsushi Shibayama

Abstract:

This study investigates the removal of silica, alumina and phosphorus as impurities from Sanje iron ore using wet high-intensity magnetic separation (WHIMS). Sanje iron ore contains low-grade hematite ore found in Nampundwe area of Zambia from which iron is to be used as the feed in the steelmaking process. The chemical composition analysis using X-ray Florence spectrometer showed that Sanje low-grade ore contains 48.90 mass% of hematite (Fe₂O₃) with 34.18 mass% as an iron grade. The ore also contains silica (SiO₂) and alumina (Al₂O₃) of 31.10 mass% and 7.65 mass% respectively. The mineralogical analysis using X-ray diffraction spectrometer showed hematite and silica as the major mineral components of the ore while magnetite and alumina exist as minor mineral components. Mineral particle distribution analysis was done using scanning electron microscope with an X-ray energy dispersion spectrometry (SEM-EDS) and images showed that the average mineral size distribution of alumina-silicate gangue particles is in order of 100 μm and exists as iron-bearing interlocked particles. Magnetic separation was done using series L model 4 Magnetic Separator. The effect of various magnetic separation parameters such as magnetic flux density, particle size, and pulp density of the feed was studied during magnetic separation experiments. The ore with average particle size of 25 µm and pulp density of 2.5% was concentrated using pulp flow of 7 L/min. The results showed that 10 T was optimal magnetic flux density which enhanced the recovery of 93.08% of iron with 53.22 mass% grade. The gangue mineral particles containing 12 mass% silica and 3.94 mass% alumna remained in the concentrate, therefore the concentrate was further treated in the second stage WHIMS using the same parameters from the first stage. The second stage process recovered 83.41% of iron with 67.07 mass% grade. Silica was reduced to 2.14 mass% and alumina to 1.30 mass%. Accordingly, phosphorus was also reduced to 0.02 mass%. Therefore, the two stage magnetic separation process was established using these results.

Keywords: Sanje iron ore, magnetic separation, silica, alumina, recovery

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Authors: Celina Pestano-Gabino, Concepcion Gonzalez-Concepcion, M. Candelaria Gil-Fariña

Abstract:

Some estimation methods for VARMA models, and Multivariate Time Series Models in general, rely on the use of a Hankel matrix. It is known that if the data sample is populous enough and the dimension of the Hankel matrix is unnecessarily large, this may result in an unnecessary number of computations as well as in numerical problems. In this sense, the aim of this paper is two-fold. First, we provide some theoretical results for these matrices which translate into a lower dimension for the matrices normally used in the algorithms. This contribution thus serves to improve those methods from a numerical and, presumably, statistical point of view. Second, we have chosen an estimation algorithm to illustrate in practice our improvements. The results we obtained in a simulation of VARMA models show that an increase in the size of the Hankel matrix beyond the theoretical bound proposed as valid does not necessarily lead to improved practical results. Therefore, for future research, we propose conducting similar studies using any of the linear system estimation methods that depend on Hankel matrices.

Keywords: covariances Hankel matrices, Kronecker indices, system identification, VARMA models

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Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

Abstract:

In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied. The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length. To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed. Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition. The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work. The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: buckling, finite strip, different sides support, plates on foundation

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Authors: Khosrow Maleknejad, Yaser Rostami

Abstract:

In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Fang Bo Yu, Li Bo Guan

Abstract:

Biogas slurry is a low-cost source of crop nutrients and can offer extra benefits to soil fertility and fruit quality. However, its current utilization mode and low content of active ingredients limit its application scale. In this report, one growing season field research was conducted to assess the effects of concentrated biogas slurry on soil property, tomato fruit quality, and composition of the microflora in both non-rhizosphere and rhizosphere soils. The results showed that application of concentrated slurry could cause significant changes to tomato cultivation, including increases in organic matter, available N, P, and K, total N, and P, electrical conductivity, and fruit contents of amino acids, protein, soluble sugar, β-carotene, tannins, and vitamin C, together with the R/S ratios and the culturable counts of bacteria, actinomycetes, and fungi in soils. It could be concluded as the application is a practicable means in tomato production and might better service the sustainable agriculture in the near future.

Keywords: concentrated slurry, fruit quality, soil fertility, sustainable agriculture

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Authors: Somya R. Patro, Arnab Banerjee, G. V. Ramana

Abstract:

A flexural beam carrying elastically mounted concentrated masses, such as engines, motors, oscillators, or vibration absorbers, is often encountered in mechanical, civil, and aeronautical engineering domains. To prevent resonance conditions, the designers must predict the natural frequencies of such a constrained beam system. This paper investigates experimental and analytical studies on vibration suppression in a cantilever beam with a tip mass with the help of spring-mass to achieve local resonance conditions. The system consists of a 3D printed polylactic acid (PLA) beam screwed at the base plate of the shaker system. The top of the free end is connected by an accelerometer which also acts as a tip mass. A spring and a mass are attached at the bottom to replicate the mechanism of the spring-mass resonator. The Fast Fourier Transform (FFT) algorithm converts time acceleration plots into frequency amplitude plots from which transmittance is calculated as a function of the excitation frequency. The mathematical formulation is based on the transfer matrix method, and the governing differential equations are based on Euler Bernoulli's beam theory. The experimental results are successfully validated with the analytical results, providing us essential confidence in our proposed methodology. The beam spring-mass system is then converted to an equivalent two-degree of freedom system, from which frequency response function is obtained. The H2 optimization technique is also used to obtain the closed-form expression of optimum spring stiffness, which shows the influence of spring stiffness on the system's natural frequency and vibration response.

Keywords: euler bernoulli beam theory, fast fourier transform, natural frequencies, polylactic acid, transmittance, vibration absorbers

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Authors: Vedat Senol, Gursoy Turan, Anders Helmersson, Vortechz Andersson

Abstract:

In developing a mathematical model of a real structure, the simulation results of the model may not match the real structural response. This is a general problem that arises during dynamic motion of the structure, which may be modeled by means of parameter variations in the stiffness, damping, and mass matrices. These changes in parameters need to be estimated, and the mathematical model is updated to obtain higher control performances and robustness. In this study, a linear fractional transformation (LFT) is utilized for uncertainty modeling. Further, a general approach to the design of an H∞ control of a magneto-rheological damper (MRD) for vibration reduction in a building with mass, damping, and stiffness uncertainties is presented.

Keywords: uncertainty modeling, structural control, MR Damper, H∞, robust control

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Authors: William Middleton, Nodumo Zulu, Sue Harrison

Abstract:

Open raceway ponds are currently the most used system for the commercial cultivation of algal biomass, as it is a cost-effective means of production. However, raceway ponds suffer from lower algal productivity when compared to closed photobioreactors. This is due to poor gas exchange between the fluid and the atmosphere. Carbon dioxide (CO₂) mass transfer is a large concern in the production of algae in raceway pond systems. The utilization of atmospheric CO₂ does not support maximal growth; however, CO₂ supplementation in the form of flue gas or concentrated CO₂ is not cost-effective. The introduction of slopes into the raceway system presents a possible improvement to the mass transfer from the air, as seen in previous work conducted at CeBER. Slopes improve turbulence (decreasing the concentration gradient of dissolved CO₂) and can cause air entrainment (allowing for greater surface area and contact time between the air and water). This project tests the findings of previous studies conducted in an indoor lab-scale raceway on a larger scale under outdoor conditions. The addition of slopes resulted in slightly increased CO₂ mass transfer as well as algal growth rate and productivity. However, there were reductions in energy consumption and average fluid velocity in the system. These results indicate a potential to improve the economic feasibility of algal biomass production, but further economic assessment would need to be carried out.

Keywords: algae, raceway ponds, mass transfer, algal culture, biotechnology, reactor design

Procedia PDF Downloads 51