Archive

Abstract:

The transportation problems (TPs) are a fundamental case-study topic in operations research, particularly in the field of linear programming (LP). The TPs are solved in full resolution by using two types of methods: initial basic feasible solution (IBFS) and optimal methods. In this paper, we suggest a novel IBFS method for enhanced reduction in the transportation cost associated with the TPs. The new method searches for the range in columns of the transportation table only, and selects the maximum range to carry out allocations, and is therefore referred to as the maximum range column method (MRCM). The performance of the proposed MRCM has been compared against three traditional methods: North-West-Corner (NWCM), Least cost (LCM) and Vogel’s approximation (VAM) on a comprehensive database of 140 transportation problems from the literature. The optimal solutions of the 140 problems obtained by using the TORA software with the modified distribution (MODI) method have been taken as reference from a previous benchmark study. The IBFSs obtained by the proposed method against NWCM, LCM and VAM are mostly optimal, and in some cases closer to the optimal solutions as compared to the other methods. Exhaustive performance has been discussed based on absolute and relative error distributions, and percentage optimality and nonoptimality for the benchmark problems. It is demonstrated that the proposed MRCM is a far better IBFS method for efficiently solving the TPs as compared to the other discussed methods, and can be promoted in place of the traditional methods based on its performance.

Keywords:

Transportation problem,optimal solution,MODI method,TORA software,Minimum cost,Initial basic feasible solution,Maximum range,

Refference:

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XI. Kalhoro H. B., Abdulrehman H., Shaikh, M. M., Soomro, A. S. (2020). A pioneering and comprehensive database of balanced and unbalanced transportation problems for ready performance evaluation of existing and new methods. J. Mech. Cont.& Math. Sci., Vol. 15, No.11, pp. 149-159.
XII. Korukoğlu, Serdar, and Serkan Ballı. “A Improved Vogel’s Approximation Method for the Transportation Problem.” Mathematical and Computational Applications 16.2 (2011): 370-381.
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XXVII. Winston, Wayne L. “Transportation, Assignment, and Transshipment Problems.” Operations Research Applications and Algorithms, Duxbury Press, California (1994): 338.
XXVIII. Yousaf, M., Shaikh M. M., & Shaikh A. W. (2020). Some Efficient Mathematical Programming Techniques for Balancing Equations of Complex Chemical Reactions., : J. Mech. Cont. & Math. Sci.,Vol. 15, No.10, pp. 53-66.

STRUM-LIOUVILLE FORM AND OTHER IMPORTANT PROPERTIES OF MODIFIED ORTHOGONAL BOUBAKER POLYNOMIALS

Authors:

Nazeer Ahmed Khoso, Muhammad Mujtaba Shaikh, Abdul Wasim Shaikh

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00007

Abstract:

In this paper, some classical properties of modified orthogonal Boubaker polynomials (MOBPs) are considered, which are: the three-term recurrence relation, Rodriguez formula, characteristic differential equation and the Strum-Liouville form. The only properties of the MOBPs known so far are orthogonality evidence, weight function, orthonormality evidence and zeros. The new properties established in this work will to the applicability of the MOBPs in different areas of science and engineering where the classical non-orthogonal Boubaker polynomials could be applied, and even in cases where these cannot be applied.

Keywords:

Recurrence relation, Rodriguez’s formula, Orthogonality, Strum-Liouville form.,Rodriguez’s formula,Orthogonality,Strum-Liouville form,

Refference:

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ENHANCING STRUCTURAL RESPONSE USING INERTER DAMPERS

Authors:

Shahad Nazar Jabbar, Waleed K. Al-Ashtari

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00008

Abstract:

This paper deals with one kind of dampers which is inerter damper, Inerter is a new mechanical element proposed by Professor Malcolm C. Smith from Cambridge University, which is defined as a mechanical two-terminal, one-port device with the property that the equal and opposite force applied at the terminals is proportional to the relative acceleration between the terminals the principle work of inerter damper is how to convert the linear motion into rotational motion to mitigation the external excitation. Theoretical analysis was presented first part is the analytical study which made modeling for the damping structure proposed and get the equation of motion for the inerter behavior, secondly numerical analysis where the program (ANSYS WORK-Bench 18.2) was adopted, and study the parameters which effected on the damping behavior of inerter structure proposed that is (stiffness, coefficient of friction and mass of flywheel). Where it was found that when the stiffness of the springs increased gradually from (0.2, 0.3, 0.4, 0.6 and 0.8) Kn/mm the amplitude reduced from (25.791, 17.194, 12.896, 8.5974 to 6.4482) mm respectively for each stiffness reading, also the mass of inerter when increased gradually (200,400,600,800 and 1000) g with a constant coefficient of friction and constant stiffness 0.4, 0.6 Kn/mm respectively, the amplitude decrease from 6.3525 to 4.036290. Finally, to study the effect inerter mass on the structures, the mass of inerter increased from (200,400,600,800 to 1000) g gradually to the constant cantilever mass structure equal to 130g. The ratio of the inerter mass to the threshold mass is approximately 1.5 to 7.5 As results obtained from the previous study, the amplitude obtained for each mass (1.0778, 1.069, 1.0509, 0.9514 to 0.872) respectively

Keywords:

Inerter damper,enhancing response,ball-screw inerter,

Refference:

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Ichchou, Design of semi-active dry friction dampers for steady-state vibration: sensitivity analysis and experimental studies School of Energy and Power Engineering, Beihang University, Beijing, 100191, China

EXPERIMENTAL INVESTIGATION OF MECHANICAL PROPERTIES OF SOLID CONCRETE BLOCK MASONRY EMPLOYING DIFFERENT MORTAR RATIOS

Authors:

Muhammad Rizwan, Hanif Ullah, Ezaz Ali Khan, Nayab Khan, Talha Rasheed

DOI NO:

https://doi.org/10.26782/jmcms.2021.01.00009

Abstract:

This research work aims to investigate experimentally the mechanical properties of solid concrete blocks as an individual unit and assembly (block masonry) employing different mortar mix ratios. The material properties of the concrete block unit, such as compressive strength and unit weight were explored by taking three samples from the four local factories. The block masonry assemblages were subjected to various load patterns for the evaluation of compressive strength, diagonal tensile strength and shear strength. For the bond, four types of mortars i.e., cement - sand (1:4), cement - sand (1:8), cement – sand - khaka (1:2:2) and cement - sand - khaka (1:4:4) were used in the joints of concrete block masonry assemblages. (Khaka is a by-product formed in the stone crushing process). For each type of mortar, three samples of block masonry were fabricated for compressive strength, shear strength and diagonal tensile strength, and tested in the laboratory. It is observed that the replacement of sand by khaka enhanced the mechanical properties of masonry.

Keywords:

block masonry,mortar,khaka,compressive strength,diagonal tensile strength,shear strength,

Refference:

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XII. G. Mohamad, F. S. Fonseca, A. T. Vermeltfoort, D. R. Martens, and P. B. Lourenço, “Strength, behavior, and failure mode of hollow concrete masonry constructed with mortars of different strengths,” Construction and Building Materials, vol. 134, pp. 489-496, 2017.
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MODIFIED SIRD MODEL OF EPIDEMIC DISEASE DYNAMICS: A CASE STUDY OF THE COVID-19 CORONAVIRUS

Authors:

Asish Mitra

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00001

Abstract:

The present study shows that a simple epidemiological model can reproduce the real data accurately. It demonstrates indisputably that the dynamics of the COVID-19 outbreak can be explained by the modified version of the compartmental epidemiological framework Susceptible-Infected-Recovered-Dead (SIRD) model. The parameters of this model can be standardized using prior knowledge. However, out of several time-series data available on several websites, only the number of dead individuals (D(t)) can be regarded as a more reliable representation of the course of the epidemic. Therefore it is wise to convert all the equations of the SIRD Model into a single one in terms of D(t). This modified SIRD model is now able to give reliable forecasts and conveys relevant information compared to more complex models.

Keywords:

COVID-19,Epidemic Disease,Modified SIRD Model,Parameter Estimation,

Refference:

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EXPERIMENTAL STUDY OF SPACE HEATING BY AIR HEATER SOLAR WITH PHASE CHANGE THERMAL STORAGE

Authors:

Duaa Saad Saleh, Najim Abid Jassim

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00002

Abstract:

In the current research, studied experimentally of a solar air collector was conducted using latent thermal storage (wax of paraffin), in which energy of solar is collected during the time day, and released after sunset. Experimental studies were conducted under the Climate of Iraq - Baghdad (longitude 44.4 degrees east and latitude 33.34 degrees north). At various rates of mass flow air 0.027 kg / s, 0.03255 kg / s, and 0.038 kg / s in winter 2020 and on clear days, measurements and experimental work were conducted. The experimental findings indicated that the speed of paraffin wax melting is reversely proportional to the rate of mass flow of air. In m=0.038kg/s, the maximum heat gain value occurs. An increase in the rate of air mass flow decreases heat storage time.

Keywords:

Air heater solar,Thermal storage,paraffin wax,Space heating,Phase Change Material (PCM).,

Refference:

I. A. E. Kabeel, A. Khalil, S. M. Shalaby, and M. E. Zayed, “Experimental investigation of thermal performance of flat and v-corrugated plate solar air heaters with and without PCM as thermal energy storage,” Energy Convers. Manag., vol. 113, pp. 264–272, 2016.

II. A. S. Mahmood, “Experimental Study on Double-Pass Solar Air Heater with and without using Phase Change Material,” J. Eng., vol. 25, no. 2, pp. 1–17, 2019.

III. Alaa A.Ghulam, Ihsan Y. Hussain, : PERFORMANCE ENHANCEMENTS OF PHASE CHANGE MATERIAL (PCM) CASCADE THERMAL ENERGY STORAGE SYSTEM BY USING METAL FOAM, J. Mech. Cont. & Math. Sci., Vol.-15, No.-5, May (2020) pp 159-173.

IV. Firas Ahmed Khalil, Najim Abed Jassim, : THERMAL PERFORMANCE OF A SOLAR-ASSISTED HEAT PUMP WITH A DOUBLE PASS SOLAR AIR COLLECTOR UNDER CLIMATE CONDITIONS OF IRAQ, J. Mech. Cont.& Math. Sci., Vol.-14, No.-6 November-December (2019) pp 426-449.
V. J. A. Duffie, W. A. Beckman, and N. Blair, Solar engineering of thermal processes, photovoltaics and wind. John Wiley & Sons, 2020.

VI. K. Bin Sopian, M. Sohif, and M. Alghoul, “Output air temperature prediction in a solar air heater integrated with phase change material,” Eur. J. Sci. Res., vol. 27, no. 3, pp. 334–341, 2009.

VII. K. I. Abaas, “The Effect of Using a Paraffin Wax-Aluminum Chip Compound As Thermal Storage Materials in a Solar Air Heater,” Al-Rafidain Univ. Coll. Sci., no. 34, pp. 259–284, 2014.

VIII. M. Sajawal, T. Rehman, H. M. Ali, U. Sajjad, A. Raza, and M. S. Bhatti, “Experimental thermal performance analysis of finned tube-phase change material based double pass solar air heater,” Case Stud. Therm. Eng., vol. 15, p. 100543, 2019.

IX. O. Ojike and W. I. Okonkwo, “Study of a passive solar air heater using palm oil and paraffin as storage media,” Case Stud. Therm. Eng., vol. 14, p. 100454, 2019.

X. P. Charvat, L. Klimes, and O. Pech, “Experimental and numerical study into solar air collectors with integrated latent heat thermal storage,” Cent. Eur. Towar. Sustain. Build. Low-tech high-tech Mater. Technol. Sustain. Build., pp. 1–4, 2013.

XI. S. Bouadila, S. Kooli, M. Lazaar, S. Skouri, and A. Farhat, “Performance of a new solar air heater with packed-bed latent storage energy for nocturnal use,” Appl. Energy, vol. 110, pp. 267–275, 2013.

XII. S. M. Salih, J. M. Jalil, and S. E. Najim, “Experimental and numerical analysis of double-pass solar air heater utilizing multiple capsules PCM,” Renew. Energy, vol. 143, pp. 1053–1066, 2019.

TWO-DIMENSIONAL HYDRODYNAMIC EROSION MODEL APPLIED TO SPUR DYKES

Authors:

Fayaz A. Khan, Humna Hamid, Yasir I. Badrashi

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00003

Abstract:

With the advances in the field of computing, robust CFD models have evolved in the last two decades. Initially, one and two-dimensional models were used but these days, three-dimensional models are used frequently that produce more accurate results. However, the solution of 3D models is expensive not only in terms of computational costs but is time-consuming. In this work, a two-dimensional CFD model that is based on shallow water equations coupled with an erosion model is presented. The equations are solved using finite volume formulation and high-resolution shock capturing methods. This study is an attempt to cover accuracy issues with 2D models by incorporating high-resolution shock capturing methods as compared to 3D models, the solution of which is based on conventional schemes. The model is initially used to simulate dam-break problems over fixed and mobile beds to assess the model stability and hydraulic performance in terms of simulating the flow and bed morphology. The assessment has shown the model to be stable throughout the simulation and the produced results have shown the hydro-dynamic capability of the model. The model is then applied to simulate flow over an erodible sediment bed in a channel with spur dykes on its flood plain. The simulated results are compared with experimental results and numerical results of a 3D model. The comparison has shown a close agreement both with experimental and numerical 3D model results that show that the model could be applied to study bed morphology confidently.

Keywords:

CFD,High Resolution,Shock Capturing,Mobile Beds,

Refference:

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VIII. F. Bahmanpouri, M. Daliri, A. Khoshkonesh, M. Montazeri Namin, and M. Buccino, “Bed compaction effect on dam break flow over erodible bed; experimental and numerical modeling,” J. Hydrol., 2020.
IX. G. Kesserwani, A. Shamkhalchian, and M. J. Zadeh, “Fully Coupled Discontinuous Galerkin Modeling of Dam-Break Flows over Movable Bed with Sediment Transport,” J. Hydraul. Eng., vol. 140, no. 4, 2014.
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AN ANALYTICAL APPROACH FOR SOLVING THE NONLINEAR JERK OSCILLATOR CONTAINING VELOCITY TIMES ACCELERATION-SQUARED BY AN EXTENDED ITERATION METHOD

Authors:

B. M. Ikramul Haque, Md. Iqbal Hossain

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00004

Abstract:

The technique to evade jerk from a dynamical system is to reduce the rate of acceleration or deceleration. It is an important issue for our real life. In motion control systems the term “jerk” is the main topic. The jerk equation containing velocity times acceleration-squared describes the characteristics of chaotic behaviour in many nonlinear phenomena, cosmological analysis, kinematical physics, pendulum analysis etc. Thus, the mentioned equation is important in its own right. An extended iteration method, based on Haque’s approach has been applied to find the analytical solution of the oscillator. The recently various method has been developed for finding analytical solutions of the nonlinear equation but; modified extended iteration method based on Haque’s approach is faster and straight forward than others.

Keywords:

Jerk equation,Nonlinear oscillator,Extended iteration technique,Truncated Fourier series,

Refference:

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XIV. Haque, B.M.I., Selim Reza A.K.M. and Mominur Rahman M., “On the Analytical Approximation of the Nonlinear Cubic Oscillator by an Iteration Method” Journal of Advances in Mathematics and Computer Science, vol. 33, pp. 1-9, 2019.
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NUMERICAL SOLUTION OF TIME FRACTIONAL TIME REGULARIZED LONG WAVE EQUATION BY ADOMINAN DECOMPOSITION METHOD AND APPLICATIONS

Authors:

Bhausaheb Sontakke, Rajashri Pandit

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00005

Abstract:

In the paper, we develop the Adomian Decomposition Method for the fractional-order nonlinear Time Regularized Long Wave Equation (TRLW) equation. Caputo fractional derivatives are used to define fractional derivatives. We know that nonlinear physical phenomena can be explained with the help of nonlinear evolution equations. Therefore solving TRLW is very helpful to obtain the solution of many physical theories. In this paper, we will solve the time-fractional TRLW equation which may help researchers with their work. We solve some examples numerically, which will show the efficiency and convenience of the Adomian Decomposition Method.

Keywords:

Time Regularized Long Wave equation,Fractional derivative,Adomian Decomposition Method,Convergence,Mathematica,

Refference:

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GENERATION OF NEW OPERATIONAL MATRICES FOR DERIVATIVE, INTEGRATION AND PRODUCT BY USING SHIFTED CHEBYSHEV POLYNOMIALS OF TYPE FOUR

Authors:

Faiza Chishti, Fozia Hanif, Urooj Waheed, Yusra Khalid

DOI NO:

https://doi.org/10.26782/jmcms.2021.02.00006

Abstract:

While solving the fractional order differential equation the requirement of the higher-order derivative is obvious therefore, this paper gives a definite expression for constructing the operational matrices of derivative which is the direct method to find the derivative of higher-order according to the requirement of the total differential equation. The proposed work expands the Chebyshev polynomial of type four up to six degrees that could help get the accuracy for the numerical solution of a given differential equation. Previously Chebyshev polynomial of the third type has been used by cutting the domain from [-1, 1] to [0, 1]. This study also generates the integrational operational matrix for solving the integral equation as well as an integrodifferential equation by using the Chebyshev polynomial of type four and expand it up to six order and generate the matrix by cutting the domain from [-1, 1] to [0, 1]. This is the first attempt to generate an integrational operational matrix that has never been highlight nor generate by any researcher. Another contribution of this paper is the generation of categorical expressions for the product of two Chebyshev vectors that will help in solving the differential equation of several kinds.

Keywords:

Operational matrix of derivative,Operational matrix of integration,Operational matrix of the product of Shifted Chebyshev polynomials of type four,

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