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Essential Mathcad for Engineering, Science, and Math
Using the author's considerable experience of applying Mathcad to engineering problems, Essential Mathcad introduces the most powerful functions and features of the software and teaches how to apply these to create comprehensive calculations for any quantitative subject. The simple, step-by-step approach makes this book an ideal Mathcad text for professional engineers as well as engineering , science, and math students. Examples from a variety of fields demonstrate the power and utility of Mathcad's tools, while also demonstrating how other software, such as Excel spreadsheets, can be incorporated effectively. A companion CD-ROM contains a full non-expiring version of Mathcad (North America only). *Many more applied examples and exercises from a wide variety of engineering, science, and math fields* New: more thorough discussions of differential equations, 3D plotting, and curve fitting.* Full non-expiring version of Mathcad software included on CD-ROM (North America only)* A step-by-step approach enables easy learning for professionals and students alike
eBook
Essential Mathcad for Engineering, Science, and Math W/ CD
Essential Mathcad for Engineering, Science, and Math w/ CD, Second Edition, introduces the most powerful functions and features of the software and teaches their application to create comprehensive calculations for any quantitative subject.
eBook
The Influence of the Stiffness of a Hyperstatic Elastic Beam on the Internal Forces Diagrams and on the Bending Deformations
An algorithm using the step function Φ(x-a) from the MATHCAD professional calculation program was used to calculate the bending deformations of an elastic beam suspended by means of tie rods (cables). It allowed the writing of analytical relations of shear and bending internal forces in the beam subjected to bending and the drawing of the corresponding diagrams. Also, the algorithm allowed the writing of the analytical relations of the deformations of the beam (arrows and rotations) with the help of the loading function Ψ (x), respectively its derivative Ψd(x). The numerical simulation presented in this paper allowed finding the practical solution for the proposed problem.
Journal Article
Comparative Study of Stresses Due to Forced Mounting of a Shaft Located on Four Bearings for Three Cases: Coaxial Bearings, Rigid Non-Coaxial Bearings and Elastic Non-Coaxial Bearings
The paper presents a comparative study of the stresses that occur for three cases of shaft mounting in a speed reducer: the maximum stresses in a continuous beam located on four coaxial rigid supports, the maximum stresses in the same beam located on four coaxial rigid supports and the maximum stresses in the same beam on four non-coaxial rigid and elastic supports. In the first case of shaft mounting, it is mounted on four bearings with non-coaxial and rigid support, in the second case, the shaft is mounted on the four coaxial and rigid bearings, and in the third case the shaft is mounted on four bearings with non-coaxial rigid and elastic end bearings, the intermediate bearings being mounted in the support by means of elastic elements. The statically indeterminate problem is solved in this paper using the load function method ψ from Strength of Materials and the numerical calculation is done for a particular numerical case, using the step function Φ(x-a) from the professional program MATHCAD. The solution method allows the numerical calculation of reactions, the drawing of internal stress diagrams and the calculation of maximum stresses in the dangerous section.
Journal Article
Calculating of square-wave voltammograms—a practical on-line simulation platform
Square-wave voltammetry (SWV) is a widely used technique for getting insight into mechanistic and kinetic aspects of various electrochemical reactions. To date, this pulse-voltammetric technique has been utilized in numerous electrochemical studies and it remains one of the most sophisticated electrochemical methods available. As a result of its higher sensitivity and its potential to provide insights similar to cyclic voltammetry for electrode mechanisms characterization, the SWV is increasingly being included in undergraduate electrochemistry laboratory curriculums. The features of experimental SW voltammograms are affected by various factors, such as kinetics of charge transfer, diffusion, adsorption phenomena, and chemical reactions coupled to electron transfer step. To understand some of the physical and chemical phenomena hidden in a single experimental SW voltammogram, it is inevitable to get a help of computer simulations. The purpose of this article is to offer a basic introduction to SWV written in a simple language, intended to engage students and familiarize them with the fundamentals of this technique. The ultimate objective is to provide the aspiring young electrochemists with a simulation procedure using the MATHCAD software, which can be employed to compute SW voltammograms following a rather easy simulation approach. A detailed tutorial on simulating SW voltammograms with MATHCAD software is presented. The simple tutorial offers a step-by-step breakdown of the simulation process of a square-wave voltammogram. Additionally, a MATHCAD ready-to-use file for simulation of a common electrode mechanism is provided. The current work aims to assist undergraduate students in learning about electrochemical simulations that serve as a corner stone to more advanced studies in SWV.
Journal Article
Study of the Influence of the Longitudinal Slipping of a Package of Suspended Bars on Stress Diagrams and on its Deformations
To calculate the bending deformations of a package of elastic beams suspended by means of tie rods, a calculation algorithm using the step function Φ (x-a) from the professional MATHCAD calculation program was used. The step function Φ (x-a) allowed the writing of the analytical relations of the internal shear and bending forces in the beam subjected to bending and the drawing of the corresponding diagrams. Also, the calculation algorithm allowed the writing of the analytical relations of the deformations of the bar (arrows and rotations) with the help of the loading function Ψ (x), respectively its derivative Ψ d(x). The numerical simulation presented in this work allowed the study of the influence of longitudinal sliding on the internal shear and bending force and deformation diagrams for two presumptive connection situations of package beams that were expressed by the degree of preventing sliding (δ =50% and δ =100%), which is defined as the ratio between the moment of inertia of the hexagonal section comprising the n beams as a unitary whole and the one calculated as the sum of the moments of inertia of the sections of the n beams
Journal Article
Visual Basic and MathCAD used for Visualization and modeling STEM education
The goal of the study is to create Visual Basic and MATHCAD apps to create programs that show the core force using physical forces as an example. The research subjects are high school teachers and students; the inherent context is high school STEM courses. Programs for computer visualization have been developed, and theoretical investigations have been conducted. They are used to determine how planets move in relation to the stars, simulate a particle’s motion in the gravitational field along elliptical, parabolic, and hyperbolic trajectories, validate the second and third Kepler laws, simulate the deflection of alpha particles in the atomic nucleus’ repulsion field, and model a particle’s motion in a field of force that defies the law of inverse squares. Following a series of tests, the ball’s trajectories on the glass plane were found to be hyperbola, parabola, elliptical, and circular. The created programs are compatible with current Visual Basic and MathCAD visualization techniques for physical phenomena, and they can be used to teach math, computer science, and astronomy. They can also serve as the foundation for future studies on the central force distribution in particle motion.
Journal Article
Calculation of the Main Parameters of the Two-Line Helical Traction Transmission of an Electric Locomotive Based on Diagnostic Parameters
Gearboxes used in electric locomotives are a critical unit, especially in freight rolling stock. The article presents the calculation of the main parameters of the two-way oblique traction transmission of the VL-80s electric locomotive (which is operated on the railways of Uzbekistan) based on a comprehensive analysis of the diagnostic parameters obtained using the Poisson normal distribution method for the identified failures according to the Uzbekistan depot data. Also, a Pareto diagram was constructed for the chassis of 3VL-80s electric locomotives based on the data of the Locomotive Operation Department of JSC Uzbekistan Temir Yollari, and probabilistic and statistical analyses of the failures and breakdowns of the wheel pair and the large gear wheel of the traction gearbox of the VL-80s electric locomotives were carried out. An algorithm and methodology for assessing the reliability of the large gear wheel of the traction gearbox of an electric locomotive are presented. As a result of a numerical calculation of the coefficients of the empirical regression equations using approximation and spline interpolation methods, a regression equation was obtained for the dependence of the standard deviation of the wear of the tooth of the large gear wheel of the traction reducer of the VL80s electric locomotive on the mileage.
Journal Article
Consistent and Efficient Modeling of the Nonlinear Properties of Ferroelectric Materials in Ceramic Capacitors for Frugal Electronic Implants
In recent years, the development of implantable electronics has been driven by the motivation to expand their field of application. The main intention is to implement advanced functionalities while increasing the degree of miniaturization and maintaining reliability. The intrinsic nonlinear properties of the electronic components, to be used anyway, could be utilized to resolve this issue. To master the implementation of functionalities in implantable electronics using the nonlinear properties of its electronic components, simulation models are of utmost importance. In this paper, we present a simulation model that is optimized in terms of consistency, computing time and memory consumption. Three circuit topologies of nonlinear capacitors, including hysteresis losses, are investigated. An inductively coupled measurement setup was realized to validate the calculations. The best results were obtained using the Trapezoid method in ANSYS with a constant step size and a resolution of 500 k points and using the Adams method in Mathcad with a resolution of 50 k points. An inductive coupling factor between 7% and 10% leads to a significant improvement in consistency compared to lower coupling factors. Finally, our results indicate that the nonlinear properties of the voltage rectifier capacitor can be neglected since these do not significantly affect the simulation results.
Journal Article