Advanced Mathematical Techniques in Engineering Sciences

Mangey Ram, J. Paulo Davim, Mangey Ram, J. Paulo Davim

• Publisher: CRC Press
• Year: 2018
• Print ISBN: 9781138554399
• eBook ISBN: 9781351371889
• Edition: 1
• Topic: Matemáticas
• Subtopic: Matemática aplicada

The goal of this book is to publish the latest mathematical techniques, research, and developments in engineering. This book includes a comprehensive range of mathematics applied in engineering areas for different tasks. Various mathematical tools, techniques, strategies, and methods in engineering applications are covered in each chapter.

Mathematical techniques are the strength of engineering sciences and form the common foundation of all novel disciplines within the field. Advanced Mathematical Techniques in Engineering Sciences provides an ample range of mathematical tools and techniques applied across various fields of engineering sciences. Using this book, engineers will gain a greater understanding of the practical applications of mathematics in engineering sciences.

Features

• Covers the mathematical techniques applied in engineering sciences
• Focuses on the latest research in the field of engineering applications
• Provides insights on an international and transnational scale
• Offers new studies and research in modeling and simulation

chapter one

Application of the Laplace transform in problems of studying the dynamic properties of a material system and in engineering technologies

Lubov Mironova

Russian University of Transport (MIIT)

Leonid Kondratenko

Moscow Aviation Institute (State National Research University)

Contents

1.1 Designation

1.2 Laplace transform and operations mapping

1.3 Linear substitutions

1.4 Differentiation and integration

1.5 Multiplication and curtailing

1.6 The image of a unit function and some other simple functions

1.7 Examples of solving some problems of mechanics

1.8 Laplace transform in problems of studying oscillation of rods

1.9 Relationship between the velocities of the particles of an elementary volume of a cylindrical rod with stresses

1.10 An inertial disk rotating at the end of the rod

1.11 Equations of torsional oscillations of a disk

1.12 Equations of longitudinal oscillations of a disk

1.13 Application of the Laplace transform in engineering technology

1.13.1 Method of studying oscillations of the velocities of motion and stresses in mechanisms containing rod systems

1.13.2 Features of functioning of a drive with a long force line

1.13.3 Investigation of dynamic features of the system in the technologies of deephole machining

References

This chapter is written by engineers for engineers. The authors try to convey to the reader the simplicity and accessibility of the methods in a concise form with the illustration of the calculation schemes. For a more extensive study of the stated problems of mathematical modeling, at the end of the chapter are given the literature sources, from which the reader can obtain the necessary additional explanations. The list of authors includes well-known scientists in the field of mathematics and mechanics – G. Doetsch, A.I. Lur’e, L.I. Sedov, V.A. Ivanov, and B.K. Chemodanov. In compiling the theoretical material, we refer to the authors mentioned. This chapter reflects the experience of lecturing on mathematical methods of modeling, as well as the personal participation of the authors in the work in this technical field.

The...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• Editors
• Contributors
• Chapter 1 Application of the Laplace transform in problems of studying the dynamic properties of a material system and in engineering technologies
• Chapter 2 Fourier series and its applications in engineering
• Chapter 3 Soft computing techniques and applications
• Chapter 4 New approach for solving multi-objective transportation problem
• Chapter 5 An application of dual-response surface optimization methodology to improve the yield of pulp cooking process
• Chapter 6 Time-dependent conflicting bifuzzy set and its applications in reliability evaluation
• Chapter 7 Recent progress on failure time data analysis of repairable system
• Chapter 8 View-count based modeling for YouTube videos and weighted criteria–based ranking
• Chapter 9 Market segmentation-based modeling: An approach to understand multiple modes in diffusion curves
• Chapter 10 Kernel estimators for data analysis
• Chapter 11 A new technique for constructing exact tolerance limits on future outcomes under parametric uncertainty
• Chapter 12 Design of neural network–based PID controller for biped robot while ascending and descending the staircase
• Chapter 13 Modeling fertility in Murrah bulls with intelligent algorithms
• Chapter 14 Computational study of the Coanda flow for V/STOL
• Chapter 15 Introduction to collocation method with application of B-spline basis functions to solve differential equations
• Chapter 16 Rayleigh’s approximation method on reflection/refraction phenomena of plane SH-wave in a corrugated anisotropic structure
• Index