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2019 | Book

Vectors Read chapter Read first chapter

Eigenvalue and Eigenvector Problems in Applied Mechanics

Authors: Prof. Dr. Sorin Vlase, Prof. Dr. Marin Marin, Prof. Dr. Andreas Öchsner

Publisher: Springer International Publishing

Book Series : Advanced Structured Materials

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This book presents, in a uniform way, several problems in applied mechanics, which are analysed using the matrix theory and the properties of eigenvalues and eigenvectors. It reveals that various problems and studies in mechanical engineering produce certain patterns that can be treated in a similar way. Accordingly, the same mathematical apparatus allows us to study not only mathematical structures such as quadratic forms, but also mechanics problems such as multibody rigid mechanics, continuum mechanics, vibrations, elastic and dynamic stability, and dynamic systems. In addition, the book explores a wealth of engineering applications.

Table of Contents

Frontmatter
Chapter 1. Vectors
Abstract
Mechanics uses physical quantities that cannot be characterized only by their magnitude (how it happens with a scalar) but also need other attributes to define them, namely the direction, or point of application (fixed or mobile).
Sorin Vlase, Marin Marin, Andreas Öchsner
Chapter 2. Matrices
Abstract
We introduce in the following the basic notions about matrices and the basic properties interesting for our presentation. A number of other properties will be presented in the following chapters. A matrix of dimension m × n is represented by a table with m lines and n columns (in box bracket or parentheses).
Sorin Vlase, Marin Marin, Andreas Öchsner
Chapter 3. Quadratic Forms
Abstract
In the following paragraphs we will introduce the notion of quadratic forms of two or more variables. These forms can be introduced starting from several types of problems in which they have a central role.
Sorin Vlase, Marin Marin, Andreas Öchsner
Chapter 4. Rigid Body Mechanics
Abstract
Knowing the position of a rigid body means to know the position of all its points.
Sorin Vlase, Marin Marin, Andreas Öchsner
Chapter 5. Strain and Stress
Abstract
Considering a continuous solid, a deformation of this means that a curve changes its length when it changes its position.
Sorin Vlase, Marin Marin, Andreas Öchsner
Chapter 6. Modal Analysis
Abstract
In many problems of mechanics of discrete systems, by linearizing the forces that are manifested between different components of the system, the motion equations are obtained in the form
Sorin Vlase, Marin Marin, Andreas Öchsner
Chapter 7. Dynamical Systems
Abstract
This chapter aims to present only some aspects of the dynamical systems related to the subject of this book.
Sorin Vlase, Marin Marin, Andreas Öchsner
Metadata
Title
Eigenvalue and Eigenvector Problems in Applied Mechanics
Authors
Prof. Dr. Sorin Vlase
Prof. Dr. Marin Marin
Prof. Dr. Andreas Öchsner
Copyright Year
2019
Electronic ISBN
978-3-030-00991-5
Print ISBN
978-3-030-00990-8
DOI
https://doi.org/10.1007/978-3-030-00991-5

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