Mechanical vibrations : an introduction / György Szeidl, László Péter Kiss.
This book presents a unified introduction to the theory of mechanical vibrations. The general theory of the vibrating particle is the point of departure for the field of multidegree of freedom systems. Emphasis is placed in the text on the issue of continuum vibrations. The presented examples are ai...
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| Main Authors: | , |
|---|---|
| Format: | Ebook |
| Language: | English |
| Published: |
Cham :
Springer,
2020.
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| Series: | Foundations of Engineering Mechanics Ser.
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| Subjects: | |
| Online Access: | Springer eBooks |
Table of Contents:
- Intro
- Preface
- Contents
- 1 Introduction
- 1.1 Model Creation
- 1.2 Kinematic Relations-A Summary
- 1.2.1 Motion of a Material Point (Particle)
- 1.2.2 Motion of a Rigid Body
- 1.3 Fundamental Relations of Kinetics-A Summary1
- 1.3.1 The First Moment of a Mass Distribution
- 1.3.2 Momentum Distribution-Vector System of Momenta
- 1.3.3 Moment of Momentum for a Rigid Body
- 1.4 Parallel Axis Theorem
- 1.5 Fundamental Theorems of Kinetics
- 1.5.1 Introductory Remarks
- 1.5.2 Force Systems
- 1.5.3 Systems of Effective Forces
- 1.5.4 The Fundamental Theorem of Dynamics
- 1.5.5 Kinetic Energy of a Rigid Body. Power
- 1.5.6 Principle of Work and Energy
- 1.6 Problems
- References
- 2 Impact
- 2.1 What Is Meant by Impact
- 2.2 Central Impact
- 2.3 Eccentric Impact
- 2.3.1 Impact of Two Bodies Which Perform Free Plane Motion
- 2.3.2 Impact of Two Bodies if One or Two Bodies Rotate About a Fixed Point
- 2.4 Problems
- Reference
- 3 Some Vibration Problems
- 3.1 Single Degree of Freedom Systems
- 3.1.1 Introductory Remarks
- 3.1.2 Classification
- 3.2 Machine Foundations and Vibration Isolation
- 3.2.1 Introductory Remarks
- 4.1.2 Principle of Virtual Work
- 4.1.3 Derivation of Lagrange's Equation of Motion of the Second Kind
- 4.2 Applications of Lagrange's Equations
- 4.2.1 Calculations of Generalized Forces
- 4.3 Multidegree of Freedom Systems with Solutions
- 4.3.1 Examples for Multidegree of Freedom Systems
- 4.3.2 Two Degree of Freedom Systems
- 4.3.3 Free Vibrations of Two Degree of Freedom Spring-Mass Systems
- 4.3.4 Forced Vibrations of Two Degree of Freedom Systems
- 4.3.5 Vibration Absorbers
- 4.4 Problems
- References
- 5 Some Problems of Multidegree of Freedom Systems
- 5.1 Equations of Motion
- 5.1.1 Spring-Mass Systems
- 5.1.2 The General Form of the Equation of Motion
- 5.2 Eigenvalue Problem of Symmetric Matrices
- 5.2.1 Eigenvalues and Eigenvectors
- 5.2.2 Calculation of the Eigenvectors
- 5.2.3 Orthogonality of the Eigenvectors
- 5.2.4 Repeated Roots
- 5.2.5 The Natural Frequencies Are Real Numbers
- 5.2.6 Uncoupled Equations of Motion
- 5.3 Rayleigh Quotient
- 5.3.1 Definition and Properties
- 5.3.2 Matrix Iteration
- 5.3.3 Convergence of the Iteration Algorithm
- 5.3.4 Properties of the Iteration Algorithm