# Mechanics and Strength of Materials, Volume 1

## 1st Edition

**Authors:**Bogdan Skalmierski

**eBook ISBN:**9781483102559

**Imprint:**Elsevier

**Published Date:**1st January 1979

**Page Count:**442

**View all volumes in this series:**Studies in Applied Mechanics

## Table of Contents

Preface

Introduction

Chapter 1. Kinematics

1.1. Motion of a Single Particle

1.2. Description of the Motion of a Rigid Body

1.3. Relative Motion

1.4. Plane Motion of a Rigid Body

1.5. Examples of the Determination of Velocities and Accelerations in the Motion of Plane Mechanisms

Chapter 2. The Dynamics of a Particle

2.1. Fundamental Definitions and Theorems

2.2. Motion of a Particle

2.3. Center of Mass and Center of Gravity of a Particle System

2.4. Law of Variation of Momentum

2.5. Law of Variation of angular Momentum

Chapter 3. Statics

3.1. Equations of Equilibrium

3.2. Couple

3.3. Spatial System of Forces. Wrench

3.4. Analytical and graphical Methods in the Statics of Plane Systems

Analytical Methods

Graphical Methods (Funicular Polygon)

3.5. Examples

Triple-Jointed System

Free-Ends Beam

Plane Trusses

3.6. The Distributive Character of Transverse Loads in Simple Rods

3.7. The Equilibrium of Rods Loaded with Transverse Forces

3.8. Friction

Friction on an Inclined Plane

Bearing Friction

Friction of Rope against Wheel

Problem of Friction in the Case of a Cylinder Rolling on Plane Surface

Chapter 4. The Statics of Elastic Systems

4.1. Hooke's Law

4.2. Safety Factor

4.3. Statically Indeterminate Systems

4.4. Problems of Simple Beam-Bending

4.5. Geometric Moments of Inertia

4.6. Strength Calculations of Beams

4.7. The Equation for the axis of a Deflected Beam

4.8. Graphical Methods of Determining Deflections of Simple Beams (Mohr's Analogy)

4.9. Oblique Bending

4.10. Some Special Problems of Bending Theory

4.11. Clapeyron's Systems

4.12. Buckling Problems of axially Compressed Rods

4.13. Highly Curved Rods

4.14. Torsion of Rods with Circular Cross-Section

4.15. Springs

4.16. Simultaneous Bending and Torsion of Rods with Circular Cross-Section

Chapter 5. The Dynamics of Rigid Bodies

5.1. Moments of Inertia of Rigid Bodies

5.2. The Angular Momentum of a Rigid Body in General Motion

5.3. Angular Momentum in Circular Motion

5.4. Euler's Equations

5.5. The Kinetic Energy of Rigid Bodies in General Motion

Chapter 6. Dynamics in Relative Motion

6.1. Differential Equation of the Motion of a Particle in a Non-Inertial System

6.2. The Dynamics of Rigid Bodies in Relative Motion

Chapter 7. Fundamentals of Analytical Mechanics

7.1. Generalized Coordinates and Degrees of Freedom of a Mechanical System

7.2. D'Alembert's Principle

7.3. Hamilton's Principle

7.4. Lagrange Equations of the First Order

7.5. Lagrange Equations of the Second Order

7.6. Kinetic Energy of a System

7.7. Impulsive Motion

7.8. Gyroscopic and Dissipative Forces

7.9. The Lagrange Equations for Electromechanical Systems

7.10. Hamilton's Canonical Equations

7.11. The Total Energy of a Mechanical System

7.12. Configurational Space

7.13. The Stability of Mechanical Systems

Chapter 8. Vibrations of Systems with One Degree of Freedom

8.1. Preliminary Discussion

8.2. Free Vibrations of Harmonic Oscillators

8.3. The Influence of Dissipative Forces in the Free Vibrations of Harmonic Oscillators

8.4. Forced Vibrations of Harmonic Oscillators

8.5. Vibrations of Harmonic Oscillators with Kinematical Input

8.6. Vibrations of Harmonic Oscillators under Periodic Input Forces

8.7. Vibrations of Non-Linear Systems

Chapter 9. Vibrations Of Systems with Many Degrees of Freedom

9.1. Preliminary Discussion

9.2. Problems of Linearization of the Equations

9.3. Free Vibrations of Conservative Systems

9.4. Normal Coordinates

9.5. Forced Vibrations of a System

9.6. Free Vibrations of Dissipative Systems

9.7. Forced Vibrations in Dissipative Systems

9.8. Vibrations of Clapeyron's Systems

Chapter 10. Some Methods of Describing Random Phenomena in Mechanics

10.1. Basic Concepts

10.2. Methods of Describing Stochastic Processes

10.3. Stochastic Linearization

10.4. Random Vibrations of Linear Systems with One Degree of Freedom

10.5. Random Vibrations of Systems with Many Degrees of Freedom

10.6. The Problem of Departures

10.7. Fokker—Planck—Kolmogorov Equations

10.8. Proposal for a Method of Direct Determination of Probability Density

Bibliography

Subject Index

## Description

Mechanics and Strength of Materials focuses on the methodologies used in studying the strength of materials. The text first discusses kinematics, and then describes the motion of a single particle; description of the motion of a rigid body; plane motion of a rigid body; and examples of the determination of velocities and accelerations in the motion of plane mechanism. The book explains the dynamics of a particle and statics, including the center of mass and gravity of a particle system; law of variation of angular momentum; analytical and graphical methods in the statics of plane systems; and spatial system of forces. The text also discusses the statics of elastic systems, and then describes the strength calculations of beams; problems of simple beam-bending; geometric moments of inertia; buckling problems of axially compressed rods; and simultaneous bending and torsion of rods with circular cross-section. The book focuses on the dynamics of rigid bodies, dynamics in relative motion, and fundamentals of analytical mechanics. The text further looks at vibrations of systems with one degree and many degrees of freedom. The book is a good source of data for readers interested in studying the strength of materials.

## Details

- No. of pages:
- 442

- Language:
- English

- Copyright:
- © Elsevier 1979

- Published:
- 1st January 1979

- Imprint:
- Elsevier

- eBook ISBN:
- 9781483102559