Theoretical and applied mechanics / Valentin Molotnikov, Antonina Molotnikova.

Format:

Book

Author/Creator:

Molotnikov, Valentin, author.

Molotnikova, Antonina, author.

Language:

English

Subjects (All):

Mechanics.

Physical Description:

1 online resource (687 pages)

Place of Publication:

Cham, Switzerland : Springer, [2023]

Summary:

This textbook summarizes the course of engineering mechanics, designed for one or two semesters, at the undergraduate or graduate level for a range of academic majors. The book covers all the main components of the discipline including: Theoretical Mechanics, Theory of Mechanisms and Machines, Resistance of Materials, Machine Parts and Design Basic; and Interchangeability, Standardization, and Technical Measurements. It can also be used by students of other technical areas in to achieve competence in each of the listed disciplines. The concise presentation facilitates concentration on the most important elements of the concepts presented while also outlining the current state of mechanics, demonstrating engineering applications using various computer packages (MathCad, CosmosWorks, Inkscape, AutoCad), and updating data on engineering materials. Examples of both simple and complex engineering calculations are given at the end of each chapter along with self-assessment questions.

Contents:

Intro

Abstract

Acknowledgements

Introduction

Contents

Notation Conventions

Theoretical Mechanics

Theory of Mechanisms and Machines

Resistance of Materials

Machine Parts and Design Basics

Introduction to CAD Based on AutoCad AutoLisp

Part I Theoretical Mechanics

1 Statics

1.1 Introduction

1.2 The Subject and Tasks of Theoretical Mechanics

1.3 Strength. Force syste

1.4 Axioms of Theoretical Mechanics

1.5 Connections and Their Reactions

1.5.1 Classification of Constraints

1.6 Conditions for the Equilibrium of Converging Forces

1.7 A System of Parallel Forces: Power Pairs

1.8 Moment of Force Relative to the Point and Axis

1.9 Basic Theorem of Statics

1.10 Equilibrium of an Arbitrary System of Forces

1.11 Solving Problems on the Balance of Systems of Forces

1.11.1 General Comment

1.11.2 Example 1

1.11.3 Example 2

1.11.4 Example 3

1.12 Truss Calculation

1.12.1 Calculation of a Triangular Cantilever Truss

1.12.2 Calculation of a Symmetrical Bridge Girder

1.13 Computer Calculation of Truss

1.14 Center of Parallel Forces

1.15 The Center of Gravity of a Rigid Body

Self-Test Questions

Control Tasks for the Section ``Statics''

Example of Completing a Task

References

2 Kinematics

2.1 Ways to Set the Movement

2.2 Speed and Acceleration of the Point

2.3 The Simplest Movements of a Solid Body

2.3.1 Forward Motion of a Solid Body

2.3.2 Rotation of a Solid Body Around a Fixed Axis

2.4 Complicated Motion of a Point

2.5 Flat Solid Motion

2.5.1 Equations of Plane Motion of a Solid Body

2.5.2 Angular Velocity and Angular Acceleration in Plane Motion

2.5.3 Speed Points in Planar Movement of the Body

2.5.4 Instant Center of Velocity

2.5.5 Speed Plan.

2.5.6 Determination of Accelerations of Points of a Body in Flat Motion

2.6 Complex Motion of Points in the General Case

2.6.1 Absolute and Relative Derivatives of a Vector Function of a Scalar Argument

2.6.2 Addition of Velocities

2.6.3 Acceleration of a Point in the General Case of Portable Motion

Control Tasks for the Section ``Kinematics''

3 Dynamics

3.1 Point Dynamics

3.2 Dynamic Coriolis Theorem

3.3 General Theorems of Dynamics of a Point

3.3.1 Basic Concepts and Definitions

3.3.2 Theorem on Changing the Amount of Motion Material Point

3.3.3 Theorem on Changing the Kinetic Energy of a Point

3.3.4 Theorem on Changing the Moment of the Amount of Motion of a Point

3.4 System Dynamics

3.4.1 The Geometry of the Masses

3.4.2 Theorem on the Motion of the Center of Mass of the System

3.4.3 Theorem on Changing the Amount of Motion of a System

3.4.4 Theorem on Changing the Moment of Quantity of Motion of the System

3.4.5 Theorem on Changing the Kinetic Energy of aSystem

3.5 The d'Alembert Principle

Control Tasks for the Section ``Dynamics''

4 Theory of Impact

4.1 Impact Phenomenon and Its Main Characteristics

4.2 Basic Theorems of the Theory of Impact

4.3 Impact of a Point on a Stationary Surface

4.4 Experimental Determination of the Recovery Factor

4.5 Impact of Two Bodies

4.6 Carnot's Theorem

4.7 Rotating Body Blow

Control Tasks for the Section ``Theory of Impact''

Variant 1

Variant 2

Variant 3

Variant 4

Variant 5

Variant 6

Variant 7

Variant 8

Variant 9

Variant 10

References.

5 Elements of Analytic Mechanics

5.1 The Principle of Possible Movements

5.2 Generalized Coordinates: Generalized Forces

5.3 The Case of Conservative Forces

5.4 Equilibrium Conditions of the System in Generalized Coordinates

5.5 General Equation of System Dynamics

5.6 Equations in generalized coordinates

5.6.1 The Case of Conservative Forces

Control Tasks for the Section ``Analytical Mechanics''

Task

Investigation of the Equations of Motion of a System with Two Degrees of Freedom by the Method of Lagrange Equations of the Second Kind (Example)

6 Dynamics of Controlled Systems

6.1 Mathematical Model of the Controlled System

6.2 Basic Information About Functionals and Function Spaces

6.3 Variations of Comparison Curves and Functionals

6.4 Statement of the Mayer Variational Problem

6.5 The Maximum Principle

6.6 Erdmann-Weierstrass Conditions: First Integral

6.7 The Simplest Problem of Optimal Performance

6.7.1 Building a Mathematical Model

6.7.2 Border Conditions

6.7.3 Functional

6.7.4 Getting Additional Ratios

6.7.5 Traction Control Program

6.7.6 Integration of Differential Equations of the Problem

6.7.7 Completion of the Integration of Problem Equations

6.8 Flying the Drone to the Maximum Range

6.8.1 Building a Mathematical Model

6.8.2 Border Conditions

6.8.3 Minimizing Functional

6.8.4 Additional Ratios

6.8.5 Necessary Conditions for a Strong andWeak Minimum

6.8.6 Preparing to Integrate the Aggregate Equations of the Problem

6.8.7 Traction Control Program

6.8.8 Completion of the Integration of the Differential Equations of the Problem

7 Stability of Mechanical Systems

7.1 Stability and Instability.

7.2 Work and Classification of Forces

7.3 Stability with Conservative and Dissipative Forces

7.4 Lyapunov-Chetaev Theorem

7.5 Instability in the First Approximation

7.6 Critical Load

7.7 The Theorem on Stability by the First Approximation

7.8 The Raus-Hurwitz Criterion

7.9 Main Types of Stability Loss

7.10 Methods for Determining Critical Load

7.11 The Perturbed Motion of the Compressed Rod

7.12 Stability Under Non-conservative Load (Example)

7.12.1 Equations of Perturbed Motion

7.12.2 Area of Valid Stability

7.12.3 Investigation of the Value μ, (Formula (7.31))

7.12.4 Investigation of the Effect of Friction

7.12.5 The Influence of the Spacing of the End Masses

Stability of the Equilibrium State of a Conservative Mechanical System

Part II Elements of the Theory of Mechanisms and Machines

8 Basic Concepts

8.1 Conditional Classification of Machines

8.2 Components of the Mechanism

8.3 Kinematic Pairs and Chains

9 Structural Analysis of Mechanisms

9.1 The Degree of Mobility of the Kinematic Chain

9.2 Structural Classification of Mechanisms

9.2.1 Example of a Structural Analysis of a Mechanism

10 Kinematic Analysis of Mechanisms

10.1 Objectives and Methods of Kinematic Analysis

10.2 Building Plans for the Provisions of the Mechanism

10.3 Kinematic Diagrams

10.3.1 Displacement Diagrams

10.3.2 Plotting Velocity and Acceleration Diagrams

10.4 Speed and Acceleration Plans

10.4.1 Building a Speed Plan

10.4.2 Building an Acceleration Plan

10.5 Analytical Study of the Kinematics of Mechanisms

Questions for Self-Test

11 Dynamic Analysis of Mechanisms.

11.1 Classification of Forces

11.2 Kinetostatics Problems

11.3 Methods of Force Calculation of Mechanisms

11.3.1 Force Plans Method

11.3.2 Decomposition of Forces

11.3.3 Analytical Method

11.3.4 Determination of Balancing Force

Part III Strength of Materials

12 Initial Concepts and Definitions

12.1 Objectives of the Course on Strength of Materials

12.2 External Forces: The Saint-Venant Principle

12.3 The Simplest Stress States

12.4 Deformations and Displacements

12.5 Material Testing: Hooke's Law

13 Calculation of Parts in Tension-Compression

13.1 Internal Tensile-Compressive Forces

13.2 Stresses

13.3 Determination of Deformations and Displacements

13.4 Potential Deformation Energy of the Body

13.5 Strength Calculations

13.6 Statically Indeterminate Tasks

13.7 Calculation by permissible loads

14 Tense State: Strength Theories

14.1 Material Strength Hypotheses

14.2 Types of Stress

14.3 Generalized Hooke's Law

14.4 Plane State

14.4.1 General Provisions

14.4.2 Analysis of the Plane Stress State

14.5 Strength Theories

14.5.1 Question Statement

14.5.2 Working Strength Theories

15 Shear and Torsion

15.1 Shear

15.2 Torsion of the Circular Shaft

15.3 Calculation of Shafts for Strength and Rigidity

16 Bending

16.1 The Concept of Bending Deformation

16.2 Internal Bending Forces

16.2.1 Example of Defining Internal Effort

16.3 Differential Bending Dependencies

16.4 Normal Bending Stresses

16.5 Tangential Bending Stresses.

16.6 Strength Calculation Based on Permissible Stresses.

Notes:

Includes bibliographical references and index.

Description based on print version record.

Other Format:

Print version: Molotnikov, Valentin Theoretical and Applied Mechanics

ISBN:

3-031-09312-7