SolidWorks Simulation 2024 Black Book

By Gaurav Verma and Matt Weber

The SolidWorks Simulation 2024 Black Book, is 11th edition of the book written to help professionals as well as students in performing various tedious jobs of Finite Element Analysis. The book follows a step-by-step methodology. This book explains the background work running behind your simulation analysis screen. The book covers almost all the information required by a learner to master the SolidWorks Simulation. The book starts with basics of FEA, goes through all the simulation tools and ends up with practical examples of analysis. Chapters on manual FEA ensure the firm understanding of FEA concepts through SolidWorks Simulation. The book contains our special sections named "Why?" and notes. We have given reasons for selecting most of the options in analysis under the "Why?" sections. The book explains the Solver selection, iteration methods like Newton-Raphson method and integration techniques used by SolidWorks Simulation for functioning. A chapter on Topology Study helps you understand the procedures of modifying component based on analysis results. New tips and notes have been added in this book for various analyses. Some of the salient features of this book are:

 

In-Depth explanation of concepts

Every new topic of this book starts with the explanation of the basic concepts. In this way, the user becomes capable of relating the things with real world.

 

Topics Covered

Every chapter starts with a list of topics being covered in that chapter. In this way, the user can easily find the topic of his/her interest easily.

 

Instruction through illustration

The instructions to perform any action are provided by maximum number of illustrations so that the user can perform the actions discussed in the book easily and effectively. There are about 750 illustrations that make the learning process effective.

 

Tutorial point of view

The book explains the concepts through the tutorial to make the understanding of users firm and long lasting. Each chapter of the book has tutorials that are real world projects.

 

"Why?"  

The book explains the reasons for selecting options or setting a parameter in tutorials explained in the book. 

 

Project

Projects and exercises are provided to students for practicing.

 

For Faculty

If you are a faculty member, then you can ask for video tutorials on any of the topic, exercise, tutorial, or concept. As faculty, you can register on our website to get electronic desk copies of our latest books, self-assessment, and solution of practical. Faculty resources are available in the Faculty Member page of our website once you login. Note that faculty registration approval is manual and it may take two days for approval before you can access the faculty website.

• Language: English
• Publisher: CADCAMCAE Works
• Release date: Jan 9, 2024
• ISBN: 9798224883233

Gaurav Verma

Gaurav Verma is currently a Full Professor at the Panjab University, Chandigarh, India (Dr. SS Bhatnagar University Institute of Chemical Engineering and Technology, and Adjunct Faculty at the Department of Nanoscience and Nanotechnology). He is a former CV Raman Post-Doctoral fellow from the Department of Chemical Engineering, Massachusetts Institute of Technology (MIT), USA. His research focuses on the areas of applied nanoscience and nanostructured materials.

Book preview

SolidWorks_Simulation_2024_Cover_BW.jpg

SolidWorks Simulation 2024 Black Book

By

Gaurav Verma

Matt Weber

(CADCAMCAE Works)

Edited by

Kristen

Published by CADCAMCAE WORKS, USA. Copyright © 2024. All rights reserved. No part of this publication may be reproduced or distributed in any form or by any means, or stored in the database or retrieval system without the prior permission of CADCAMCAE WORKS. To get the permissions, contact at [e-mail] or [e-mail]

NOTICE TO THE READER

Publisher does not warrant or guarantee any of the products described in the text or perform any independent analysis in connection with any of the product information contained in the text. Publisher does not assume, and expressly disclaims, any obligation to obtain and include information other than that provided to it by the manufacturer.

The reader is expressly warned to consider and adopt all safety precautions that might be indicated by the activities herein and to avoid all potential hazards. By following the instructions contained herein, the reader willingly assumes all risks in connection with such instructions.

The Publisher makes no representation or warranties of any kind, including but not limited to, the warranties of fitness for a particular purpose or merchantability, nor are any such representations implied with respect to the material set forth herein, and the publisher takes no responsibility with respect to such material. The publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or part, from the reader’s use of, or reliance upon, this material.

DEDICATION

To teachers, who make it possible to disseminate knowledge

to enlighten the young and curious minds

of our future generations

To students, who are the future of the world

THANKS

To my friends and colleagues

To my family for their love and support

Table of Contents

Preface xi

About Author xiii

Chapter 1 : Introduction to Simulation

Simulation 1-2

Types of Analyses Performed in SolidWorks Simulation 1-2

Static Analysis 1-2

Dynamic Analysis 1-3

Thermal analysis 1-7

Drop Test Studies 1-7

Fatigue Analysis 1-7

Pressure Vessel Design Study 1-7

Design Study 1-8

FEA 1-8

Optimum process of FEA through SolidWorks Simulation 1-10

Starting SolidWorks Simulation 1-16

On clicking Simulation Advisor 1-16

On clicking New Study 1-17

Chapter 2 : Basics of Analyses in SolidWorks Simulation

Starting Analysis 2-2

Applying Material 2-2

Adding Custom Materials 2-3

Role of Material Properties in FEA 2-6

Defining Fixtures 2-9

Fixtures Advisor 2-9

Fixed Geometry 2-10

Roller/Slider 2-14

Fixed Hinge 2-15

Elastic Support 2-16

Advanced Fixtures 2-18

External Load Advisor 2-24

External Loads Advisor 2-24

Force 2-25

Torque 2-27

Pressure 2-28

Gravity 2-30

Centrifugal Force 2-31

Bearing Load 2-32

Remote Loads/Mass 2-33

Distributed Mass 2-35

Temperature 2-36

Flow Effects/Thermal Effects 2-37

Connections Advisor 2-39

Connections Advisor 2-40

Local Interactions 2-40

Component Interaction 2-47

Interaction Viewer 2-49

Spring 2-51

Pin 2-54

Bolt 2-57

Spot Welds 2-59

Edge Weld 2-59

Link 2-60

Bearing 2-61

Rigid Connection 2-62

Linkage Rod 2-62

Meshing 2-64

Diagnostic Tools 2-67

Underconstrained Bodies 2-67

Simulation Evaluator 2-68

Mesh Failure Diagnostics 2-69

Mesh Quality Diagnostics 2-70

Running Analysis 2-71

Results Advisor 2-72

Results Advisor 2-72

Model Only (No Results) 2-73

New Plot 2-73

List Stress, Displacement, and Strain 2-75

List Result Force 2-77

Chapter 3 : Preparing Model for Analysis

Introduction 3-2

Reference Geometry 3-2

Plane 3-2

Plane Parallel to Screen 3-4

Axis 3-5

Coordinate System 3-7

Point 3-9

Center of Mass 3-10

Bounding Box 3-10

Mate Reference 3-11

Simplify 3-12

Extruded Boss/Base Tool 3-13

Revolved Boss/Base Tool 3-17

Extruded Cut 3-19

Fillet 3-20

Constant Size Fillet 3-20

Variable Radius Fillet 3-22

Face fillet 3-23

Full round fillet 3-23

FilletXpert 3-24

Chamfer 3-24

Mirror 3-26

Split Line tool 3-28

Mid Surface 3-31

Split Tool 3-33

Combine Tool 3-34

Adding Solid Bodies 3-34

Subtracting Solid Bodies 3-34

Common of Solid Bodies 3-34

Intersect Tool 3-35

Move/Copy Bodies Tool 3-36

Importing Part 3-37

Chapter 4 : Static Analysis

Linear static analysis 4-2

Assumptions 4-2

Performing Static Analysis 4-4

Starting the Static Analysis 4-4

Applying Material 4-5

Applying Fixtures 4-6

Applying Loads 4-7

Meshing the model 4-8

Running the Analysis 4-11

Results (Factor of Safety) 4-11

Optimizing product 4-12

Shell Manager 4-14

Performing Static Analysis Using Study Advisor 4-16

Starting the Static Analysis 4-16

Static Analysis on Assembly 4-25

Starting Analysis 4-26

Applying Material to Parts of Assembly 4-26

Setting Global Interactions 4-27

Setting Interaction Manually 4-28

Creating Virtual Wall 4-30

Creating Foundation Bolt connection 4-31

Applying Load 4-32

Meshing 4-33

Running Analysis 4-33

Adaptive Meshing 4-36

h-Adaptive Meshing 4-36

p-Adaptive Meshing 4-40

Submodeling Study 4-41

Load case Manager 4-45

Trend Tracker 4-47

Chapter 5 : Non-Linear Static Analysis

Non Linear Static Analysis 5-2

Theory Behind Non-Linear Analysis 5-2

Role of Time in Non-Linear Analysis 5-4

Starting Nonlinear Static Analysis 5-5

Applying Material 5-6

Applying Fixtures 5-6

Applying Time Varying Force 5-7

Running the analysis 5-11

Setting Properties for Non-linear Static Analysis 5-12

Performing Non-linear Static analysis on an assembly 5-13

Starting Non-Linear Static Analysis 5-13

Applying the Material 5-14

Applying Fixtures 5-14

Applying Forces 5-14

Applying Connections 5-15

Running the analysis 5-18

Performing Nonlinear Static analysis on

a ring under application of Torque 5-19

Starting Non-Linear Static Analysis 5-19

Applying the Material 5-19

Applying Fixtures 5-19

Applying Forces 5-20

Running the analysis 5-21

2D Simplification 5-22

Starting Non-Linear Static Analysis with 2D Simplification 5-22

Apply Boundary Conditions 5-24

Interpreting Results 5-25

Chapter 6 : Non-Linear Dynamic Analysis

Non Linear Dynamic Analysis 6-2

Preparing Part and Starting Nonlinear Dynamic Analysis 6-3

Applying Material 6-5

Applying Fixtures 6-6

Applying Contact Interaction 6-7

Setting Initial Conditions 6-8

Global Damping 6-9

Rayleigh Damping 6-10

Applying Force 6-10

Running the analysis 6-11

Types of Results for Non Linear Dynamic Analysis 6-12

Setting Parameters in Nonlinear Dynamic Analysis 6-14

Newton-Raphson and Modified N-R Method 6-15

Integration Method 6-16

Chapter 7 : Frequency Analysis

Introduction 7-2

Starting Frequency Analysis 7-3

Applying Material 7-3

Applying Fixtures 7-3

Applying Forces 7-4

Setting Parameters for the analysis 7-5

Running the analysis 7-6

Results 7-6

Mass Participation 7-7

Chapter 8 : Linear Dynamic Analysis

Linear Dynamic Analysis 8-2

Objectives of a dynamic analysis 8-2

Damping 8-2

Types of Dynamic Analysis 8-5

Modal Time History Analysis 8-5

Harmonic Analysis 8-5

Random Vibration Analysis 8-6

Response Spectrum Analysis 8-7

Starting Random Vibration Analysis 8-7

Applying Material 8-8

Applying Fixtures 8-8

Applying Force Vibrations 8-8

Applying Global Damping 8-9

Running the analysis 8-9

Properties for Random Vibration Study 8-10

Modal Time History Analysis 8-12

Modal Time History Properties 8-16

Harmonic Analysis 8-17

Applying Global Damping 8-20

Harmonic Analysis Properties 8-21

Response Spectrum Analysis 8-22

Properties of Response Spectrum Analysis 8-25

Chapter 9 : Thermal Analysis

Introduction 9-2

Important terms related to Thermal Analysis 9-2

Thermal Loads 9-4

Temperature 9-4

Convection 9-7

Heat Power 9-8

Heat Flux 9-9

Radiation 9-9

Contact Set 9-10

Thermal Resistance Interaction 9-11

Bonded Interaction 9-11

Insulated Interaction 9-11

Practical on Steady State Thermal Analysis 9-12

Starting the analysis 9-12

Applying Material 9-12

Applying convection to the model 9-13

Applying heat generated by gas combustion on the head of the piston 9-13

Running the Analysis 9-14

Switching from steady state analysis to transient thermal analysis 9-16

Specifying Initial Temperature 9-18

Running the analysis 9-18

Using Probe to find out temperature 9-18

Chapter 10 : Buckling Analysis

Introduction 10-2

Use of Buckling Analysis 10-3

Starting the Buckling Analysis 10-3

Setting the Number of Buckling Modes 10-3

Applying Material 10-4

Applying Fixture 10-5

Applying the Force 10-6

Running the Analysis 10-7

Manual Solution of Buckling Analysis 10-7

Elastic Buckling Validation 10-8

Chapter 11 : Fatigue Analysis

Introduction 11-2

Stages of Failure Due to Fatigue 11-2

Starting Fatigue Analysis 11-2

Initiating Fatigue Analysis 11-5

Applying or Editing S-N data 11-6

Modifying the Static Analysis earlier performed 11-7

Running the Fatigue Analysis 11-8

Changing Properties of Fatigue Analysis 11-9

Running Constant Amplitude Events on the model 11-11

Performing Harmonic Fatigue Study 11-12

Chapter 12 : Drop-Test

Introduction 12-2

Starting Drop Test 12-2

Applying Material 12-3

Creating Mesh 12-3

Parameters for Drop 12-5

Running the Analysis 12-7

Chapter 13 : Pressure Vessel Design and Design Study

Introduction 13-2

Thermal Analysis 1 13-2

Static Analysis 1 & 2 13-2

Starting Pressure Vessel Design Study 13-3

Setup for Design Study 13-4

Running the Design Study 13-5

Design Study 13-6

Starting Design Study 13-7

Setting options for Design Study 13-8

Specifying parameters 13-9

Specifying restrictions for changes 13-11

Setting Goal for the study 13-13

Running the Study 13-14

Chapter 14 : Topology Study

Topology Study 14-2

Starting Topology Study 14-2

Applying Material 14-4

Goals and Constraints 14-5

Manufacturing Controls 14-22

Manufacturing Controls 14-22

Add Preserved Region 14-22

Specify Thickness Constraint 14-25

Specify De-Mold Direction 14-27

Specify Symmetry Plane(s) 14-28

Chapter 15 : Fundamentals of FEA

Introduction 15-2

General Description of FEM 15-2

A Brief Explanation of FEA for a Stress Analysis Problem 15-3

Finite Element Method v/s Classical Methods 15-5

FEM VS Finite Difference Method (FDM) 15-6

Need to Study FEA 15-7

Warning To FEA Package Users 15-8

Geometric Discontinuities 15-8

Discontinuity of Loads 15-9

Discontinuity of Boundary conditions 15-10

Material Discontinuity 15-10

Refining Mesh 15-11

Use of Symmetry 15-11

Higher Order Elements v/s Refined Mesh 15-11

Chapter 16 : Project on Analysis

Project 16-2

Starting Simulation 16-3

Performing the Static Analysis 16-3

Performing the Frequency Analysis 16-6

Performing Fatigue Study 16-7

Practice Questions

Preface

SolidWorks Simulation 2024 is an extension to SolidWorks package. Easy-to-use CAD-embedded analysis capabilities enable all designers and engineers to simulate and analyze design performance. You can quickly and easily employ advanced simulation techniques to optimize performance while you design, to cut down on costly prototypes, eliminate rework and delays, and save you time and development costs.

The SolidWorks Simulation 2024 Black Book, is 11th edition of the book written to help professionals as well as students in performing various tedious jobs of Finite Element Analysis. The book follows a step by step methodology. This book explains the background work running behind your simulation analysis screen. The book covers almost all the information required by a learner to master the SolidWorks Simulation. The book starts with basics of FEA, goes through all the simulation tools and ends up with practical examples of analysis. Chapters on manual FEA ensure the firm understanding of FEA concepts through SolidWorks Simulation. The book contains our special sections named Why? and notes. We have given reasons for selecting most of the options in analysis under the Why? sections. The book explains the Solver selection, iteration methods like Newton-Raphson method and integration techniques used by SolidWorks Simulation for functioning. A chapter on Topology Study helps you understand the procedures of modifying component based on analysis results. New tips and notes have been added in this book for various analyses. Some of the salient features of this book are:

In-Depth explanation of concepts

Every new topic of this book starts with the explanation of the basic concepts. In this way, the user becomes capable of relating the things with real world.

Topics Covered

Every chapter starts with a list of topics being covered in that chapter. In this way, the user can easy find the topic of his/her interest easily.

Instruction through illustration

The instructions to perform any action are provided by maximum number of illustrations so that the user can perform the actions discussed in the book easily and effectively. There are about 750 illustrations that make the learning process effective.

Tutorial point of view

The book explains the concepts through the tutorial to make the understanding of users firm and long lasting. Each chapter of the book has tutorials that are real world projects.

Why?

The book explains the reasons for selecting options or setting a parameters in tutorials explained in the book.

Project

Free projects and exercises are provided to students for practicing.

For Faculty

If you are a faculty member, then you can ask for video tutorials on any of the topic, exercise, tutorial, or concept. As faculty, you can register on our website to get electronic desk copies of our latest books, self-assessment, and solution of practical. Faculty resources are available in the Faculty Member page of our website (www.cadcamcaeworks.com) once you login. Note that faculty registration approval is manual and it may take two days for approval before you can access the faculty website.

Formatting Conventions Used in the Text

All the key terms like name of button, tool, drop-down etc. are kept bold.

Free Resources

Link to the resources used in this book are provided to the users via email. To get the resources, mail us at [e-mail] or [e-mail] with your contact information. With your contact record with us, you will be provided latest updates and informations regarding various technologies. The format to write us e-mail for resources is as follows:

Subject of E-mail as Application for resources of ............... Black Book.

You can give your information below to get updates on the book.

Name:

Course pursuing/Profession:

Contact Address:

E-mail ID:

About Author

The author of this book, Matt Weber, has authored many books on CAD/CAM/CAE books. He has also authored SolidWorks 2024 Black Book as a CAD companion for this book. SolidWorks Simulation 2024 Black Book covers details of simulation and the SolidWorks 2024 Black Book covers all the tools and techniques of modeling. The author has hand on experience on almost all the CAD/CAM/CAE packages. If you have any query/doubt in any CAD/CAM/CAE package, then you can directly contact the author by writing at [e-mail]

The technical editor of the book, Gaurav Verma, has authored books on different CAD/CAM/CAE packages. He has authored SolidWorks Flow Simulation 2024 Black Book, SolidWorks Electrical 2024 Black Book, Creo Manufacturing 10.0 Black Book, MasterCAM 2023 for SolidWorks Black Book, AutoCAD Electrical 2024 Black Book, Autodesk Inventor 2024 Black Book, Autodesk Fusion 360 Black Book (V 2.0.15293), and many others.

For Any query or suggestion

If you have any query or suggestion please let us know by mailing us on [e-mail] or [e-mail]. Your valuable constructive suggestions will be incorporated in our books and your name will be addressed in special thanks area of our books.

Chapter 1

Introduction to Simulation

The major topics covered in this chapter are:

•Simulation.

•Types of Analyses performed in SolidWorks Simulation.

•FEA

•User Interface of SolidWorks Simulation.

Simulation

Simulation is the study of effects caused on an object due to real-world loading conditions. Computer Simulation is a type of simulation which uses CAD models to represent real objects and it applies various load conditions on the model to study the real-world effects. SolidWorks Simulation is one of the Computer Simulation programs available in the market. In SolidWorks Simulation, we apply loads on a constrained model under predefined environmental conditions and check the result (visually and/or in the form of tabular data). The types of analyses that can be performed in SolidWorks are given next.

Types of Analyses Performed in SolidWorks Simulation

SolidWorks Simulation performs almost all the analyses that are generally performed in Industries. These analyses and their uses are given next.

Static Analysis

This is the most common type of analysis we perform. In this analysis, loads are applied to a body due to which the body deforms and the effects of the loads are transmitted throughout the body. To absorb the effect of loads, the body generates internal forces and reactions at the supports to balance the applied external loads. These internal forces and reactions cause stress and strain in the body. Static analysis refers to the calculation of displacements, strains, and stresses under the effect of external loads, based on some assumptions. The assumptions are as follows.

1.All loads are applied slowly and gradually until they reach their full magnitudes. After reaching their full magnitudes, load will remain constant (i.e. load will not vary against time).

2.Linearity assumption: The relationship between loads and resulting responses is linear. For example, if you double the magnitude of loads, the response of the model (displacements, strains, and stresses) will also double. You can make linearity assumption if:

•All materials in the model comply with Hooke’s Law which says stress is directly proportional to strain.

•The induced displacements are small enough to ignore the change is stiffness caused by loading.

•Boundary conditions do not vary during the application of loads. Loads must be constant in magnitude, direction, and distribution. They should not change while the model is deforming.

If the above assumptions are valid for your analysis, then you can perform Linear Static Analysis. For example, a cantilever beam fixed at one end and force applied on other end; refer to Figure-1.

If the above assumptions are not valid, then you need to perform the Non-Linear Static analysis. For example, an object attached with a spring being applied under forces; refer to Figure-2.

Dynamic Analysis

In general, we have to perform dynamic analysis on a structure when the load applied to it varies with time. The most common case of dynamic analysis is the evaluation of responses of a building due to earthquake acceleration at its base. Every structure has a tendency to vibrate at certain frequencies, called natural frequencies. Each natural frequency is associated with a certain shape, called mode shape that the model tends to assume when vibrating at that frequency. When a structure is excited by a dynamic load that coincides with one of its natural frequencies, the structure undergoes large displacements. This phenomenon is known as ‘resonance’. Damping prevents the response of the structures to resonant loads. In reality, a continuous model has an infinite number of natural frequencies. However, a finite element model has a finite number of natural frequencies that is equal to the number of degrees of freedom considered in the model.

The first few modes of a model (those with the lowest natural frequencies), are normally important. The natural frequencies and corresponding mode shapes depend on the geometry of the structure, its material properties, as well as its support conditions and static loads. The computation of natural frequencies and mode shapes is known as modal analysis. When building the geometry of a model, you usually create it based on the original (un-deformed) shape of the model. Some loading, like a structure’s self-weight, is always present and can cause considerable changes in the structure’s original geometry. These geometric changes may have, in some cases, significant impact on the structure’s modal properties. In many cases, this effect can be ignored because the induced deflections are small.

The following few topics – Random Vibration, Response Spectrum analysis, Time History analysis, Transient vibration analysis, and Vibration modal analysis are extensions of dynamic analysis.

Random Vibration

Engineers use this type of analysis to find out how a device or structure responds to steady shaking of the kind you would feel riding in a truck, rail car, rocket (when the motor is on), and so on. Also, things that are riding in the vehicle, such as on-board electronics or cargo of any kind, may need Random Vibration Analysis. The vibration generated in vehicles from the motors, road conditions, etc. is a combination of a great many frequencies from a variety of sources and has a certain random nature. Random Vibration Analysis is used by mechanical engineers who design various kinds of transportation equipment.

Response Spectrum Analysis

Engineers use this type of analysis to find out how a device or structure responds to sudden forces or shocks. It is assumed that these shocks or forces occur at boundary points, which are normally fixed. An example would be a building, dam, or nuclear reactor when an earthquake strikes. During an earthquake, violent shaking occurs. This shaking transmits into the structure or device at the points where they are attached to the ground (boundary points).

Mechanical engineers who design components for nuclear power plants must use response spectrum analysis as well. Such components might include nuclear reactor parts, pumps, valves, piping, condensers, etc. When an engineer uses response spectrum analysis, he is looking for the maximum stresses or acceleration, velocity and displacements that occur after the shock. These in turn lead to maximum stresses.

Time History Analysis

This analysis plots response (displacements, velocities, accelerations, internal forces, etc.) of the structure against time due to dynamic excitation applied on the structure.

Transient Vibration Analysis

When you strike a guitar string or a tuning fork, it goes from a state of inactivity into a vibration to make a musical tone. This tone seems loudest at first, then gradually dies out. Conditions are changing from the first moment the note is struck. When an electric motor is started up, it eventually reaches a steady state of operation. But to get there, it starts from zero RPM and passes through an infinite number of speeds until it attains the operating speed. Every time you rev the motor in your car, you are creating transient vibration. When things vibrate, internal stresses are created by the vibration. These stresses can be devastating if resonance occurs between a device producing vibration and a structure responding to. A bridge may vibrate in the wind or when cars and trucks go across it. Very complex vibration patterns can occur. Because things are constantly changing, engineers must know what the frequencies and stresses are at all moments in time. Sometimes transient vibrations are extremely violent and short-lived. Imagine a torpedo striking the side of a ship and exploding, or a car slamming into a concrete abutment or dropping a coffeepot on a hard floor. Such vibrations are called shock, which is just what you would imagine. In real life, shock is rarely a good thing and almost always unplanned. But shocks occur anyhow. Because of vibration, shock is always more devastating than if the same force were applied gradually.

Vibration Analysis (Modal Analysis)

By its very nature, vibration involves repetitive motion. Each occurrence of a complete motion sequence is called a cycle. Frequency is defined as so many cycles in a given time period. Cycles per seconds or Hertz. Individual parts have what engineers call natural frequencies. For example, a violin string at a certain tension will vibrate only at a set number of frequencies, which is why you can produce specific musical tones. There is a base frequency in which the entire string is going back and forth in a simple bow shape.

Harmonics and overtones occur because individual sections of the string can vibrate independently within the larger vibration. These various shapes are called modes. The base frequency is said to vibrate in the first mode, and so on up the ladder. Each mode shape will have an associated frequency. Higher mode shapes have higher frequencies. The most disastrous kinds of consequences occur when a power-driven device such as a motor for example, produces a frequency at which an attached structure naturally vibrates. This event is called resonance. If sufficient power is applied, the attached structure will be destroyed. Note that ancient armies, which normally marched in step, were taken out of step when crossing bridges. Should the beat of the marching feet align with a natural frequency of the bridge, it could fall down. Engineers must design so that resonance does not occur during regular operation of machines. This is a major purpose of Modal Analysis. Ideally, the first mode has a frequency higher than any potential driving frequency. Frequently, resonance cannot be avoided, especially for short periods of time. For example, when a motor comes up to speed it produces a variety of frequencies. So it may pass through a resonant frequency.

Buckling Analysis

If you press down on an empty soft drink can with your hand, not much will seem to happen. If you put the can on the floor and gradually increase the force by stepping down on it with your foot, at some point it will suddenly squash. This sudden scrunching is known as buckling.

Models with thin parts tend to buckle under axial loading. Buckling can be defined as the sudden deformation, which occurs when the stored membrane(axial) energy is converted into bending energy with no change in