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Dynamic Finite Element Analysis 

NAFEMS e-Learning Course    

Basic & Advanced Classes

Choose to take the Basic class (5 sessions), or the Advanced class (3 sessions), or both (8 sessions)

Course Overview

Many problems facing designers and engineers are dynamic in nature. The response of a structure cannot be simply assessed using static assumptions.

The nature of the problem may be to understand the resonant frequencies of your design, so that key driving frequencies such as equipment rotational speed, acoustic or external pressure frequencies, ground motion frequency content or vehicle passing frequency.

Your design may face external driving forces from adjacent components; cams, push rods, pistons or from vehicle input sources such as a bumpy road, wave loading, air pressure or inertial forces.

Whatever the nature of the challenge, this objective of this course is to break down the dynamic problem into clearly defined steps, give an overview of the physics involved and show how to successfully implement practical solutions using Finite Element Analysis.

Modular Approach

The course is broken down into two Modules, a Basic Section and an Advanced Section. The two Modules are arranged to run sequentially so attendees have the option to select one or both. There is no pre-requisite on the Advanced Module to attend the Basic Module. Similarly, continuing to the Advanced Module is optional for those on the Basic Module.

Course Process and Details 

This course is completely code independent. No software is required.

Each topic in the class is treated as a building block and is presented using an overview of the physics and theory involved. The math is kept simple and the emphasis is on practical examples from real life to illustrate the topic. The mapping to Finite Element analysis techniques is shown with numerous workshops. The tutor will be running analysis interactively and involving the students in the process via Q and A periods during each session, follow up emails and a Course Bulletin Board

Students are shown the various approximation methods and how to judge which are acceptable and appropriate for solving a wide range of practical problems. Practical considerations of loadings, boundary conditions, damping and  structural details are shown by numerous examples.

Of equal importance is the assessment and interpretation of results. This starts with ensuring the modal frequencies and mode shapes are feasible and accurate. Techniques are shown to confirm this and to make sure the basic modal response of a design is fully understood. Comparison against test or hand calculations is shown. A range of hints and tips are shown for producing subsequent efficient and accurate response analyses.

Interaction is encouraged throughout the course, with the planning and design of complete FEA projects. Options for mass and stiffness modeling, damping, loads and boundary conditions and solution methods are discussed interactively with the students.  The tutor then runs the analyses using this input and the results are investigated. Using this approach, classic errors are shown and corrected in a real world scenario.

The session covers a wide range of application techniques available and shows typical applications and best practices across industry. The objective is to show students how to assess the nature of the dynamic environment and what tools can be used, together with the scope of the various solutions.

Students are welcome to send in problems from Industry and these will be discussed as time permits.

Full notes are provided for the students, together with personal passwords for e-learning backup material, bulletin board access, etc.

Supporting Excel Spreadsheets are provided to illustrate the processes and allow experimentation. These are free to the students. Many students have found them useful tools outside of the training course.

Students will join the audio portion of the meetings by utilizing the VoIP (i.e. headset connected to the computer via headphone and microphone jacks) or by calling into a standard toll line. If you are interested in additional pricing to call-in using a toll-free line, please send an email to: e-learning @ .

Who Should Attend?

This course is aimed at practicing engineers who wish to learn more about how to apply finite element techniques to dynamic analysis in the most effective manner. Ideally a student should have some experience of FEA analysis, but this is not essential. The material that is presented is independent of any particular software package, making it ideally suited to current and potential users of all commercial finite element software systems. This course is a must for all engineers aiming to use Finite Element Analysis as a reliable predictive tool for dynamic analysis.

E-learning classes are ideal for companies with a group of engineers requiring training. E-learning classes can be provided to suit your needs and timescale. Contact us to discuss your requirements.

Course Program

Note: Each session represents one 2-hour session each week (Note: Sessions may last for 2.5-3 hours, including the Q&A sessions.) Recordings of each session are made available to course attendees in the event they are unable to participate in one or more of the live meetings, or if they wish to review the material following each session. 

Basic Dynamics

Session BD1:

  • Introductions
  • FEA Overview
  • What are Natural Frequencies, Normal Modes
  • Equation of Motion
  • Undamped Free Vibration
  • Undamped Single Degree of Freedom Systems
  • Undamped Multiple Degrees of Freedom
  • Eigen vector normalization
  • Importance of Mode Identification – use of post processing
  • Checklist for Normal Modes assessment
  • Homework session 1

Session BD2:

  • Review Homework
  • Eigenvalue Extraction Methods
  • Rigid Body Modes
  • Importance of Mass modeling
  • Accurate Idealization – joints and boundary conditions
  • Meshing quality
  • Typical Errors
  • QA for normal modes analysis
  • Modal Coordinates
  • Introduction to Modal Effective Mass
  • Homework session 2

Session BD3:

  • Homework Review
  • Introduction to Damping
  • Damped, Free vibration
  • Practical Damping
  • Overview of Response Analysis
  • Modal and Direct methods
  • Introduction to Forcing Functions and Damping
  • Damped, Forced vibration
  • Workshops
  • Homework session 3

Session BD4:

  • Homework Review
  • Transient Analysis background
  • Direct Transient Analysis
  • Examples
  • Accurate time step prediction
  • Results checking
  • Errors and traps
  • Examples
  • Base Motion
  • Examples
  • Homework session 4

Session BD5:

  • Homework Review
  • Frequency Response Analysis refresher
  • Direct Frequency Response
  • Strategy for Frequency Response calculation points
  • Example with Direct Frequency Response Analysis
  • Modal Frequency Response
  • Example with Modal Frequency Response Analysis
  • Checking Frequency response, importance of peaks and spectral spread
  • Homework session 5

Advanced Dynamics

Session AD1:

  • Importance of Dynamic Effects in Shock
  • Shock Spectra Analysis
  • Response Spectra Overview
  • DDAM overview
  • Response Spectra Analysis – creation of a spectra
  • Response Spectra Analysis – application of a spectra
  • Examples
  • Homework session 1

Session AD2:

  • Homework Review 
  • Probability and Random theory review
  • PSD definition
  • Random FE Analysis Overview
  • Application of Random Analysis results for Fatigue
  • Checking with Miles Equation
  • Examples
  • Homework session 2

Session AD3:

  • Homework Review
  • Dynamic Nonlinearity
  • Nonlinear Strategy
  • Example of Geometric Nonlinearity
    • Theoretical Solution
    • Numerical solution
  • Background to Material Nonlinearity
  • Example of Material Nonlinearity
    • Theoretical Solutions
    • Numerical solutions
  • Overview of Implicit versus Explicit Solutions
  • Examples

Feedback from former Dynamic FE Analysis e-Learning students:

"This course did everything right. From organization to presentation to interaction, this is a good model for what online training should be."   B.T.

"Tony's command over the subject and excellent teaching skills made this course worthwhile." G.K.

"Super! Doesn't get better than this. Good idea to start having e-Learning courses." R.P.

"I'm really happy not to pay a big fraction of my annual training budget to airlines and hotels. A BIG plus to e-learning."V.G.


The PSE Competencies from the Dynamics and Vibration technical area that are addressed by this training course are listed below.

IDCompetence StatementTraining Course
DVkn1 State Newton's 2nd Law or, equivalently, the d'Alembert Force Method. Basic Dynamics
DVkn2 Define the relationships amongst instantaneous acceleration, velocity and distance. Basic Dynamics
DVkn3 Define the basic equation for Kinetic Energy. Basic Dynamics
DVkn7 State the Mass Moment of Inertia in general and define it for a circular cylindrical rod rotating about an end. Basic Dynamics
DVkn9 Define the terms frequency, period, phase angle, and amplitude for a harmonic time signal Basic Dynamics
DVkn10 State the typical matrix structure of the discrete differential equation system for linear MDOF systems Basic Dynamics
DVkn11 Define the terms free and forced vibration Basic Dynamics
DVkn12 State typical values for damping in various engineering structures. Basic Dynamics
DVco5 Explain the term Instantaneous Centre of Zero Velocity. Basic Dynamics
DVco9 Explain the term Conservative Forces, Potential, and Strain energy Basic Dynamics
DVco12 Explain the use of physical, analytical and mathematical models in a structural dynamics modelling process. Basic Dynamics
DVco13 Discuss the full discrete linear differential Equation of Motion in matrix terms and explain the terms Free Response and No Damping. Basic Dynamics
DVco14 Explain the derivation of the General Matrix Eigenvalue Problem (characteristic equation) from the Equation of Motion. Basic Dynamics
DVco15 Explain different physical forms of Dynamic Loading (Excitation) in a Force Response analysis. Basic Dynamics
DVco16 Explain Harmonic, Periodic, Transient, and Random time response. Basic Dynamics
DVco18 Explain steady-state response for harmonic excitation. Basic Dynamics
DVco19 Explain the term complex Frequency-Response Function, Magnification Factor, and Phase Angle in relation to frequency ratio and damping. Basic Dynamics
DVco20 Discuss the term Natural Frequency in relation to a continuum and a discretized system. Basic Dynamics
DVco21 Discuss the phenomenon of Resonance. Basic Dynamics
DVco22 Explain the terms Mode Shape/Eigenvector, Modal Mass, Modal Damping, and Modal Stiffness Factors. Basic Dynamics
DVco24 Discuss the variables in an Impact Analysis. Advanced Dynamics
DVco25 Discuss the characteristics of mass and damping matrices. Basic Dynamics
DVco26 Describe the difference between Viscous, Dry-Friction (Coulomb), and Hysteretic Damping. Basic Dynamics
DVco27 Describe the effect of damping on natural frequencies and resonance. Basic Dynamics
DVco28 Describe Free Vibration of undamped and damped systems. Basic Dynamics
DVco29 Explain the Logarithmic Decrement Method. Basic Dynamics
DVco30 Discuss the concept of mass and stiffness proportional (Rayleigh) damping. Basic Dynamics
DVco31 Discuss the term non-proportional damping. Advanced Dynamics
DVco33 Discuss the steady state and total response of a damped system subjected to harmonic excitation. Basic Dynamics
DVco34 Describe the terms Intertia force, Damping force and Stiffness force. Basic Dynamics
DVco35 Discuss the integral equation for element mass, highlighting the variables which it is dependent upon. Basic Dynamics
DVco37 Describe the terms Lumped mass matrix and Consistent mass matrix and identify which formulation is appropriate to elements being used. Basic Dynamics
DVco38 Discuss various strategies for extraction of eigenvalues and mode shapes, including Lanczos and Subspace Iteration. Basic Dynamics
DVco39 Discuss how the solution of the Free Vibration Problem depends upon a truncation of range of natural frequencies and mode shapes. Basic Dynamics
DVco40 Explain methods to compare Experimental with Analytical Modal Analysis data (e.g., MAC, COMAC). Basic Dynamics
DVco42 Explain why in a free vibration problem, an analysis system may report 6 frequencies of small magnitude. Basic Dynamics
DVco44 Explain the terms Implicit Solution and Explicit Solution for the time integration of the equations of motion and the appropriate associated problem classes of dynamic analyses. Advanced Dynamics
DVco45 Contrast Modal Superposition and Direct Time Integration methods for transient response analysis. Basic Dynamics
DVco47 Contrast mesh density requirements in static and dynamic problems. Basic Dynamics
DVco48 Discuss why joints can prove to be problematic in a dynamic analysis. Basic Dynamics
DVco49 Discuss possible sources of nonlinearity in a dynamic problem. Advanced Dynamics
DVco50 Explain the term Power Spectral Density. Advanced Dynamics
Dvco53 Discuss frequency range obtainable by FE modal analysis. Basic Dynamics
DVco54 Discuss various approaches to Seismic Analysis and highlight relevant philosophy and analysis considerations. Advanced Dynamics
DVco56 Explain the term response spectra. Advanced Dynamics
DVap1 Employ Free Body Diagrams effectively, showing initial and final conditions where appropriate. Basic Dynamics
DVap3 Employ a range of post-solution checks to determine the integrity of dynamic FEA results. Basic Dynamics
DVap5 Employ an analysis system for the determination of natural frequencies and mode shapes. Basic Dynamics
DVap6 Employ an analysis system for the determination of steady state response and frequency response function for a periodic excitation Basic Dynamics
DVap7 Employ an analysis system for the determination of transient response in a range of linear and nonlinear systems. Basic and Advanced Dyanmics
DVap8 Employ an analysis system for the determination of seismic response in a range of linear and nonlinear systems. Basic and Advanced Dyanmics
DVap9 Employ an analysis system for the determination of response in a range of linear and nonlinear systems, to random vibration. Advanced Dynamics
DVap10 Employ an analysis system for the simulation of impact. Advanced Dynamics
DVap11 Employ an analysis system for the determination of dynamic stresses, where appropriate. Basic Dynamics
DVap13 Illustrate the approximate nature of finite element analysis, through dynamic examples chosen from your industry sector. Basic Dynamics
DVan1 Analyse the results from dynamic analyses and determine whether they are consistent with assumptions made and the objectives of the analysis. Basic Dynamics
DVan2 Analyse the results from and modelling for dynamic analyses by comparing measured modal data (EMA) with those obtained from FE analytical modal analysis. Basic Dynamics
DVsy1 Prepare a dynamic analysis specification, highlighting any assumptions relating to geometry, mass distribution, loads, boundary conditions, damping, and material properties. Basic Dynamics
DVsy2 Plan a dynamic analysis, specifying necessary resources and timescale. Basic Dynamics
DVsy3 Prepare quality assurance procedures for dynamic finite element analysis activities within an organisation. Basic Dynamics
DVsy4 Specify ancillary Pilot Studies and complementary Experimental Studies, where appropriate. Basic Dynamics
DVev1 Select appropriate idealisation(s) for components / structures, which are consistent with the objectives of the dynamic analyses. Basic Dynamics
DVev2 Assess the significance of neglecting any feature or detail in any dynamic idealisation. Basic Dynamics
DVev3 Assess the significance of simplifying geometry, material models, mass, loads or boundary conditions and damping assumptions on a dynamic analysis. Basic Dynamics

Special Note(s):

Telephony surcharges may apply for attendees who are located outside of North America, South America and Europe. These surcharges are related to individuals who join the audio portion of the web-meeting by calling in to the provided toll/toll-free teleconferencing lines. We have made a VoIP option available so anyone attending the class can join using a headset (headphones w/ microphone) connected to the computer. There is no associated surcharge to utilize the VoIP option, and is actually encouraged to ensure NAFEMS is able to keep the e-Learning course fees as low as possible. Please send an email to the e-Learning coordinator (e-learning @ ) to determine if these surcharges may apply to your specific case. 

Just as with a live face-to-face training course, each registration only covers one person. If you plan to register a large group (5+), please send an email to e-learning @ in advance for group discounts.

Related News:

Review the NAFEMS "Introductory Dynamic Finite Element Analysis " webinar presented by Tony Abbey on April 2nd, 2009. The purpose of this webinar is to provide some technical content to the NAFEMS community, and to introduce the Dynamic FE Analysis e-Learning course listed on this page.

For more information, please email e-learning @ .

Upcoming Session:

View the NAFEMS Professional Simulation Engineer competence statements addressed by this training course.

Not Available to Attend this Time? 

Would you like us to notify you when the next course on Fluid Dynamics Review for CFD is open for enrollment? If so, add yourself to the eLearning Waitlist!

Course Tutor:
Tony Abbey 

Tony Abbey - NAFEMS Tutor

Read Tony Abbey's bio on the NAFEMS tutors page