# Introduction to Dynamics using Finite Elements Analysis (FEA)

 Duration: 1 day Delivery: E-learningOnsite Classroom Language: English Level: Introductory Availability: Worldwide Tutor(s): Tony Abbey

• Do you know if your model is realistic?
• What is the importance of normal modes analysis?
• How do you calculate transient and frequency response input parameters effectively?

### Get the answers to these questions and more with this industry-leading, code-independent course.

This course covers a range of topics, all aimed at structural designers and engineers who are moving into the area of dynamic analysis, including:

• Normal Modes Analysis
• Damping
• Modal Coordinates
• Modal effective Mass
• Transient Response
• Frequency Response

## What will you learn?

• The importance of normal modes analysis
• Techniques for identifying and characterising normal modes
• Roadmaps for simple and effective calculation of transient and frequency response input parameters
• A QA checklist covering normal modes and dynamic response analysis
• Practical hints and tips on all aspects of normal modes and dynamic response analysis

## What questions will this course answer?

• What are the most important dynamic analysis topics?
• What theoretical background do I need to understand the implications of my analysis?
• What practical hints and tips do I need to be able to carry out analysis effectively?

## Who should attend?

Designers and engineers who are moving into the area of dynamic analysis. Familiarity with FEA is assumed, but no other background knowledge is required.

The objective of this course is to break down any Dynamics problem into clearly defined steps and show how to successfully implement practical solutions using Finite Element Analysis.

Dynamic analysis needs a clear set of objectives and analysis plan to:

• Predict what natural frequencies will be important
• Avoid guessing the size or number of time steps in a transient analysis
• Adopt an accurate and logical method to define frequency response calculation points
• Make informed decisions on damping
• Make an engineering assessment – is your model realistic
• Check the answers – guilty until proven innocent!

This class covers all the FEA solution types required to carry out normal modes and basic frequency response analysis.

## Course Program

### Background to Dynamics

• 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
• Eigenvector normalization
• Importance of Mode Identification – use of post-processing
• Checklist for Normal Modes assessment

### Dynamics in FEA

• Homework Review
• 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

### Dynamic Analysis Building Blocks

• Homework Review
• Modal Coordinates
• Introduction to Modal Effective Mass
• Introduction to Damping
• Damped, Free vibration
• Forms of Damping
• Practical Damping
• Workshops

### Overview of Response Analysis

• Homework Review
• Modal and Direct methods
• Residual Vectors
• Introduction to Forcing Functions and Damping
• Damped, Forced vibration
• Workshops

### Transient Analysis

• Homework Review
• Transient Analysis background
• Direct Transient Analysis
• Direct Transient Examples
• Accurate time step prediction, results checking, aliasing
• Modal Transient Analysis
• Modal Transient Examples
• Dynamic Base Motion
• Base Motion Examples

### Frequency Response Analysis

• Homework Review
• Frequency Response Analysis background
• 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 - importance of peaks and spectral spread

## PSE Competencies addressed by this training course

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

### Interested in this Course?

Please complete this form if you are interested in scheduling an on-site training session, or if you would like to be notified of the next public course session.

#### Notes:

Six Session Online Training Course - 2 hours per session also available as a 3-Day Course, contact Tricia Hughes, our Corporate Training Executive for more info.