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- Introduction to Dynamics using FEA

- 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?

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

- 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 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?

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.

- 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

- 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

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

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

- 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

- 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

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. |

**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.**

- Advanced Dynamic Finite Element Analysis
- Basic Finite Element Analysis
- Composite Finite Element Analysis
- Computational Fluid Dynamics for Structural Designers and Analysts
- Elements of Turbulence Modeling
- Fatigue & Fracture Mechanics in Finite Element Analysis
- Introduction to Dynamics using FEA
- Introduction to Engineering Simulation for Non-Specialists
- Introduction to Practical Computational Fluid Dynamics
- Non-Linear Finite Element Analysis
- Practical Modelling of Joints and Connections
- Structural Optimization in Finite Element Analysis
- 10 Steps to Successful Explicit Dynamic Analysis

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