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The University of Southampton

ISVR6146 Vibration Engineering Practice

Module Overview

Vibration and shock of engineered structures occur due to dynamic loads arising during operation, e.g. in transportation vehicles, motors/generators and buildings. Analytical and numerical prediction tools are required during virtual prototyping to design structures to withstand their in-service loads, whilst experimental techniques are generally applied to scale models, components and assembled structures for model validation, parameter estimation and trouble-shooting purposes. By the end of this module you will have gained an appreciation for commonly occurring vibration and shock phenomena and the predictive and experimental tools available to design and mitigate against them. Whilst focussed on industrial tools of the trade, this module begins briefly with analytical descriptions of beams and plates. Such simple structural components often prove useful qualitative models in practical situations and provide helpful insight into vital concepts. For quantitative predictions, finite element (FE) analysis is universally used to obtain mass and stiffness matrices of distributed and complex structures. FE analysis is introduced briefly but the emphasis is on analysis options available in commercial software for condensing such models, computing modal and harmonic solutions and incorporating damping. Common sources of vibration are discussed, and methods are met for characterising and modelling sources. Two specific and ubiquitous examples are considered in detail: random excitation, which has implications for structural fatigue, and rotating machinery. The most commonly used experimental technique is that of transfer function measurement, from which modes of vibration can be inferred. Almost invariably, transfer functions are measured using either an instrumented hammer test or a shaker test, both of which enable the structure to be excited in a controlled and measurable way. Both techniques are discussed in detail, and you will become competent at hammer testing through a practical laboratory. Another type of vibration testing concerns the structural integrity of components and structures that are subjected to large dynamic loads, such as electronic equipment during a rocket launch. Commonly used standards for such tests are outlined, and a visit to a commercial test facility may be possible.

Aims and Objectives

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

  • An in-depth knowledge of the theoretical framework for both continuous and discrete structural dynamic models
  • An understanding of the benefits and limitations of characterising the dynamics of a structure in terms of its vibration modes
  • An understanding of the process and limitations of Finite Element Analysis (FEA) for built-up structures
  • Familiarity with typical vibration instrumentation and how it can be used to measure quantities of interest
  • Knowledge of commonly occurring vibration sources and their symptomatic responses
Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

  • Ability to analyse the free and forced behaviour of simple structures using the modal approach
  • Ability to select an appropriate experimental technique for diagnosing or characterising a vibration problem.
Transferable and Generic Skills

Having successfully completed this module you will be able to:

  • Ability to translate mathematical formulations into computer code such as Python or Matlab
  • Ability to question the validity of modelling assumptions in the light of experimental data
Subject Specific Practical Skills

Having successfully completed this module you will be able to:

  • Ability to perform a vibration based transfer function measurement using an instrumented hammer and a commercial frequency analyser
  • Ability to assess the reliability of measured transfer functions
  • Ability to process/interpret measured transfer functions using an experimental modal analysis technique


Introduction - 1 Lecture: - Showcase of some industrial vibration problems and module overview Continuous Systems - 3 Lectures - Equations of motion, characteristic equations, free vibration, forced vibration, modal summation. - Timoshenko beam theory and then reduction to Euler-Bernoulli beam theory. - Love-Kirchhoff plate theory and approximate solutions/descriptions. Discrete Multiple Degree of Freedom (MDOF) systems - 6 Lectures - Review of 2 DOF & extension to n DOF systems. - Free response (eigen problem), orthogonality and scaling of modes. - Forced response (direct and modal summation). - Use of finite element analysis to obtain system matrices. - Model reduction (Guyan) - Damping matrices, normal and complex modes, damping loss factor. Rotating machinery - 3 Lectures - Lumped parameter models - Shaft whirling - Gyroscopic effects - Campbell diagrams - Order analysis Experimental techniques - 7 Lectures - 1 Lab (3hrs) - Transfer function measurement (instrumentation, shaker & hammer testing). - Experimental modal analysis (quad picking, circle fitting, rational fraction polynomial method). - Model validation (Modal Assurance Criterion, modal energy distributions) - Qualification testing (MIL and other standards) Random vibration - 6 Lectures - Time and frequency domain representations (excitation and response) - Fatigue under random vibration – cycle counting and spectral methods - Structural response prediction under random vibration Shock - 3 Lectures - Force and motion inputs - Shock Response Spectra (SRS) - Shock isolation - Nonlinear shock mounts Sources of vibration – 3 Lectures - Self-excited, impacts, reciprocating mass, acoustic (e.g. aerospace and space/launch vehicles), flow related excitation and electrical transformers. - Source characterisation (force and velocity sources) - Vibration isolation (with resonant source and receiver) - Transfer Path Analysis

Learning and Teaching

Teaching and learning methods

Teaching sessions include PowerPoint based lectures, tutorials, an in-class quiz and a supervised hands-on laboratory. The two assignments facilitate independent study in numerical and experimental methods.

Completion of assessment task50
Follow-up work20
Preparation for scheduled sessions5
Specialist Laboratory 3
Total study time150



MethodPercentage contribution
Closed book Examination  (2 hours) 70%
Quantitative practical write-up 15%
Simulation 15%


MethodPercentage contribution
Examination 100%

Repeat Information

Repeat type: Internal

Linked modules

Pre-requisites: FEEG2002 or ISVR6141

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