Vibration Engineering Practice | ISVR6146 | University of Southampton

Module overview

Vibration and shock affect engineered structures whenever dynamic loads arise in operation, from vehicles and motors to buildings. Analytical and numerical tools are needed during virtual prototyping to design structures that withstand their in-service loads, while experimental techniques are applied to models, components and assemblies for validation, parameter estimation and troubleshooting. By the end of this module you will appreciate common vibration phenomena and the predictive and experimental tools used to design and mitigate against them. Whilst focused on the industrial tools of the trade, the module begins briefly with analytical descriptions of beams and plates, which provide useful qualitative models and insight into vital concepts. For quantitative predictions, finite element (FE) analysis is universally used to obtain the mass and stiffness matrices of complex structures. FE analysis is introduced briefly, but the emphasis is on the options available in commercial software for condensing models, computing modal and harmonic solutions and incorporating damping. The most common experimental technique is transfer function measurement, from which modes of vibration can be inferred, usually via an instrumented hammer or shaker test. Both are discussed in detail, and you will become competent at conducting hammer testing and interpreting data through a practical laboratory. The second half of the module comprises a hands-on investigation, undertaken in small groups, in which you select and apply the most appropriate measurement, analysis, simulation and mitigation strategies to solve a practical problem and report your findings to a fictitious client. Talks are also scheduled on unassessed topics of special interest, possible examples include shock response, FE model validation, digital twin modelling and rotating machinery. By the end, you will be equipped to predict, measure and control vibration in real structures, ready for professional work and advanced study in structural dynamics.

Linked modules

Pre-requisites: FEEG2002 or ISVR6141

Aims and Objectives

Learning Outcomes

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.

Knowledge and Understanding

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

An understanding of the benefits and limitations of characterising the dynamics of a structure in terms of its vibration modes
An in-depth knowledge of the theoretical framework for both continuous and discrete structural dynamic models
Knowledge of commonly occurring vibration sources and their symptomatic responses
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

Full CEng Programme Level Learning Outcomes

Having successfully completed this module you will be able to:

Comprehensive treatment of the principles of how structures and systems vibrate and how this is modelled and measured in industry, referring to standards where appropriate. There is a specific focus on how to deal with complex systems judiciously, e.g. choices of model reduction and options for damping models. Finite element model validation is also covered, which is a research interest of the module lead.
The laboratory offers a range of instrumentation and students are required to select and use that which is most appropriate. They follow an experimental process, the success of which is critically dependent on a range of decisions, particularly in relation to signal processing parameters.
Students select and apply analytical modelling techniques to predict the response of structures to harmonic, random and transient forces. They implement a computational (finite element) model of a structure from scratch in Matlab/Python and discuss the limitations of the results obtained.
Students complete a practical laboratory to investigate the intrinsic vibration characteristics of an engineered component. This involves the use of industry standard instrumentation. They follow best practice, but are also encouraged to deviate from it specifically to demonstrate its importance.
Students complete a vibration experiment on an engineered component and are required to apply principles of vibration and signal processing to the interpretation of data. They are required to discuss limitations of the techniques and how best to acquire a necessarily incomplete dataset that best captures the features of interest.

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

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

Syllabus

Introduction - Showcase of some industrial vibration problems and module overview Continuous Systems - 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 - 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 - Damping models - Model reduction (Guyan) Rotating machinery - Lumped parameter models - Shaft whirling - Gyroscopic effects - Campbell diagrams - Order analysis - Balancing (BS ISO 21940-1:2019 Mechanical vibration. Rotor balancing. Introduction). Experimental techniques - 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 (BS EN 60068-2-64:2008+A1:2019 (Environmental testing. Tests. Vibration, broadband random and guidance, BS EN 60068-2-80:2005 Environmental testing). Random vibration - Time and frequency domain representations (excitation and response) - Structural response prediction under random vibration Shock - 'Classic' shock inputs - Methods for computing response - Shock Response Spectra (BS ISO 18431-4:2007, MIL-STD-810H) - Industrial case study Sources of vibration - 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) - Elastomeric isolation mounts: characteristics and dynamic stiffness measurement (ISO 10846- parts 1-3)

Learning and Teaching

Teaching and learning methods

Teaching sessions include PowerPoint based lectures, tutorials, and a supervised hands-on practical sessions. During the first half of the module. students develop understanding of and competences in modelling and experimentation through two summatively assessed exercises. In the second half of the module, students complete an investigation in which they select and apply the most appropriate measurement, analysis, simulation and mitigation strategies studied previously to address a practical problem.

Study time
Type	Hours
Preparation for scheduled sessions	32
Practical classes and workshops	5
Completion of assessment task	40
Wider reading or practice	40
Lecture	30
Specialist Laboratory	3
Total study time	150

Assessment

Summative

This is how we’ll formally assess what you have learned in this module.

Breakdown
Method	Percentage contribution
Simulation	25%
Quantitative practical write-up	25%
Consultancy Report	50%

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.

Breakdown
Method	Percentage contribution
Quantitative practical write-up	25%
Consultancy Report	50%
Simulation	25%

Repeat Information

Repeat type: Internal