The University of Southampton
Courses

# ISVR6141 Fundamentals of Vibration

## Module Overview

Vibrations are the oscillation of a mechanical structure. Vibration may be desirable as in the strings of a guitar or in the human vocal cords. More often vibrations are undesirable as for the vibrations of an electrical motor or of an entire car. In both case modelling can inform the designer so that vibration can be precisely obtained or avoided. Although the optimal and cost effective way to minimise the vibration of a structure is by careful engineering early in the design cycle, frequently the engineer must turn to palliative measures to control vibration at a stage in the design when even minor modifications to the structure are prohibitively costly or detrimental to other performance targets. The general aims of this module are to introduce students with little or no previous experience of mechanical vibrations, and with quite different backgrounds, to the basic concepts of vibrational behaviour, to provide a general introduction to vibration modelling, analysis and control and to give students some experience of vibration measurement. This module also promotes the principles which can influence the design process of mechanical structures and it presents a number of commonly adopted techniques for trouble-shooting vibration problems.

### Aims and Objectives

#### Module Aims

• To introduce students with little or no previous experience of mechanical vibrations to the basic concept of vibrational behaviour. • To introduce the main theoretical procedures used for the analysis of practical vibration problems. • To demonstrate the influence of the various model parameters on vibrational behaviour. • To give students the understanding of the basic methods to face vibration problems. • To give students some experience of vibration measurement.

#### Learning Outcomes

##### Disciplinary Specific Learning Outcomes

Having successfully completed this module you will be able to:

• Interpret the behaviour of vibrating systems through an understanding of basic principles and the role of mass, stiffness and damping.
• Select appropriate techniques for the solution of analytical problems in vibrations.
• Undertake measurement of vibration quantities and measure modes of vibration on a simple structure
• Describe the behaviour of structures by modal and wave approaches.
• Develop the equations of motion for free and forced vibration of simple systems.
• Show understanding of the benefits and limitations of basic vibration control methods

### Syllabus

1. Introduction (2 sessions) Vibration problems in engineering. Terminology. Basic principles. 2. Single degree of freedom system (6 sessions) Free vibration of mass-spring system: natural frequency. Free vibration with damping: damping factor. Energy methods. Time harmonic forced vibration: resonance. Isolation, base excitation and other applications. Structural damping. Transient vibration; response to transient excitation; Duhamel’s Integral; forced vibration with various loads including earthquake; impulse response. 3. Multiple degree of freedom systems (4 sessions) Free vibration of two degree of freedom systems: developing stiffness and mass matrices for lumped parameter systems, modes of vibration, natural frequencies and mode shapes. Multiple degree of freedom systems: matrix methods. Time harmonic forced vibration with damping: modal decomposition. Time domain solutions. Multi-storey structure. Introduction to vibration treatment and dynamic vibration absorbers. 4. Modelling methods (3 sessions) Rayleigh’s method. Lagrange’s equations for free undamped vibration. Applications. Finite Element Method (FEM) basis. 5. Continuous systems (6 sessions) Free vibrations of strings, bars and shafts: equation of motion, boundary conditions. Modes of vibration: natural frequencies and mode shapes. Bending vibration of beams. Forced vibration of continuous systems: modes and resonance. Introduction to structural wave motion in one dimension: propagation, reflection and transmission; coincidence. 6. Fundamentals of Vibration Control (5 sessions) Sources of vibration. Mobility/Impedance Methods. Vibration Isolation: mobility approach, energy considerations. . Vibration Damping (different types of damping, viscoelastic damping, damping treatments, measurements of damping). 7. Vibration measurement and analysis (Lab sessions) Vibration transducers and measurement of frequency response functions and modal damping.

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### Learning and Teaching

#### Teaching and learning methods

TypeHours
Supervised time in studio/workshop6
Revision93
Tutorial3
Lecture24
Total study time150

Frank Fahy and John Walker Editors (2004). Advanced Applications in Acoustics, Noise and Vibration.

F J Fahy J G Walker (eds) (1998). Fundamentals of Noise and Vibration.

WT Thomson, Unwin Hyman (1993). Theory of Vibration with Applications.

S S Rao,Addison-Wesley (2011). Mechanical Vibrations.

### Assessment

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#### Summative

MethodPercentage contribution
Exam  (120 minutes) 80%
Laboratory Report 10%
Laboratory Report 10%

#### Referral

MethodPercentage contribution
Exam  (120 minutes) 100%

#### Repeat Information

Repeat type: Internal & External