Engineering and the Environment, University of Southampton

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

• The analysis of simple vibrating systems
• The way in which damping affects a vibrating system
• Various ways of measuring damping
• The factors governing the transient response of a single-degree-of-freedom system

Cognitive (thinking) skills
Having successfully completed the module, you will be able to:

• Read, understand and interpret introductory literature relating to vibration
• Develop an analytical model of a simple practical system and be able to analyse this system

Practical, subject specific skills
Having successfully completed the module, you will be able to:

• Design an experiment to measure damping
  
• Choose appropriate damping treatment for a vibration problem

Key transferable skills
Having successfully completed the module, you will be better able to:

• Carry out experimental work
• Write-up laboratory work
• Use MATLAB to process experimental data

The aim of this module is to:

·give students an understanding of the mechanisms of damping
·to introduce students to multi-degree-of-freedom systems
·to introduce the concept of shock

• To introduce the concepts of damping modelling
• To show how to measure damping
• To introduce the transient response of a single-degree-of-freedom system
• To analyse a two-degree-of-freedom system using matrix methods

Review

• Free and Forced vibration of a damped single-degree-of-freedom system
• Viscous damping

Damping mechanisms

• Representation of Coulomb damping and hysteretic damping and the relationship with viscous damping

Energy dissipated by damping

• Damping definitions and relationships between the various forms of damping
  
• Quantification of the energy dissipated per cycle

Viscoelastic damping

• Models of behaviour – Maxwell and Voigt, Nature of behaviour
  
• Temperature - frequency relationship

Damping treatments

• Characteristics of damping materials and use of constrained and unconstrained damping treatments
  
• Use of tuned-mass-damper

Measurement of Damping

• Decay of free vibration
  
• Half-power point method

Transient response of a single-degree-of-freedom system

• Convolution
  
• Shock spectra

Two-degree-of-freedom systems

• Equations of motion
  
• Matrix methods
  
• Free vibration; natural frequencies and mode shapes
  
• Forced response
  
• Dynamic vibration absorber

This is a one-semester course, two lectures per week with one laboratory session

Lectures in the classroom with occasional demonstrations.

Two tutorial sessions are provided, where the students work on problems sheets

Hands-on laboratory work for the students one afternoon. The students are arranged in groups of three so that each student participates in the experiment

The students have to write-up one laboratory. Students are encouraged to read supporting texts and a booklist is provided.

Secondary text

Theory of Vibration with Applications, W.T. Thompson, Chapman and Hall

Vibration Damping, 1985, A.D. Nashif
D.I.G. Jones
J.P. Henderson, John Wiley
0471867721