# ES386 - Dynamics of Vibrating Systems

• Module code: ES386
• Module name: Dynamics of Vibrating Systems
• Department: School of Engineering
• Credit: 15

## Module content and teaching

###### Principal aims

Vibrations exert a significant influence on the performance of the majority of engineering systems. All engineers should understand the basic concepts and all mechanical engineers should be familiar with the analytical techniques for the modelling and quantitative prediction of behaviour. This module therefore introduces students to the use of Lagrange’s equations (applied to 1D and 2D systems only for this module) and to techniques for modelling both lumped and continuous vibrating systems. It includes some coverage of approximate methods both as an aid to physical understanding of the principles and because of their continuing immediate usefulness.At the end of the module students should have a sound understanding of the wide application of vibration theory and of the underlying physical principles. In particular, they should be able to use either Newtonian or Lagrangian mechanics to analyse 2D systems, and to determine the response of simple damped and undamped multi-DOF systems to both periodic and aperiodic excitation.

###### Principal learning outcomes

By the end of the module the student should be able to: Identify and apply an appropriate co-ordinate system for the modelling of planar mechanical systems by Newton’s or Lagrange’s equations; Use either Newtonian mechanics or Lagrangian mechanics to analyse the vibration of planar systems; Make simplifying approximations to more complex engineering mechanisms to enable analysis using a lumped system model or a simple distributed mass and stiffness model; Determine the natural frequencies and modes of vibration of a multi-DOF damped or undamped linear system using standard matrix methods; Determine estimates for the fundamental natural frequency of an undamped or lightly damped vibrating mechanism using approximate methods; Determine the response of a single DOF system to aperiodic excitation and of a multi-DOF system to periodic excitation; Appreciate the application of the methods referred to above to important engineering systems.

###### Timetabled teaching activities

Spring. This module includes 30 hours of lectures and computational exercises.Required self-study: 117 hours

http://www2.warwick.ac.uk/fac/sci/eng/eso/modules/year3/es386a

## Module assessment

Assessment group Assessment name Percentage
15 CATS (Module code: ES386-15)
D (Assessed/examined work) Assessed Course Work 20%
Examination - Main Summer Exam Period (weeks 4-9) 80%
Assessed Course Work 100%

## Module availability

This module is available on the following courses:

###### Core
• BEng Mechanical Engineering (H310) - Year 3
• MEng Mechanical Engineering (H311) - Year 3
• MEng Mechanical Engineering with Intercalated Year (H312) - Year 3
• MEng Mechanical Engineering with Intercalated Year (H312) - Year 4
• MEng Mechanical Engineering with Year in Research (H313) - Year 3
• MEng Mechanical Engineering with Year in Research (H313) - Year 4
• BEng Systems Engineering (HH36) - Year 3
• MEng Systems Engineering (HH63) - Year 3
• MEng Systems Engineering with Intercalated Year (HH64) - Year 3
• MEng Systems Engineering with Intercalated Year (HH64) - Year 4
• MEng Systems Engineering with Year in Research (HH65) - Year 3
• MEng Systems Engineering with Year in Research (HH65) - Year 4

N/A

###### Optional
• BEng Engineering (H106) - Year 3
• MEng Engineering (H107) - Year 3
• MEng Engineering with Intercalated Year (H109) - Year 3
• MEng Engineering with Intercalated Year (H109) - Year 4
• MEng Engineering with Year in Research (H110) - Year 3
• MEng Engineering with Year in Research (H110) - Year 4