# 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. Thus, this module provides students with fundamental skills necessary for the analysis of the dynamics of mechanical systems, as well as providing opportunities to apply these skills to the modelling and analysis of vibration. This third-year module is mandatory for students pursuing a degree in Mechanical Engineering, building upon competences acquired earlier in the course. This module 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 usefulness. The module assumes basic understanding of mechanics and linear algebra consistent with the level of Year 2 modules. 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-degrees of freedom (DOF) systems to both periodic and aperiodic excitation. They should also be familiar with engineering solutions for measuring and influencing vibrational behaviour.

###### Principal learning outcomes

By the end of the module the student should be able to: 1. Model planar mechanical systems using Newton’s or Lagrange’s equations: Determine appropriate co-ordinate systems, analyse vibrations. 2. Abstract more complex engineering mechanisms: analyse using lumped system models or simple distributed mass and stiffness models. 3. Evaluate the natural frequencies and modes of vibration of a multi-degree of freedom damped or undamped linear system. 4. Use initiative to apply sensible approximations to develop practical models of complex vibrating systems, to find key parameters such as the natural frequency. 5. Evaluate complex (single- and multi-degree of freedom) systems and via a systematic approach show an understanding of the response of the system to periodic excitations. 6. Demonstrate a sound understanding of the application of vibration analysis to key engineering systems.

###### Timetabled teaching activities

30 1-hour lectures spread evenly over 1 term. 2-hour laboratory session (including preparation/evaluation). 2 x 1 hr revision classes. Total 34 hours

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

###### Other essential notes

Advice and feedback hours are available for answering questions on the lecture material (theory and examples).

## Module assessment

Assessment group Assessment name Percentage
15 CATS (Module code: ES386-15)
D (Assessed/examined work) Computational Exercise plus Computer Code Solution 20%
3 hour examination (Summer) 80%
VA (Visiting students only) 100% assessed (part year) visiting 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 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 Year in Research (HH65) - Year 3
• MEng Systems Engineering with Year in Research (HH65) - Year 4
###### Optional Core
• MEng Mechanical Engineering with Intercalated Year (H312) - Year 3
• MEng Mechanical Engineering with Intercalated Year (H312) - Year 4
###### 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
• BSc Engineering (H112) - Year 3