# Dynamics of Engineering Systems

## Module summary

Module code: MECH1083
Level: 5
Credits: 15
School: Engineering and Science
Department: Engineering
Module Coordinator(s): Kaushika Hettiaratchi

## Specification

### Pre and co requisites

Engineering Principles 1 and Engineering Principles 2

### Aims

This module aims to enhance students understanding of engineering mechanics and dynamics in engineering systems. Mechanics and dynamics are core requirements for mechanical engineers. This module will enable students to determine kinetic and kinematic (dynamic) responses due to the actions applied to mechanical systems. This will enable engineering students to predict and evaluate the performance of dynamic systems.

### Learning outcomes

On successful completion of this module a student will be able to:
1 Analyse dynamic systems in terms of their kinematics and kinetics and apply methods of solution to problems involving rigid bodies.

2 Investigate and analyse the behaviour of systems undergoing vibrations.

3 Demonstrate understanding of the how to predict and control the response of systems using engineering components.

4 Demonstrate understanding of the methods applied to analyse engineering systems.

### Indicative content

ENGINEERING MECHANICS
• Introduction to dynamics. Newton’s Laws of Motion. Kinematics and kinetics of particles and rigid bodies. Free body diagrams. Friction in systems. Kinetic energy and potential energy. Energy transfer and the work energy principle. Equations of motion and equations of motion in differential form. Impulse and momentum. Circular motion and motion of vehicles on banked surfaces.
• Introduction to Vibration Analysis. Free vibrations; Lumped parameter models for one degree of freedom systems. Velocity and acceleration vectors; Fundamental frequencies; Solution for simple harmonic motion; Second order differential equation; Energy transfer in vibrating systems.
• Damped Vibrations. Damping in systems and energy loss; Non-linear second order differential equation; Damping ratio; Logarithmic decay and determination of damping coefficients.
• Two Degree of Freedom Systems. Characteristic equations; Matrix forms; Mass and stiffness matrices; Eigenvalues and eigenvectors. Fundamental and higher frequencies; Mode shape diagrams; Torsional vibrations; Equivalent systems; Single rotor and two rotor systems; Nodal positions. Nodal diagrams.
• Forced Vibrations; Phasor diagrams; Phase lag and lead; Rotational imbalance; Normalised frequencies and frequency ratio; Amplitude ratio; Transmissibility and transmissibility ratio; Forces transmitted to supports; Vibration isolators; Design of Systems. Holzer’s Method
• Structural Vibrations: Vibrations of continuous systems; Modes of vibration; Selection of mode shapes; Vibration of beam with different support systems. Rayleigh’s Method.
• Case studies of vibrations in engineering systems.

### Teaching and learning activity

This module is analytically challenging and hence, the learning and teaching activities have been spread across a standard double term to allow students sufficient time to grasp the principles involved. The following activities will be used to support students’ learning:
Lectures: The lectures are designed to provide students with the knowledge and information to solve problems in engineering dynamics. The lectures will cover the principles and methods used to solve real world problems. A mixture of PowerPoint slides and supplementary Module notes will be used. The lectures will include case studies where possible to emphasise the link between theory and practice. Additional information to supplement the students’ learning will be provided via moodle.
Tutorials: To ensure that students understand the methods for tackling problems, tutorial sessions with worked examples will be incorporated into the lecture programme. The tutorials will also provide the opportunity for students to demonstrate their understanding and application of principles.
Mini-project, group presentation and case Studies: This Module has a major objective of helping students understand how to analyse the dynamics of engineering systems. Therefore, as well as lectures and tutorial classes, students will be given a case study to broaden their learning, where they can further demonstrate their understanding. This activity will be used to help students to critically appraise and investigate key components in dynamic systems. The case study will be a group activity with students giving a presentation to demonstrate their understanding.
Laboratory Work: Laboratory exercises will further aid understanding of the subject matter in addition to further developing practical, analytical and presentational skills.

### Assessment

Lab Report - 30%
LO - 1, 2.
Pass mark - 40%
1500 words.
Module Laboratory.

Exam - 70%
LO - 1, 3, 4.
Pass mark - 40%
2 hours. Unseen exam based on topics covered during the lecture programme.

Nature of FORMATIVE assessment supporting student learning:
In-class tutorial assignments will be used to help students to grasp concepts discussed in the lecture programme. One to one feedback will also be given. Supporting solutions to tutorial problems will also be provided on moodle. A formative timed mock exam will be carried out in-class. This will mimic exam conditions and help prepare students for the final summative exam at the end of the academic year.