Mechanics and Dynamics of Engineering Systems

Module summary

Module code: MECH1081
Level: 5
Credits: 15
School: Engineering and Science
Department: Engineering
Module Coordinator(s): Michael Okereke

Specification

Aims

This course aims to enhance students understanding of the principles of engineering mechanics and dynamics in analysis of engineering structures. Engineering mechanics and dynamics are core subjects for every mechanical engineer. This course shall empower the students to undertake computation of deformations, deflections, internal forces (or stresses) within structures, and the dynamics of motion and associated force analysis of such engineering structures. Such knowledge will help engineers evaluate the performance of existing structures whilst also developing the knowledge required to design structurally sound engineering applications.

Learning outcomes

On successful completion of this course a student will be able to:
1. Analyse the mechanical behaviour of materials under diverse loading conditions and apply engineering principles in the analysis of motions and effect of forces on systems and structures.
2. Analyses systems and structures based on concepts of stress and strain, bending, buckling, non-linear responses and vibrations.
3. Demonstrate understanding of the design requirements for stable, resilient engineering systems.
4. Demonstrate understanding of the methods applied to analyse engineering systems and structures.

Indicative content

Principles of Mechanics of Materials.
• Mechanical properties of materials: Elasticity, Plasticity, Yield, Stress-Strain graphs; linear elastic material model, plastic deformation of materials; Mechanical Testing: Tensile, Compression, Shear, combined loading.
• Behaviour of structures under complex loads: 2D Stress States; 2D Stress Tensor; Stress transformations; Principal Stresses and Strains; Construction of Mohr Circle; introduction to 3D Stress Analysis.
• Torsion of Shaft: Torsional deformation of circular shafts; Torsion formula; Angle of Twist; Power transmissions; static indeterminacy and torsion; torsional deformation of solid non-circular shafts; torsion of thin-walled open cross-sections; stress concentration and torsion effects; inelastic torsion; residual stresses and ultimate torque;
• Mechanics of Pressure Vessels: Thin and thick-walled cylindrical pressure vessels; spherical vessels;
• Structures loaded in Bending: Statically Determinate Structures, Statically Indeterminate structures; Construction of Axial force, Shear Force and Bending Moment Diagrams.
• Flexural Response of Structures: Pure bending; normal stresses and strains in beams; flexure formula; stress-concentrations in bending; shear stresses in beams; design of prismatic beams; design of beams with constant strength; design of composite beams;
• Deflection of beams: The elastic curve; Method of integration; discontinuity functions method; Method of superposition; Moment-Area method; continuous beams;
• Buckling collapse of axially loaded structures: Stability of structures; ideal columns; critical load; buckling of pinned-end columns; Euler load; columns with different support types; buckling of real columns; secant formula; Concentric and Eccentric loading.

Principles of Engineering Dynamics.
• Non-linear Dynamics. Equations of motion; Differential equations; Time dependent functions; Displacement dependent functions; Application to motion of bodies in different media.
• Introduction to Vibration Analysis. Free vibrations; Lumped parameter models for one degree of freedom systems. Free body diagrams; 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; 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 mechanical and structural vibrations.

Teaching and learning activity

The course is a very analytical course requiring intense learning over a sustained period of time. Therefore, the learning and teaching activities have been spread across a standard double term to allow students enough time to understand the principles of mechanics and dynamics of structures. The following are a set of activities that will be used to support learning:
Lectures: These are designed to introduce the students to the concepts of Engineering mechanics and dynamics of structures. There are about 12 blocks of lectures for the first and second terms. Lectures are presented using PowerPoint slides and supplemented, where possible with lecture notes. The slides will be made available also to the students after each class.
Tutorials: In order to ensure students, understand the analysis procedure for tackling problems, tutorial classes have been included as part of this course. Tutorial questions will be given to students ahead of the class and students should attempt these questions before arriving at the classes. The teaching team will meticulously go through some of the questions with the students in these classes. Also, tutorials will provide an opportunity for the students to demonstrate their understanding and application of principles to real problems.
Seminars, Mini-projects, group presentations or Case Studies: This course has a major objective of helping students understand how to analyse the mechanics and dynamics of engineering structures. Therefore, as well as lectures and tutorial classes, students might have to present group presentations/seminars/case studies or mini group projects of at least once over the year during which the students demonstrate their understanding and application of engineering mechanics and dynamics in analysis of an engineering structure. These learning activities will be used to help student to critically appraise and investigate key components in dynamic systems. The teaching team will also frequently offer case studies to help establish the link between theory and practice.
Laboratory Work: Laboratory exercises will further aid understanding of the subject matter in addition to further developing practical and analytical skills.

Assessment

Summative Assessment.
Examination - Weighting 70%, Pass Mark 40%.
Outcomes Assessed - 4.
Outline Details - Examination will be based on topics covered during the lecture programme.

Laboratory - Weighting 30%, Pass Mark 40%.
Outcomes Assessed - 1-3.
Outline Details - Portfolio of lab activities /laboratory reports.

Students are not required to pass all elements of summative assessment in order to pass the module.

Formative Assessment.
In-class assessments can be offered to help students quickly grasp concepts introduced during the class. This can be based on clicker technologies like Mentimeter, Zeetings, etc. Instant feedback from these in-class exercises will help the teaching team gauge students’ understanding and where reinforcement of learning will be presented. The teaching team can also offer formative mock exams which will be carried out in-class and/or offered over a timed session via a course Moodle page. These should mimic exam conditions and difficulties and will help prepare students for the final summative examination.