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.