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DRPS : Course Catalogue : School of Engineering : Mechanical

Undergraduate Course: Advanced Dynamics and Applications 5 (MECE11014)

Course Outline
SchoolSchool of Engineering CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Year 5 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis course follows from previous courses on dynamics (D3 and D4). It aims to provide the students with an advanced understanding on linear and non-linear dynamic systems for a range of applications from micro- to macro-structures. The course covers the dynamic behaviour of micro-mechanical systems (Module I), non-linear dynamic behaviour of materials and impulsive loading of structures (Module II). Teaching/learning will be focused on specific devices (i.e., micro-beams, plates and membranes) and target applications (i.e., industrial accidents, civil and military protection systems, etc.)
Course description MODULE 1: Micro-mechanical systems (10 lectures)
- Introduction to micro electro-mechanical systems, vibrations of lumped-parameter systems using MEMS examples (micro beams, plates and membranes).
- Review on Single-Degree-of-Freedom (SDOF) systems (example: MEMS gyroscopes and accelerometers); review on Two-Degree-of-Freedom (2-DOF) systems: (example: MEMS band-pass filter).
- Lumped-parameter modelling and damping (energy loss) in MEMS:
Equivalent stiffness coefficient and equivalent mass. Construction of spring-mass models. Damping, focussing on Squeeze-Film damping SQFD (model of SQFD with continuum-based approach using Reynolds equation).
- Dynamics of micro-beams:
Linear equation of motion. Static response. Natural frequencies and mode shapes. Effect of axial load on natural frequency. Orthogonality of mode shapes. Forced vibration and modal analysis.
- Non-linear dynamics applied to MEMS:
Introduction to non-linearity (bifurcation and non-linear oscillation). Nonlinear models of beams. Nonlinear dynamics of electrostatically actuated resonator.

MODULE 2: Structural Impact and Applications (10 lectures)
- Introduction to impact mechanics:
Terminology, analysis methods and ruling dynamic principles. Low and high energy impact. These topics will be introduced with examples and applications in structural dynamics and structural impact, crashworthiness and vehicle safety, armour and protection systems.
- Low energy impact:
One dimensional rigid body impact: equations of motion, compression and restitution and energy balance. Multi-dimensional rigid body impact: planar and three-dimensional collisions, impact of smooth bodies, and the role of friction on collinear and non-collinear impact.
- Dynamic behaviour of structures:
Governing equations, types of dynamic loads, influence of supports (simple, clamped, cantilever, etc.). Static versus dynamic behaviour of structures: beams, plates and shells. Impulsive loads and dynamic plastic behaviour: governing equations for beams and plates, examples and applications.
- Dynamic behaviour of materials:
Applications of high strain rate behaviour of materials. Elastic and plastic waves: wave velocity and propagation, impact of finite length bars. Shock waves: hydrodynamic behaviour of materials, relationships between shock parameters and shock wave profiles. Shock wave interaction, reflection and attenuation. Material response to shock waves: equations of state, experimental and theoretical methods to obtain equations of state.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Dynamics 3 (MECE09008) AND Dynamics 4 (MECE10002)
Prohibited Combinations Other requirements None
Additional Costs n/a
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. Recognise, analyse and evaluate the dynamic behaviour of micro-mechanical structures (e.g. beams and plates).
  2. Solve and reflect on energy-loss issues in micro-mechanical structures.
  3. Discuss non-linear dynamic behaviour of mechanical resonators.
  4. Evaluate the role of energy absorption mechanisms (deformation, fracture, etc.) on the protective capability of structures.
  5. Characterise the influence of the strain rate on the dynamic behaviour of materials for engineering applications.
Reading List
M. I. Younis, MEMS Linear and Nonlinear Statics and Dynamics, Springer, 2011.
N. Jones, Structural impact, Cambridge University Press, 1997.
M.A. Meyers, Dynamic behaviour of materials, John Wiley & Sons, 1994.
W. Goldsmith, Impact: The theory and physical behaviour of colliding solids, Dover Publications, 2001.
W.J. Stronge, Impact mechanics, Cambridge University Press, 2000.
Additional Information
Graduate Attributes and Skills Not entered
Special Arrangements None
KeywordsMicro-mechanical systems,resonators,non-linear dynamics,impact dynamics,impulsive load
Course organiserDr Enrico Mastropaolo
Tel: (0131 6)50 5651
Course secretaryMiss Emily Rowan
Tel: (0131 6)51 7185
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