Undergraduate Course: Advanced Dynamics and Applications 5 (MECE11014)
Course Outline
| School | School of Engineering |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 11 (Year 5 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This 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.) The coursework for Module II will be the design of a specific protection system or analysis/discussion of a real case accident scenario. |
| Course description |
MODULE 1: Micro-mechanical systems (10 lectures)
- Introduction to micro electro-mechanical systems and vibrations of lumped-parameter systems using MEMS examples:
MEMS structures examples: micro beams, plates and membranes. Review on Single-Degree-of-Freedom (SDOF) systems: undamped vibration and damped vibration, forced harmonic excitation (example: MEMS gyroscopes and accelerometers); response of SDOF systems to arbitrary excitation (example: drop test for the reliability of portable devices, electronics and MEMS). Review on Two-Degree-of-Freedom (2-DOF) systems: undamped free vibration and eigenvalue problems; modal analysis and resonances in 2-DOFs 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.
- Mechanical shock in MEMS:
Modelling shock (in lumped-parameter models and micro beams). Mechanical shock influence on electrostatic actuated systems. Mechanical shock in resonators.
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.
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Entry Requirements (not applicable to Visiting Students)
| Pre-requisites |
Students MUST have passed:
Dynamics 3 (MECE09008) AND
Dynamics 4 (MECE10002)
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Co-requisites | |
| Prohibited Combinations | |
Other requirements | None |
| Additional Costs | n/a |
Information for Visiting Students
| Pre-requisites | None |
Course Delivery Information
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| Academic year 2014/15, Available to all students (SV1)
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Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 20,
Seminar/Tutorial Hours 10,
Formative Assessment Hours 1,
Summative Assessment Hours 6,
Revision Session Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
59 )
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| Assessment (Further Info) |
Written Exam
60 %,
Coursework
40 %,
Practical Exam
0 %
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| Additional Information (Assessment) |
Written Exam %: 60%
Practical Exam %: 0%
Coursework %: 40% (two small design projects)
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| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
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| Main Exam Diet S1 (December) | | 2:00 | | | Resit Exam Diet (August) | | 2:00 | |
Learning Outcomes
Upon successful completion, students will be able to:
- Describe the functionality of a range of micro-mechanical systems.
- Construct equivalent lumped-parameter models.
- Calculate the static and dynamic behaviour of simple mechanical microsystems, e.g. cantilevers and membranes.
- Describe and understand energy-loss mechanisms in micro-mechanical structures.
- Evaluate the effect of axial loading on the natural frequencies of the structure.
- Describe non-linear models of beams and understand the non-linear dynamics of mechanical resonators.
- Evaluate the effect of mechanical shocks on micro-mechanical structures.
- Identify and characterise low and high-energy impact situations.
- Apply rigid body impact equations (one and multidimensional) to structural impact cases.
- Understand the role of energy absorption mechanisms (deformation, fracture, etc.) on the protective capability of structures.
- Propose and design simple structures and systems for impact protection.
- Understand shock wave propagation and interaction, and its effect on the hydrodynamic behaviour of materials.
- Characterise the influence of the strain rate on the dynamic behaviour of materials for engineering applications.
- Work independently and in teams to define parameters and/or design adequate protection systems for common situations.
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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.
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Additional Information
| Graduate Attributes and Skills |
Not entered |
| Special Arrangements |
None |
| Keywords | Micro-mechanical systems, resonators, non-linear dynamics, impact dynamics, impulsive load |
Contacts
| Course organiser | Dr Enrico Mastropaolo
Tel: (0131 6)50 5651
Email: E.Mastropaolo@ed.ac.uk |
Course secretary | Mr Paulo Nunes De Moura
Tel: (0131 6)51 7185
Email: paulo.nunesdemoura@ed.ac.uk |
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