MECHENG 722 : Engineering Vibrations
Engineering
2020 Semester One (1203) (15 POINTS)
Course Prescription
Course Overview
This course concerns how we can model, analyse, design and measure the responses of vibrating systems. We aim to provide you with a sound understanding of the fundamentals, knowledge of how to analyse vibrating structures and an introduction to practical measurement and treatment methods. The course comprises lectures, laboratories, projects and an exam.
We have 18 two-hour lectures in total in this course. Each student attends two 2-hour labs, the first one concerned with Digital spectral analysis, the second one Vibration measurement and testing.
Capabilities Developed in this Course
| Capability 1: | Disciplinary Knowledge and Practice |
| Capability 2: | Critical Thinking |
| Capability 3: | Solution Seeking |
| Capability 4: | Communication and Engagement |
| Capability 5: | Independence and Integrity |
| Capability 6: | Social and Environmental Responsibilities |
Learning Outcomes
- Analyse and apply. Single degree-of-freedom (SDOF) vibration: Students will be able to use SDOF analysis to predict the performance and parameters (natural frequency, damping, effective mass and stiffness) of an sdof system. Multiple degree-of-freedom (MDOF) vibration: Students will be able to form the modal matrix, calculate modal forces, determine response in modal coordinates, and synthesise system response from modal responses. (Capability 1.1, 2.1, 2.2 and 3.1)
- Measure and analyse. Spectral analysis: Students will be able to measure, analyse and compare signals in terms of their spectra. (Capability 1.1, 2.1, 2.2, 3.1, 3.2, 4.1, 4.2, 5.2 and 6.1)
- Apply and predict. Vibration of continuous systems: Students will be able to apply appropriate boundary conditions to derive the characteristic equation of a uniform 1D continuous system. They will be able to solve the characteristic equation to find the natural frequencies and mode shapes of such a system. They will be able to model and predict the free and forced response of such a continuous system using modal and wave-based approaches. (Capability 1.1, 2.1, 2.2, 3.1 and 3.2)
- Evaluate. Approximate methods for vibration analysis: Students will be able to assume the proper mode shape of discrete and continuous systems and compute the Rayleigh's quotient to estimate fundamental natural frequency using Rayleigh's method. They will be able to assume a series of proper shape functions, compute the corresponding stiffness and mass matrices, and estimate a few interested natural frequencies of continuous systems using Rayleigh-Ritz method. (Capability 1.1, 2.1, 2.2, 3.1 and 3.2)
- Develop and describe. Lagrange's equations: Students will be able to compute kinetic energy, potential energy, and generalized nonconservative forces of vibrating systems and formulate the equation of motion by applying Lagrange's equations. They will be able to estimate the equilibrium positions of vibrating systems and check their stability. They will be able to linearize the equation of motion around stable equilibrium positions. (Capability 1.1, 2.1, 2.2, 3.1 and 3.2)
- Measure and Analyse. Vibration measurement and testing: Students will be able to explain the characteristics of accelerometers, force sensors and excitation systems used in vibration testing systems. They will be able to explain the principal sources of error in these systems, and how these errors can be minimised. They will be able to compute natural frequencies, damping and mode shapes from experimental measurements using both the peak amplitude method and the modal circle method. (Capability 1.1, 2.1, 2.2, 3.1, 3.2, 4.1 and 4.2)
- Explain and critically evaluate. Vibration treatment: Students will be able to explain why the various approaches to vibration treatment are effective in some applications and not in others. They will be able to specify the appropriate isolator characteristics necessary to achieve a given level of performance. They will be able to explain the fundamental differences in the performance of undamped and damped vibration absorbers. (Capability 1.1, 2.1, 2.2, 3.1, 3.2 and 6.1)
- Develop and analyse. Vibration analysis using finite elements: Students will be able to develop a simple finite element model of a 1D structure, and use that model to predict the natural frequencies, mode shapes and frequency response of the structure. (Capability 1.1, 2.1, 2.2, 3.1 and 3.2)
Assessments
| Assessment Type | Percentage | Classification |
|---|---|---|
| Project A | 10% | Individual Coursework |
| Lab report | 10% | Individual Coursework |
| Project B | 20% | Individual Coursework |
| Final Exam | 60% | Individual Examination |
| 4 types | 100% |
| Assessment Type | Learning Outcome Addressed | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |||
| Project A | ||||||||||
| Lab report | ||||||||||
| Project B | ||||||||||
| Final Exam | ||||||||||
Workload Expectations
This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.
For this course, you can expect 4 hours of lectures per week, 3 hours of reading and thinking about the content per week and 40 hours in total of work on assignments.
Digital Resources
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
Please remember that the recording of any class on a personal device requires the permission of the instructor.
Academic Integrity
The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.
Learning Continuity
In the event of an unexpected disruption we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and your assessment is fair, and not compromised. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator, and if disruption occurs you should refer to the University Website for information about how to proceed.
Class Representatives
Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.
Inclusive Learning
All students are asked to discuss any impairment related requirements privately, face to face and/or in written form with the course coordinator, lecturer or tutor.
Student Disability Services also provides support for students with a wide range of impairments, both visible and invisible, to succeed and excel at the University. For more information and contact details, please visit the Student Disability Services’ website at http://disability.auckland.ac.nz
Special Circumstances
If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.
If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page: https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
This should be done as soon as possible and no later than seven days after the affected test or exam date.
Student Feedback
At the end of every semester students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback and respond with summaries and actions.
Your feedback helps teachers to improve the course and its delivery for future students.
Class Representatives in each class can take feedback to the department and faculty staff-student consultative committees.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter (https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html).
Disclaimer
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course you may be asked to submit your coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.