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### Course Overview

To introduce the theory of dynamics and the vibration of single and multi-degree of freedom systems.

### Course Details

Study Type Level Undergraduate 3 Second Sub Session 7.5 credits (3.75 ECTS credits) Offshore No Professor Ana IvanovicProfessor Ekaterina E. Pavlovskaia

### What courses & programmes must have been taken before this course?

• Programme Level 3
• Engineering (EG)

None.

None.

No

### Course Description

This course commences with an overview of the dynamics of a particle and of general planar kinematics and dynamics before proceeding to a review of the free and forced vibration response of a linear single degree of freedom system. An introduction to the vibration of systems with two or more degrees of freedom follows, including natural frequencies and mode shapes, principal co-ordinates and calculation of the forced response using the impedance method.

The content of the course:

1. Introduction to Planar Rigid Body Dynamics: Definition of degrees of freedom. Review of the equations of motion of a rigid body in Cartesian and polar co-ordinate systems. Concept of relative and absolute co-ordinate systems.
2. Introduction to Vibration: A brief overview of vibration problems in engineering, and presentation of a general method for working through problems.
3. Single Degree of Freedom Systems: Review of the dynamics of single degree of freedom linear systems, including free vibration response, forced response due to harmonic excitation, and calculation of the forced response of a system with a transient input by use of Duhammel's Integral.
4. Matlab for simple dynamics calculations: using numerical tools for calculations of the dynamic responses of the free and forced single degree of freedom systems.
5. Systems with Two or More Degrees of Freedom: Introduction to natural frequencies and normal modes for multi-degree of freedom (MDOF) systems including semi-definite systems. Calculation of the response of MDOF systems to harmonic excitation by use of the impedance method. Analysis of the undamped tuned vibration absorber.
6. Matlab for dynamics calculations in 2 and more degrees of freedom system: using numerical tools for calculations of natural frequencies and mode shapes, and the dynamic amplitudes of forced vibrations.

### Contact Teaching Time

Information on contact teaching time is available from the course guide.

### Teaching Breakdown

Details, including assessments, may be subject to change until 31 August 2023 for 1st half-session courses and 22 December 2023 for 2nd half-session courses.

### Summative Assessments

#### Exam

Assessment Type Weighting Summative 100 40 42 Release of worked solutions and annotated submission for individual students. An in-person feedback opportunity will be available.
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
ConceptualAnalyseAnalyse dynamics of single degree of freedom systems. Calculate natural frequencies and normal modes of multi-degree of freedom systems. Apply co-ordinate transformations. Solve complex problems
ConceptualApplyDemonstrate improved problem-solving skills
ConceptualUnderstandThe basic definitions /concepts of planar rigid body dynamics, in particular how to choose an appropriate co-ordinate system Basic vibration analysis of single & two or more degrees of freedom systems

### Formative Assessment

There are no assessments for this course.

### Resit Assessments

#### Resubmission of failed elements

Assessment Type Weighting Summative 100 Retake/resubmit failed element(s) of summative assessment with grade for passed element(s) carried forward from 1st attempt.
##### Learning Outcomes
Knowledge LevelThinking SkillOutcome
Sorry, we don't have this information available just now. Please check the course guide on MyAberdeen or with the Course Coordinator

### Course Learning Outcomes

Knowledge LevelThinking SkillOutcome
ConceptualUnderstandThe basic definitions /concepts of planar rigid body dynamics, in particular how to choose an appropriate co-ordinate system Basic vibration analysis of single & two or more degrees of freedom systems
ConceptualAnalyseAnalyse dynamics of single degree of freedom systems. Calculate natural frequencies and normal modes of multi-degree of freedom systems. Apply co-ordinate transformations. Solve complex problems
ConceptualApplyDemonstrate improved problem-solving skills

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