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Curtin University Department of Mechanical Engineering Fundamentals of Mechanical Vibration ASSIGNMENT 2 Below (next page) is a schematic diagram of an actual marine propulsion system consisting of an 8-cylinder in-line engine, flywheel, coupling, gearbox, shaft and water jet. A torsional vibration damper is attached to the non-drive end of the engine. Use Holzer’s method to estimate the lowest four torsional natural frequencies of this system to the nearest ±0.1Hz. Also determine and sketch the mode shapes for each of the four natural frequencies, assuming unit amplitude for the damper (mass element number 100). Assuming that the engine is a four-stroke type (giving four power strokes per revolution in this 8-cylinder case), determine the engine running speeds, in rpm, that would cause the frequency of engine combustion torque pulses to coincide with these four system natural torsional frequencies. So that each student has a different system, the moment of inertia of mass element number 500 (the flywheel) shall be replaced with one of the following magnitude. Your 8 digit student number can be written as ' pqrstuvw'. Then let your flywheel moment of inertia be: ( ) w v I + + = 10 1 . 0 3 500 kgm 2 Where a section of shaft is labelled as ‘rigid’ simply combine the adjacent inertias and omit the shaft. By my count, you will then end up with 23 inertias. You may (and probably should! – life’s too short) use any software, including the Matlab program ‘Holzer3.m’ provided on Blackboard (see week 4). However, you must verify the answer in some way. Never trust software! The eigenvalue method covered in tutorial 5 is a good alternative. Due Date: 3.30 pm, Friday 29 th May 2015. Learning outcomes addressed by this task: Be able to apply Holzer’s method to the solution of natural frequencies of multi-dof systems. Reinforce some earlier principles of statics and dynamics. Practise generating a professional-quality engineering report. Page 1 of 2

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  • Curtin University Department of Mechanical Engineering

    Fundamentals of Mechanical Vibration

    ASSIGNMENT 2 Below (next page) is a schematic diagram of an actual marine propulsion system

    consisting of an 8-cylinder in-line engine, flywheel, coupling, gearbox, shaft and water jet. A torsional vibration damper is attached to the non-drive end of the engine.

    Use Holzers method to estimate the lowest four torsional natural frequencies of this system to the nearest 0.1Hz. Also determine and sketch the mode shapes for each of the four natural frequencies, assuming unit amplitude for the damper (mass element number 100). Assuming that the engine is a four-stroke type (giving four power strokes per revolution in this 8-cylinder case), determine the engine running speeds, in rpm, that would cause the frequency of engine combustion torque pulses to coincide with these four system natural torsional frequencies. So that each student has a different system, the moment of inertia of mass element number 500 (the flywheel) shall be replaced with one of the following magnitude. Your 8 digit student number can be written as 'pqrstuvw'. Then let your flywheel moment of inertia be:

    ( )wvI ++= 101.03500 kgm2

    Where a section of shaft is labelled as rigid simply combine the adjacent inertias and omit the shaft. By my count, you will then end up with 23 inertias.

    You may (and probably should! lifes too short) use any software, including the Matlab program Holzer3.m provided on Blackboard (see week 4). However, you must verify the answer in some way. Never trust software! The eigenvalue method covered in tutorial 5 is a good alternative.

    Due Date: 3.30 pm, Friday 29th May 2015.

    Learning outcomes addressed by this task: Be able to apply Holzers method to the solution of natural frequencies of multi-dof systems. Reinforce some earlier principles of statics and dynamics. Practise generating a professional-quality engineering report.

    Page 1 of 2

  • Some Notes

    Your submission should form an engineering design record. Your supervisor wants to know what you did, the result, and the limitations on your analysis. This is sometimes called the executive summary near the beginning of the report. The remainder of the report should allow another engineer, who has had nothing to do with the job, to understand exactly what you have done, why you made assumptions and simplifications, and your results. Whatever is needed to communicate that information should be contained within the report. By year three of this course, it is assumed that your neatness and presentation standard will be appropriate. (This is possible by hand writing. If it is not possible for you, then you should resort to typing.) Hence no marks are allocated to presentation. However, marks will be deducted for poor presentation.

    End of Assignment

    stiffness MNm/rad

    Moment of inertia kgm2

    Mass element number

    Page 2 of 2

    Fundamentals of Mechanical VibrationASSIGNMENT 2