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On the 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 + 0.1 Hz. 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:

On the 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 + 0.1 Hz. 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:

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
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On the 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 + 0.1 Hz. 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: Is00 = 3 + 0.2(5v + u) 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.
Transcribed Image Text:On the 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 + 0.1 Hz. 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: Is00 = 3 + 0.2(5v + u) 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.
Mass element Moment of inertia stiffness number kgm? MNm/rad 100 3. 56 E4 0. 79 Vib. damper 101 0. 28 arigid 200 U.013 300 0. 11 4 15. 00 4 9. 10 301 cyl 1, 43 4 7.70 302 1.00 4 1.70 cyl 303 cyl 1. 00 4 7.20 304 cyl cyl cyl 1, 43 4 7. 70 305 1. 13 4 7.70 306 1,00 4 7.20 307 cyl cyl Flywheel 1. 00 4 7.70 308 1. 43 4 9.80 500 6. 75 drigld 501 5. 22 503 0. 340 504 0. 200 Ea 3o. 00 Coupling 505 0.550 506 0. 200 507 0. 200 508 0. 436 509 0. 094 Sa0. 202 F56/5/86NC/9 4 18. 00 E4 30. 00 Coupling 18. 00 Coupling arigid Goupling Flonge drigid Georbox 42.798 5 10 Georbox 2. 409 496. 83 511. Georbox 1.826 43. 751 5 12 0. 13T 513 0.239 514 0. 968 5 15 0.087 5 16 D. 174 517 0.007 Georbox drigid Shoftline 40.232 Shoftline grigid Shaft 40.362 Shaft 40. 362 Shoft drigid 5 18 Woler jet 2.95
Transcribed Image Text:Mass element Moment of inertia stiffness number kgm? MNm/rad 100 3. 56 E4 0. 79 Vib. damper 101 0. 28 arigid 200 U.013 300 0. 11 4 15. 00 4 9. 10 301 cyl 1, 43 4 7.70 302 1.00 4 1.70 cyl 303 cyl 1. 00 4 7.20 304 cyl cyl cyl 1, 43 4 7. 70 305 1. 13 4 7.70 306 1,00 4 7.20 307 cyl cyl Flywheel 1. 00 4 7.70 308 1. 43 4 9.80 500 6. 75 drigld 501 5. 22 503 0. 340 504 0. 200 Ea 3o. 00 Coupling 505 0.550 506 0. 200 507 0. 200 508 0. 436 509 0. 094 Sa0. 202 F56/5/86NC/9 4 18. 00 E4 30. 00 Coupling 18. 00 Coupling arigid Goupling Flonge drigid Georbox 42.798 5 10 Georbox 2. 409 496. 83 511. Georbox 1.826 43. 751 5 12 0. 13T 513 0.239 514 0. 968 5 15 0.087 5 16 D. 174 517 0.007 Georbox drigid Shoftline 40.232 Shoftline grigid Shaft 40.362 Shaft 40. 362 Shoft drigid 5 18 Woler jet 2.95
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