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University of Tripoli
Faculty of Engineering
Department of Mechanical
and Industrial Engineering
Applied Mechanics Division
project supervisor:
Dr. Mohammed Ali Hjaji
preperation:
Muna jamal ben saed
used for the transmission of power. it can carry gears, pulley
and sprockets to transmit motion.
torsional loadings and eventually torsional vibrations.
due to resonance phenomenon.
successful design of rotary and non-rotary systems.
component of the total response is sustained for a long time
and is thus of great importance in fatigue design.
to dampen out quickly and is thus of no importance in
assessing the fatigue life of the shaft.
2. the exact closed-form solutions for dynamic response of torsional shaft with different boundary conditions.
3. the quasi-static response of shaft under various torsional harmonic forces.
1. the governing torsional equation of motion of shafts and the corresponding boundary conditions using both, Newton’s approach and Hamilton’s variational principle.
4. Displacements, strains and rotations are
assumed small,
1. The present formulation is valid to shafts having circular solid/hollow cross-sections,
5. The Damping effect is not included in
the present solution,
2. The shaft cross-section is assumed to
remain perfectly rigid in its own plane
throughout deformation,
3. The shaft material is assumed to
remain linearly elastic during deformation,
6. The present solution captureds only
the steady state dynamic response.
Kinematics functions:
Static analysis for torsional displacement of cantilever shaft :
1. The exact closed-form formulated in
this study is competent to efficiently capture the static and steady state dynamic responses of the shafts.
2. Moreover, it is skillfully able to extort both natural frequencies and related mode shapes of the shaft.
2. The solution developed in the present
study consistently predicts the torsional
response of shafts when compared to
exact solutions .
The methodology developed can be extended to