ID: 3490
Course type: scientific and vocational
Course coordinator: Obradović M. Aleksandar
Lecturers: Mitrović S. Zoran, Obradović M. Aleksandar
Contact: Obradović M. Aleksandar
Level of studies: Ph.D. (Doctoral) studies – Mechanical Engineering
ECTS: 5
Final exam type: oral
Introduce students to the basic concepts of linear and nonlinear oscillations and oscillations of elastic bodies.
By gaining knowledge in this course, students will be able to effectively solve complex problems of linear and nonlinear oscillations and oscillations of elastic bodies.
Stability of equilibrium of the conservative system. Linearization of the differential equations of motion. Vibration of the conservative system. Frequencies. The main mode shapes of vibration. Modal matrix. Vibration of the body on the beam supports. Damped vibration. Forced undamped vibration. Forced vibration. Resonance. Forced damped vibration of the system. Oscillations (free and forced) of elastic bodies with constant and variable cross section. Oscillations (free and forced) of plates and membranes. Properties of nonlinear oscillations. Testing of stationary systems with one degree of freedom. Phase plane, phase portraits and singular points. Lyapunov theorem. Construction of phase trajectories. The concept of auto - oscillation. Degenerative systems and the hypothesis of a jump. The effect of external harmonic force on auto - oscillation of systems with one and two degree of freedom. Stability of boundary trajectories.
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None
Total assigned hours: 65
New material: 50
Elaboration and examples (recapitulation): 0
Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0
Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 10
Review and grading of the project: 0
Test: 0
Test: 0
Final exam: 5
Activity during lectures: 0
Test/test: 0
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 50
Project: 0
Final exam: 50
Requirement for taking the exam (required number of points): 50
Meirovitch L, FUNDAMENTALS OF VIBRATIONS, Mc Graw Hill, 2001.; Rao S.S., Mechanical vibrations, Addison-Wesley Publishing Company Inc., 1995.; Rao S.S., Vibration of Continuous Systems, WILEY,2007.; Vuković, J., Obradović,A., Linear vibrations of mechanical systems, Mašinski fakultet, Beograd, 2021., .; Butenin N. V., Elements of nonlinear vibrations theory, Faculty of Mechanical Engineering, Belgrade, 1985