AZTUProgrammes

Subject · Mechanical engineering-master

Dance theory and analytical mechanicsTopics

MİFS-29816 creditsAutumn semesterElective2025-2026

Topic plan

The subject's topics and the learning outcomes attached to each one.

15 topics

  1. 1. An introduction to the theory of dances. mechanical systems and their degrees of freedom. free oscillations of the system. analysis of damped and forced oscillations in mechanical systems. longitudinal, transverse and torsional oscillations in machine shafts.

    Lecture

  2. 2. Resonance phenomenon. the number of critical cycles of the shaft. torsional dances of the crankshaft. vibrations and oscillations of reciprocating machines. masses brought in the elbow-slider mechanism.

    Lecture

  3. 3. Linear oscillations of mechanical systems with infinite degrees of freedom. differential equations of longitudinal oscillations of machine parts and their solutions. differential equations of transverse and torsional oscillations of machine parts and their solutions.

    Lecture

  4. 4. Vibrations and oscillations of reciprocating machines. masses transported in the elbow-slide mechanism. transverse dances of boards. basic simplifications and expressions. boundary conditions.

    Lecture

  5. 5. Theory of stability of movement of machines. stability of the equilibrium state of the system. lyapunov's theorem about stability of motion.

    Lecture

  6. 6. General methods of nonlinear mechanics. forced oscillations of non-linear systems (b. galerkin's method). mechanical oscillations of systems with a finite number of degrees of freedom.

    Lecture

  7. 7. Dances along the stick. transverse dances of the string. oscillatory motion of the flow of an ideal fluid in a pipeline.

    Lecture

  8. 8. Introduction to analytical mechanics. stability of the equilibrium state of the system.

    Lecture

  9. 9. A system of non-free material points. ideal and real communications.

    Lecture

  10. 10. The principle of possible displacements. general equation of dynamics.

    Lecture

  11. 11. Differential equations of motion of the system in generalized coordinates.

    Lecture

  12. 12. Equilibrium conditions of non-free system. lagrange's equations of the 2nd kind.

    Lecture

  13. 13. Study of the mechanical movement of machines by means of lagrange's equations of the 2nd type.

    Lecture

  14. 14. Generalized coordinates of the elbow-slider mechanism, application of lagrange's equations of the 2nd type to them.

    Lecture

  15. 15. Application of lagrange's equations of the 2nd type to compressors and pumps.

    Lecture