Prowadzący: prof. zw. dr hab. inż. Roman Bogacz

Wykład 30 godzinny w języku angielskim.

Treść wykładu:

1. Ordinary differential equations describing oscillatory motion. Derivation of equations. Solution for the case with damping and self-excitation.
2. Nonlinear elasticity and nonlinear damping. Limiting lines in case of nonlinear system with two degrees of freedom and limiting cycles of self-excited cycles.
3. Friction excited vibration of single degree of freedom. Characteristics dependent on velocity of relative motion.
4. Friction excited vibration of system with two and three degrees of freedom.
5. Models of friction dependent on history of a friction process (time of sticking and sign of acceleration, temperature).
6. Partial differential equations of hyperbolic type. Boundary conditions and initial conditions. Fourier and d’Alambert’s methods of solution. Examples: equation of string, rod and shaft.
7. Partial differential equations of parabolic type. Boundary conditions and initial conditions. Methods of solution. Equations of motion for case of string on an elastic foundation and various beam models.
8. Waves in one-dimensional systems. Wave number, wave length and amplitude of wave.  Reflections, scattering, dispersion and superposition of waves.
9. Continuous systems subjected to oscillatory loading. Kinematic excitations.
10. Dynamics of hybrid systems. Set of oscillators interacting with the string. Single oscillator or set of oscillators interacting with beams. Set of oscillators in relative motion with a string and the Euler beam on an elastic foundation. Linear case.
11. Stability of pipes conveying fluid. Set of oscillators in relative motion with a string and the Euler beam on an elastic foundation. Non-linear case.
12. Two beams in relative motion interacting by an elastic massless layer.
13. Single oscillator interacting in two points with a string. Dynamics of the pantograph system.
14. Conservative and non-conservative systems. Particular cases of singular points on the phase plane.

 

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