Mechanical Vibrations

Opublikowano: 06.04.2014 20:06

Subject name Mechanical Vibrations
Type of subject               Basic
Summary ECTS 3
Form of course 30h lecture, 15h exercises
Lecturer                           Prof. Włodzimierz Kurnik, Ph.D., D.Sc.
A brief outline:
Lecture
  • Harmonic motion. Synthesis of harmonic motions. Elements of harmonic analysis. Basic models of vibrating mechanical systems. Forces in vibrating systems.
  • Equations of motion of vibrating (multibody) systems. Linear vibrations of single-degree-of-freedom systems. Free vibrations.
  • Forced vibrations. Vibrations under harmonic excitation, resonance. Vibrations with periodic and arbitrary forcing. Impulse transfer function.
  • Kinematically excited vibration. Recording vibration by sejsmic sensors. Absorbing vibrations.
  • Analysis and interpretation of vibrations on the phase plane. Phase trajectories and singular points. Phase portraits.
  • Linear vibrations of multi-degree-of-freedom systems. Eigen frequencies and eigen forms.
  • Forced linear vibrations. Dynamic vibration absorber.
  • Linear vibration of single-degree-of-freedom systems with parametric excitation. Hill and Mathieu equations. Stability of motion. Parametric resonanse.
  • Analysis and properties of nonlinear vibrations of systems with a single degree of freedom. Amplitude-frequensy relation in rfee vibrations. Damping of vibration by dry friction. Linearization techniques. Nonlinear vibrations under harmonic excitation.
  • Vibrations of one-dimensional continuous systems. Equations of motion of strings, rods, shafts and beams. Initial and boundary conditions. Eigen-values and eigen-functions. Free vibrations. Vibrtations excited by harmonic distributed and concentrated forces. Kinematically excited vibrations. Discretization of continuous systems – Rayleigh and Galerkin methods.
Exercises
  • Combining harmonic vibrations. Harmonic analysis of periodic motions, spectra of vibrations.
  • Linear modelling of vibrating systems. Calculating basic parameters of free vibrations of linear single-degree-of-freedom systems.
  • Analysing and discussing vibrations under harmonic force. Vibration under harmonic kinematic excitation.
  • Calculating and discussing resonance curves under unbalance excitation.
  • Determinig and drowing phase trajectories and phase portraits of linear and nonlinear systems on the phase plane. Calculating and discussing properties of singular points.
  • Free vibrations of linear two-degree-of-freedom systems. Eigen-frequencies and eigen-forms of vibration.
  • Excited vibrations of two-degree-of-freedom systems. Resonances. Calculating parameters of dynamic vibration absorbers.
  • Calculating parameters of free and excited vibrations of strings, rods, shafts and beams. Resonances under harmonic excitations. Application of Rayleigh method of discretization. The role of external and internal damping.