To help master thesis studies by modeling of systems at the high degree and to give theorotical knowledge about various systems and analytical solutions which aren’t seen during the undergraduate education at the course of mechanical vibrations.

Concepts and introduction about vibration, Superposition principle, effect coefficients, Matrix forms of lagranfe equations, transformation of coordinate, attachment motion equations, Natural mods at the discrete systems, Eigenvalue problem, Ortagonal of eigenfunction, Modal matrix, Normal coordinates, Expansion theorem, Method of matrix iteration, finding the second eigenvectors, proportion of Rayleigh, Formula of Dunkerley, vibration of continuous systems, formulation of boundary value, Ortagonal of eigenfunctions, Expansion theorem, Vibration of beams and wires, Approximately methods at the definition of natural mod and frequencies, approach of Random vibration.