Vibrations of Systems with a Finite Number of Degrees of Freedom

This chapter is devoted to the study of vibrations of a system with finite number of degrees of freedom. The equation of motion in matrix formulation is discussed. The determination of displacements of rod systems in a matrix form is presented. General provisions, Simpson formula, pliability matrix, quasi-diagonal compliance (pliability) matrix of whole system, canonical equations in matrix form, vector matrix, etc., are discussed. The chapter presents a matrix form of determining the frequencies of free vibrations of a system with concentrated masses. Derivation of resolving equations, matrix form of determining the structure’s frequencies on vibration load, calculation of frames on vibration load by the forced method, calculation of frames on vibration load by the displacement method, derivation of resolving equations numbers of problems and solutions are discussed.