EM 514 - Vibration of Mechanical Systems (Vibrações de Sistemas Mecânicos) Fundamentals of vibration: Basic concepts of vibration, harmonic motion, harmonic analysis. Single degree of freedom systems: Free vibration with viscous damping, response of a damped system under harmonic force, response of a 35 damped system under the harmonic motion of the base, response of a damped system under rotating unbalance, frequency response function, response under a general periodic force, response under a non-periodic force, convolution integral, response spectrum. Two degree of freedom systems: Equations of motion for forced vibration, free vibration analysis of an un-damped system, coordinate coupling and principal coordinates, forced vibration analysis, semi-definite systems, un-damped vibration absorber. Multi-degree of freedom systems: Equations of motion, influence coefficients, Lagrange’s equations, eigen-value problem, expansion theorem, free vibration of un-damped systems, forced vibration of viscously damped systems. Determination of natural frequencies and mode shapes: Rayleigh’s method, vector iteration method, Jacobi’s method. Numerical integration methods in vibration analysis: Central difference method for single and multi-degree of freedom systems. Continuous systems: Transverse vibration of a string or cable, longitudinal vibration of a bar or rod, torsional vibration of a shaft or rod, lateral vibration of beams, Rayleigh’s energy method, Rayleigh-Ritz method, assumed-modes method. Objectives The purpose of this course is to present the basic concepts of the theory of vibration and the methods for analyzing the vibratory motion developed in a mechanical or structural system when it is subjected to a dynamic loading. <<<<<<<<<<  BACK  <<<<<<<<<<