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1.1.1 ME 362 Vibrations I
This course covers vibrations of single to multiple degrees of freedom systems with and without damping. In addition, it includes design for vibration isolation and suppression, practical considerations in vibration and human tolerance for vibration. The course explores the following topics:
Free Vibration of single degree of freedom linear systems: Harmonic motion, Vibration System Modelling, Energy methods and Stiffness. Response to Harmonic Excitation: Forced and Base Excitation of Undamped and Damped One-degree-of-freedom Systems, Rotating Unbalance, Coulomb and other forms of damping. General Forced Response: Impulse response functions, response to arbitrary and periodic inputs, transform methods, shock spectrum, Computer simulation of Time response of single degree of freedoms systems using Euler Method. Multiple-Degree-of-Freedom Systems: Two-Degree-of-Freedom Undamped Models, Eigenvalues and Natural Frequencies, Systems with More than Two Degrees of Freedom, Systems Viscous Damping, Forced Systems, Lagrange’s Equations. Torsional vibration systems including geared systems. Design for Vibration: Acceptable Levels of Vibration, Vibration Isolation and Suppression, Practical Speeds of Rotating Disc, Optimization. Vibration Testing and Measuring: Measuring instruments and testing.
1.1.2 ME 461 Vibrations II
Vibrations II is designed to reflect on recent advances in vibration Technology and many Accreditation Board for Engineering and Technology, criteria and increased importance of engineering design, modal analysis and measurement. Topics covered include:
Distributed-Parameter Systems: Vibration of Strings and Cables, Modes and Natural frequencies, Vibration of Rods and Bars, Bending Vibration of beams. Vibration Testing and Experimental Modal Analysis: Measurement Hardware, Digital Signal Processing, Random Signal Analysis in Testing, Vibration Testing for Endurance and Diagnostics. Introduction to Finite Element Method: Bar, Three-Element bar, Lumped Mass Matrices. Computational Consideration: Influence of Coefficients and Dunkerley’s Formula, Rayleigh’s Method, Matrix Iteration, Computer simulation of Time response of Multi- degree of freedoms systems using Euler Method. Nonlinear Vibration: Single-degree-of-freedom Phase Plots, Equation Linearization, Pendulum, Nonlinear damping and Averaging. Vibration of machine foundations.