ME 470 Mechanical System Vibrations

Course Description

Linear vibration of mechanical systems; System modeling; Derivation of governing equations using Newtonian mechanics and Lagrange’s equations; Free and forced response of single degree of freedom systems; Multiple degrees of freedom systems; Modal analysis for response calculations; Introduction to vibration of continuous systems. Prerequisites: MATH 305 (Introduction to ODEs), ENGR 261 (Dynamics), and ENGR 351 (Numerical Methods).

Course Content

a) Dynamics

Review of the essential components of dynamics; Cartesian and polar coordinates; Newtonian mechanics for particles and rigid bodies; power; work; kinetic and potential energy; Lagrange’s equations.

b) Single degree of freedom system vibration

Equations of motion; undamped and damped free response; forced response due to direct excitation, mass imbalance, and base motion; effect of damping; response to periodic and nonperiodic excitations.

c) Multi-degree of freedom system vibration

Equations of motion; eigenvalue problems; natural frequencies and vibration modes; modal analysis for response calculations; vibration absorbers; introduction to gyroscopic (spinning) system vibration.

d) Continuous system vibration

Vibration of elastic continuum, for example, strings, rods, beams, membranes, and plates. Equations of motion, natural frequencies and vibration modes, and free and forced response calculations.

References

Meirovitch, L., 2010, Fundamentals of Vibrations, Waveland Press, 2010.

Den Hartog, J.P., 1985, Mechanical Vibrations, Dover Publications, ISBN-13: 080-0759647859.

Thomson, W. T., Dahleh, M. D., 1998, Theory of Vibration with Applications, 5^th Ed., Prentice Hall.

Inman, D. J., Engineering Vibration, 4^th Edition, Prentice Hall.

Meirovitch, L., 1997, Principles and Techniques of Vibrations, Prentice Hall.

Meirovitch, L., 1980, Computational Methods in Structural Dynamics, Sijthofl & Noordhoff International Publishers.

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