ME56300 - Mechanical VibrationsFall 2018 Days:
TBD TBDCredit Hours:
Understand various methods for modeling vibrations in discrete and continuous systems and then analyzing free and forced vibrations in these systems. Develop insight into vibrations using modal analysis techniques. Appreciate the utility of Matlab for analyzing vibration phenomena.Description:
Review of modeling, Newton-Euler equations, Lagrange's equations, free vibration of single, multi-degree-of-freedom systems and continuous systems, Eigenvalue analysis, forced response of single, multi-degree-of-freedom systems and continuous systems, modal analysis for free and forced responses, applications, use of Matlab for analyzing free and forced vibrations.Topics Covered:
Equations of Motion: Newton-Euler equations, Power equation, Generalized coordinates and forces, Lagrange's equations, Linearization of EOM's, Second order continuous systems, Fourth order continuous systems; Free Response: Single DOF systems, Undamped multi DOF systems, Eigenvalue problem for discrete systems, Rigid body modes, Damped multi DOF systems, Second order continuous systems, Fourth order continuous systems, Eigenvalue problem for continuous systems, Modal uncoupling, Forced Response: Harmonic single DOF response, Periodic single DOF response, Forced multi DOF system response, Forced continuous system response, Case studies; Vibration isolation, Whirling, Dynamic sensing, Vibration absorbers.Prerequisites:
Strength of materials; modeling and analysis of dynamical systems.Applied/Theory:
Weekly homework (3-4 problems per assignment). No grades will be assigned for homework but full solutions will be provided to the student.Projects:
Two one-hour midterm exams and one two-hour final exam.Textbooks:
Recommended text --W. T. Thomson and M. Dahleh, "Theory of Vibrations with Applications", 5th ed., Prentice Hall, 1997, ISBN 0-136-51068-X. Disclaimer: final textbook listings are available in April for fall and summer semesters. Please visit the Listing of Textbooks by College or School for the most up-to-date information.
ProEd minimum computer requirements; MATLAB or equivalent software. The solutions of three to four homework assignments will often require the usage of MATLAB. Some course material will be available to the students over the Internet. Additional examples beyond that presented in lecture will be uploaded to the course web site.
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