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mae315_f08_01 - ENGINEERING ONLINE 327 Daniels Lecture...

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Unformatted text preview: ENGINEERING ONLINE 327 Daniels Lecture Notes Course Number: MAE 315 Instructor: Dr. R0 Date: 8/20/08 Lecture Number: 1 © 2007, North Carolina State University, All Rights Reserved Analysis of Vibrating Elements 1.. Mathmatical Modeling — to represent all the important features of a system for the purpose of deriving the governing equation(s) of motion a. Essential building blocks — spring, damper, mass b. Linear or nonlinear c. Iterative process in practice 2. Deriving Governing Eguation(s! — to obtain a simple mathmatical abstraction/expression of the vibrating system using dynamics principles a. Use of free body diagram b. Newton’s law, conservation of energy, etc. 3. Solving Governing Eguationgs! a. Standard ODE solution methods b. Laplace transform, matrix methods, numerical methods 4. Interpreting the results — to interpret the behavior of the system in the light of the purpose of the analysis/ synthesis © 2006, North Carolina State University, All Rights Reserved X(t)= AMM + Bcoswt‘ left A= C(os/ Md 6’- +CM/a’ flf/if—‘E -—— _ _ " Examples in Current Research - Object Transportation A flat object can be transported by either frictional or acoustic drive depending upon its ratio of mass to surface area. I amples in Crre Alternative Electronics Cooling ‘/Thermocouple Heat Source N Piezoelectric actuator ...
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