1_Introduction_1.pptx - Mechanical Vibrations Dr Tarek ELmahdy 1 What Are We Up To Title of Chapters BASIC CONCEPTS OF MECHANICAL VIBRATIONS MECHANICAL

1_Introduction_1.pptx - Mechanical Vibrations Dr Tarek...

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Mechanical Vibrations Dr. Tarek ELmahdy 1
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What Are We Up To? Title of Chapters : BASIC CONCEPTS OF MECHANICAL VIBRATIONS MECHANICAL VIBRATION SINGLE DEGREE OF FREEDOM SYSTEMS “Single Degree of Freedom” As simple as it gets… Dealing with a system like one in figure (a) System in (b) already has two degrees of freedom… 2
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What are we up to? (Cntd) Undersatand the vibration phenomena Understand how to derive equations of motion (EOM) for 1DOF systems Once we’ll have the EOMs, we’ll solve them First then, how do we derive the EOM? Newton’ Second Law Work and Energy Methods Very handy for conservative systems 3
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What is the Vibration? Vibration is a repetitive motion about a reference position. 4
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Bad Side of the Vibration Singers & windows glass Soldier march on bridges Winds effect in bridges Tacoma Narrow Bridge (when engineers dose not account for resonance) 5
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TACOMA NARROW BRIDGE 6 video.flv YouTube- Tacoma Bridge.mp4
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TACOMA TODAY 9
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Good Side of the Vibration Medical Applications destroy kidney and liver stones
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Unformatted text preview: ” Fault Detection and Diagnosis “ cars ” Modification of the Dynamic characteristics 10 SOURCE OF VIBRATION 11 Mounting of measuring units 12 Temp . Press . Flow Oil Vib . Out of balancing ✔ Miss alignment ✔ ✔ Damage in Rolling Bearing ✔ ✔ ✔ Damage in Journal Bearing ✔ ✔ ✔ ✔ ✔ Damage in Gears ✔ ✔ Mechanical Looseness ✔ Cracking ✔ Noise ✔ 13 Natural frequency X (t) F (t) K C 14 2 ( ) ( ) cos( ) ( ) ( ) cos( ) where / , n n m x t k x t F t x t x t f t k f F m m && && 15 RMS True peak - peak RMS peak For Sine waves only: a T = averaging period RMS K factor = Crest factor = K factor = RMS peak 16 A T a t dt RMS T 1 2 ( ) A A peak RMS 2 * A A peak RMS A A RMS peak A peak A peak peak A peak A peak peak Acceleration Velocity Displacement M a M d v v a d m m a d v m a v d Velocity Displacement Acceleration Time (Simple vibration) Frequency (real machine) 17...
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  • Fall '16
  • MR BIJU CV
  • Tacoma Narrow Bridge, VIBRATION SINGLE DEGREE

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