MCG 4308 Lecture Notes - Lecture 3: Damping Ratio, Natural Frequency, Kinetic Energy
22 Jan 2018
School
Department
Course
Professor
Reminder: Special tutorial Wednesday 8:30 - Site A0150
Design
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Transmission of vibrations to humans
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Can cause mechanical failure
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Fatigue in materials
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Induced stresses
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Applications such as conveyers, washing machines, toothbrush, drill
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Why study vibrations?
Basic concepts
Vibration (oscillation) is any motion that repeats itself.
store Kinetic energy (KE)
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Store Potential energy (PE)
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Energy might get lost
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Need to
Vibration; energy may be lost or added
Conservative system: No loss or gain of energy, total energy is conserved
Free vibrations: System is initially disturbed, then left to vibrate on it's own
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Forced vibrations: System receives induced forces to keep it vibrating
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Undamped vibrations: Oscillations are continuous
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Damped vibrations: Oscillations die out over a period of time
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Linear: all components behave linearly
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Deterministic vibrations: vibrations can be predicted
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Random vibrations: vibrations can't be predicted
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Terminology:
Periodic motion terminology
A: Amplitude
T: Period; time to complete one oscillation [s, min]
Period is the inverse of the frequency:
Angle frequency:
Simple harmonic motion: Any motion that can be described by SINE or COSINE
Phase: relative quantity describing time relationship b/w harmonic motion at same frequency
Natural frequency: Th frequency at which a system oscillates when it's not damped
Modeling decisions
1.
Derive equations of motion (E of M) -> Newtons, Lagrange…
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Solve equations
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Interpret
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Vibrations analysis:
Vibrations modeling
spring element -> store potential energy
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Mass/inertia energy -> KE
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Damping element (maybe)
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Jan 15th
January 15, 2018
11:33 AM
Lectures Page 1
Document Summary
Reminder: special tutorial wednesday 8:30 - site a0150. Applications such as conveyers, washing machines, toothbrush, drill. Vibration (oscillation) is any motion that repeats itself. Conservative system: no loss or gain of energy, total energy is conserved. Free vibrations: system is initially disturbed, then left to vibrate on it"s own. Forced vibrations: system receives induced forces to keep it vibrating. Damped vibrations: oscillations die out over a period of time. T: period; time to complete one oscillation [s, min] Simple harmonic motion: any motion that can be described by sine or cosine. Phase: relative quantity describing time relationship b/w harmonic motion at same frequency. Natural frequency: th frequency at which a system oscillates when it"s not damped. Derive equations of motion (e of m) -> newtons, lagrange . Vibrations modeling spring element -> store potential energy. A mass m is a lumped system since it only has mass m, no damping no springiness.
