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Forced Vibrations – concept checklist

This concept checklist covers the derivation of equations of motion, understanding of transient and steady-state response, amplitude and phase of steady-state response, resonance, high and low frequency response, determination of amplitude and damping coefficient, and designing of engineering systems for forced vibration systems.

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Forced Vibrations – concept checklist

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  1. Forced Vibrations – concept checklist You should be able to: Be able to derive equations of motion for spring-mass systems subjected to external forcing (several types) and solve EOM using complex vars,or by comparing to solution tables Understand (qualitatively) meaning of ‘transient’ and ‘steady-state’ response of a forced vibration system (see Java simulation on web) Understand the meaning of ‘Amplitude’ and ‘phase’ of steady-state response of a forced vibration system Understand amplitude-v-frequency formulas (or graphs), resonance, high and low frequency response for 3 systems Determine the amplitude of steady-state vibration of forced spring-mass systems. Deduce damping coefficient and natural frequency from measured forced response of a vibrating system Use forced vibration concepts to design engineering systems

  2. EOM for forced vibrating systems

  3. Steady-state solution – external force System vibrates at same frequency as force Amplitude depends on forcing frequency, nat frequency, and damping coeft.

  4. Steady-state solution – Base excitation

  5. Steady-state solution – Rotor excitation

  6. Using forced vibration measurements to find natural frequency and damping coefficient

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