Engineering Dynamics

Reducing Problem Vibration and Intro to Multi-DOF Vibration

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Session Overview

Covered this week: This week we discuss ways of treating vibration problems. In particular the design of vibration isolation supports. Then we consider the vibration of systems with multiple degrees of freedom. The Brooklyn Bridge is one of the oldest suspension bridges in the United States and the first steel-wire suspension bridge. Image courtesy of Daniel Stone on Flickr.

Videos

Lecture Videos

• Watch Lecture 21: Vibration Isolation

  • Video Chapters
    • Demonstration of a vibration isolation system-strobe light and vibrating beam
    • Euler’s formula for complex numbers
    • Hx/F transfer function by complex number approach
    • Base motion Hx/y transfer function-vibration isolation system design
    • Predicting natural frequency by SQRT(g/delta)
    • Vibration isolation of the source-H-Ft/Fo transferfunction-with strobe light demo

• Watch Lecture 22: Finding Natural Frequencies and Mode Shapes of a 2 DOF System

  • Video Chapters
    • Obtain the equations of motion of a 2 DOF system
    • Finding the natural frequencies by the characteristic equation
    • Finding the modes shapes of the 2 DOF system
    • Matlab simulation of the response of the 2 DOF system to initial conditions
    • Physical demonstration of the motion of a real 2 DOF system

Recitation Video and Notes

• Watch Recitation 10: Steady State Dynamics
  • This recitation covers a steady state frequency response problem.
• Recitation 10 Notes: Natural Frequency From Deflection & Frequency Response (PDF)
  • These recitation notes were compiled by Prof. David Gossard, another instructor for the course. His notes go over concepts and problems covered during the recitation sections he taught, and may not precisely correspond to the content covered in the above recitation video.

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