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SD-Lecture03-Measuring-Vibrations

# SD-Lecture03-Measuring-Vibrations - Soil Dynamics Lecture...

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Soil Dynamics Lecture 03 Measuring Vibrations © Luis A. Prieto-Portar, August 2006.

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A rotating mass type of excitation. Some machines have intentionally designed eccentric weights that shake their frames in a forceful manner. For example, steel sheet-piling vibrating machines use this principle, along with the application of water pressure, in order to create a “liquification” condition in the soil and thereby easily place these sheet-piles to great depths. A simple diagram of this type is shown below. A rotating mass excitation of a foundation-soil system.
( ) ( ) ( ) ( ) 2 2 0 0 2 2 2 1 2 2 2 2 2 2 2 1 2 1 4 e n n n n n The differential equation of motion is, mz cz kz Q sin t where Q m e U The solution maybe of the form , z Z cos( t ) where, / (U / m )( / ) Z and tan D / / D / The normalized plot of Z ω ω ω ω α ω ω ω ω α ω ω ω ω ω ω ω ω ω + + = = = = + = = + ɺɺ ɺ ( ) 2 2 1 2 2 1 n m n m resonant resonant /(U / m ) vs / is shown on the next slide. The angular resonant frequency f is, f f D The amplitude at the damped resonant frequency Z is, U / m Z D D ω ω ω = =

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A vibratory machine is commencing to place the steel casing of a drilled shaft. Notice the two counter- rotating masses on its lower part of the vibrating machine.

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Vibratory hammer driving a timber pile. Note the opposite rotating shafts on the driver.
A vibro-flotation machine. This device is used to “liquefy” granular soils and thereby densify a column of this soil. It is used for soil improvement. The vibro-flotation probe has two concentrically rotating masses within its shaft, to generate large vertical vibrations.

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Example 1.
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