SD-Lecture17-Stress-Waves-in-Infinite-Media

SD-Lecture17-Stress-Waves-in-Infinite-Media - CEG CEG-5065C...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CEG CEG-5065C Soil Dynamics 5065C Soil Dynamics Lecture #17 Lecture #17 Stress Waves in Infinite Media Luis A. Prieto-Portar 2009 The equation of motion of a stress wave in an elastic medium. Consider an element of an elastic medium, as shown below, with all the possible stresses on each of its six faces. x The equation of motion can be found through a summation of the forces along all three axes, and using Newtons second law ( F = ma ), ( )( )( ) 2 2 Consider the displacement u in the x-direction, Simplifying, and expanding to all three axes, & & & +- + +- + +- = yx zx x x x zx zx yx yx dx dydz dz dxdy dy dxdz x z y u dx dy dz t + y x x 2 2 2 2 2 2 + = + + = + + = x zx xy y zy yz xz z u y z t v x y z t w x y z t Compression stress waves (P-waves, or Primary waves or Dilatational waves). The stress wave of motion in the x-direction was developed on the previous slide, 2 2 Recall that, and and 2 therefore, = + + = = = + yx zx x yx yx zx zx x x u t x y z G G G ( ) ( ) ( ) ( ) 2 2 2 2 2 and again recall that, and 2 = + + + = + = + & = + + + x yx zx yx zx x u G G G t x y z v u u w x y z x u v u G G t x y x y & + + u w G z z x 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Simplifying, but therefore,simplifying and extending to all three axes, & = + + + + + +...
View Full Document

Page1 / 19

SD-Lecture17-Stress-Waves-in-Infinite-Media - CEG CEG-5065C...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online