Fundamentals of Wave Propagation - Civil Engineeringbartlett/CVEEN6330/5330l4.pdf · © Steven F. Bartlett, 2011 Fundamentals of Wave Propagation Thursday, January 27, 2011 8:50 AM

© Steven F. Bartlett, 2011

Fundamentals of Wave PropagationThursday, January 27, 2011 8:50 AM

Lecture 4 - Wave Propagation Theory Page 1


Waves (cont.)Thursday, January 27, 2011 8:50 AM



Waves (cont.)Thursday, January 27, 2011 8:50 AM



Wave (cont.)Thursday, January 27, 2011 8:50 AM



Wave (cont.)Thursday, January 27, 2011 8:50 AM



1D Compressional WaveThursday, January 27, 2011 8:50 AM



1D Wave Equation for Compressional WaveThursday, January 27, 2011 8:50 AM



1D Wave Equation for Compressional Wave (cont.)Thursday, January 27, 2011 8:50 AM



Speed of P wave PropagationThursday, January 27, 2011 8:50 AM



1D Torsional (Shear) WaveThursday, January 27, 2011 8:50 AM



1D Wave Equation for a Torsional WaveThursday, January 27, 2011 8:50 AM



Speed of S wave PropagationThursday, January 27, 2011 8:50 AM



Solution for 1-D Wave EquationThursday, January 27, 2011 8:50 AM



Solution for 1-D Wave Equation (cont.)Thursday, January 27, 2011 8:50 AM



Solution for 1-D Wave Equation (cont.)Thursday, January 27, 2011 8:50 AM



3D Stress NotationThursday, January 27, 2011 8:50 AM



2D Plain StrainThursday, January 27, 2011 8:50 AM



3D Strain Relations, Rigid Body Rotation, Hooke's LawThursday, January 27, 2011 8:50 AM



Hooke's Law (cont.)Thursday, January 27, 2011 8:50 AM



Hooke's Law (cont.) - Elastic ModuliThursday, January 27, 2011 8:50 AM



Derivation of Wave Equation for 3D Elastic BodyThursday, January 27, 2011 8:50 AM



Derivation of Wave Equation for 3D Elastic Body (cont.)Thursday, January 27, 2011 8:50 AM



Wave Equation for 3D Elastic Body (cont.) and P wavesThursday, January 27, 2011 8:50 AM



Wave Equation for 3D Elastic Body (cont.) and Shear WavesThursday, January 27, 2011 8:50 AM



Shear Waves (cont.)Thursday, January 27, 2011 8:50 AM



Waves in Semi-Infinite HalfspaceThursday, January 27, 2011 8:50 AM



Waves in Semi-Infinite Halfspace (cont.)Thursday, January 27, 2011 8:50 AM
























Waves in a Layered BodyWednesday, August 17, 2011 12:45 PM



Waves in a Layered Body (cont.)Wednesday, August 17, 2011 12:45 PM






























Attenuation of Stress WavesWednesday, August 17, 2011 12:45 PM



Attenuation of Stress Waves (cont.)Wednesday, August 17, 2011 12:45 PM









Finite difference calculation loop written with differential calculus

Finite difference calculation loop written with incremental approach

Solution of Wave Equation for Shear WaveWednesday, August 17, 2011 12:45 PM



Note that with this approach we can approximate the change of things that vary either in space or time, or both. In regards to time, we will use the forward differencing approach.

Solution of Wave Equation for Shear Wave (cont.)Wednesday, August 17, 2011 12:45 PM












Solution of Wave Equation for Shear Wave (cont.)Wednesday, March 05, 2014 11:45 AM






;FLAC verification of solutionconfig dynamic extra 5grid 1 10model elasticini y mul 1;set dy_damp rayl 0.05 5; 5 percent damping at 5 hzfix yprop dens 2000 bulk 9.6E6 shear 3.2E6def wave wave=amp*cos(omega*dytime)

wave=0 if dytime>=100

endifendset amp=0.3set omega = 6.283apply xvel 1 hist wave yvel=0 j=1his 1 xdisp i 1 j 1his 2 xdisp i 1 j 11his 3 xvel i 1 j 1his 4 dytimeset dytime = 0history 999 unbalancedsolve dytime 5.01save model2.sav 'last project state'




BlankWednesday, August 17, 2011 12:45 PM


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Fundamentals of Wave Propagation - Civil Engineeringbartlett/CVEEN6330/5330l4.pdf · © Steven F. Bartlett, 2011 Fundamentals of Wave Propagation Thursday, January 27, 2011 8:50 AM