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Unformatted text preview: 1 CE 316 Geotechnical Earthquake Engineering Week 6 Wave Propagation Infinitely Long Rod Constrained infinite rod for 1D wave propagation E A dx . . ( 29 ( 29 E M 2 1 1 1 + = Constrained Modulus Constrained Modulus 1D Wave Propagation, Infinite Uniform Elastic Material, P Wave 2 2 m equilibriu Dynamic t u Adx A A dx x o o x x x = + x x M = 2 2 Equation of Motion x u x t = x u x = where Inertial forces 1D Wave Propagation, Infinite Uniform Elastic Material, P Wave 2 2 2 2 2 2 2 x u v x u M t u p = = Particle Velocity: m x m m x m x m x x v v v v M t t v M t x t u u = = = = = = 2 M v p = 1D Wave Propagation, Infinite Uniform Elastic Material, S Wave 2 2 2 2 2 2 2 x v x G t s = = G v s = 1D Harmonic Stress Wave, Infinite Uniform Elastic Material 2 2 2 2 2 x u v t u = ) cos( ) cos( ) , ( kx t B kx t A t x u + = wave number k v = t cos ) ( stress harmonic state steady O t = 2 2 wavelength v vT v f k = = = = v = wave propagation velocity: time domain space domain General ThreeDimensional State of Stress on material element yx xy = zx xz = zy yz = General ThreeDimensional State of Strain on material element dx du xx = Straindisplacement components, dy dv yy = dz dw zz = dy du dx dv xy + = dz dv dy dw yz + = dx dw dz du zx + = Rotationdisplacement components,...
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This note was uploaded on 02/27/2011 for the course CIV ENG 316 taught by Professor Louis during the Spring '11 term at Missouri S&T.
 Spring '11
 Louis

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