Eduardo Kausel-Fundamental solutions in elastodynamics_ a compendium-Cambridge University Press (2006)

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function [ ] = Blast2D(pois) 205 Ur = f*T.*real(1./P); T = T*cs/r; % dimensionless time plot (T, Ur); tit = ‘Radial displacement in full space due to line blast load’; title(tit); titx = ‘Dimensionless time, t*Cs/r’; xlabel(titx); grid on; pause; EasyPlot(‘B2D TDr.ezp’, tit, titx, T, Ur, ‘r’); close; return
206 MATLAB programs function [] = Cavity2D(r, r0, pois) % Cylindrical (2-D) cavity in a full, homogeneous space % subjected to a harmonic/impulsive pressure % The pressure is scaled so that p*pi*r0ˆ2=1 % % Arguments (in consistent units) % r = distance to receiver % r0 = radius of cavity % pois = Poisson’s ratio % % Returned transfer functions are g*mu*r vs. w*r/Cp % Returned time histories are u*rho*rˆ2 vs. t*Cp/r % in which mu is the shear modulus, rho is the mass density, % and Cp is the P-wave velocity % Basic data Cs = 1; % S-wave velocity (the results do not depend on this value) a2 = (2-2*pois)/(1-2*pois); a = sqrt(a2); % Cp/Cs Cp = a*Cs; % P-wave velocity rr = r0/r; nf = 1024; wmax = 2*pi*Cp/r0; dw = wmax/nf; w = [dw:dw:wmax]; % true frequency w0 = w*r0/Cp; w1 = w*r/Cp; % dimensionless frequency wmax = wmax*r/Cp; % max. dimensionless freq. dw = dw*r/Cp; % dimensionless freq. step % Frequency domain solution f1 = r/r0/pi; % factor for cavity f2 = 0.25/i; % factor for line of pressure h0 = besselh(0,2,w0); h1 = besselh(1,2,w0); y = 2*h1-a2*w0.*h0; h1 = besselh(1,2,w1); H = [0.5/pi, f1*h1./y]; % transfer function for cylindrical cavity G = [0.5/pi, f2*w1.*h1]; % transfer function for line of pressure w1 = [0, w1]; % frequency vector plot(w1,real(H)); hold on; plot(w1,imag(H),‘r’); %plot(w1,real(G),‘:’); % Compare with TF for line of pressure %plot(w1,imag(G),‘r:’); tit = sprintf( ... ‘T. F. for pressure in cylindrical cavity, r0=%5.4f, \\nu=%5.2f’, rr, pois);
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FUNDAMENTAL SOLUTIONS IN ELASTODYNA
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Fundamental Solutions in Elastodyna
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Contents Preface page ix SECTION I:
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Contents vii SECTION V: ANALYTICAL
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Preface We present in this work a c
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SECTION I: PRELIMINARIES 1 Fundamen
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1.1 Notation and table of symbols 3
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1.3 Coordinate systems and differen
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1.4 Strains, stresses, and the elas
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2 Dipoles In most cases, we provide
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2.2 Line dipoles 29 z z z y y y x x
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2.5 Blast loads (explosive line and
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2.6 Dipoles in cylindrical coordina
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SECTION II: FULL SPACE PROBLEMS 3 T
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3.3 SH line load in an orthotropic
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3.4 In-plane line load (SV-P waves)
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3.5 Dipoles in plane strain 41 0.6
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3.6 Line blast source: suddenly app
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3.7 Cylindrical cavity subjected to
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3.7 Cylindrical cavity subjected to
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4.2 Point load (Stokes problem) 49
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4.2 Point load (Stokes problem) 51
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4.3 Tension cracks 53 given earlier
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4.5 Torsional point source 55 Spher
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4.6 Torsional point source with ver
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4.8 Spherical cavity subjected to a
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4.8 Spherical cavity subjected to a
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4.9 Spatially harmonic line source
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SECTION III: HALF-SPACE PROBLEMS 5
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5.3 Half-plane, SV-P source and rec
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5.4 Half-plane, SV-P source on surf
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5.4 Half-plane, SV-P source on surf
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5.5 Half-plane, line blast load app
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6.1 3-D half-space, suddenly applie
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6.2 3-D half-space, suddenly applie
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6.3 3-D half-space, buried torsiona
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6.3 3-D half-space, buried torsiona
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SECTION IV: PLATES AND STRATA 7 Two
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7.2 Stratum subjected to SH line so
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7.3 Plate with mixed boundary condi
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SECTION V: ANALYTICAL AND NUMERICAL
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8.1 Summary of results 99 Plane str
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8.2 Scalar Helmholtz equation in Ca
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8.3 Vector Helmholtz equation in Ca
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8.4 Elastic wave equation in Cartes
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8.4 Elastic wave equation in Cartes
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8.6 Vector Helmholtz equation in cy
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8.7 Elastic wave equation in cylind
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8.8 Scalar Helmholtz equation in sp
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8.9 Vector Helmholtz equation in sp
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8.10 Elastic wave equation in spher
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8.10 Elastic wave equation in spher
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9 Integral transform method The int
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9.1 Cartesian coordinates 127 In pa
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9.1 Cartesian coordinates 129 Writi
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9.2 Cylindrical coordinates 131 Fou
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9.2 Cylindrical coordinates 133 Hen
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9.2 Cylindrical coordinates 135 Oth
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9.3 Spherical coordinates 137 √
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9.3 Spherical coordinates 139 ∫
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10.1 Summary of method 141 special
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10.2 Stiffness matrix method in Car
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Page 166 and 167: 10.2 Stiffness matrix method in Car
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Page 198 and 199: 11.2 Spherical Bessel functions 187
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Page 206 and 207: 12.1 Fourier transforms 195 b) Wave
Page 208 and 209: 12.3 Spherical Hankel transforms 19
Page 210 and 211: function [ ] = SH2D Full( ) 199 fun
Page 212 and 213: function [ ] = SVP2D Full(x, z, poi
Page 214 and 215: function [ ] = SVP2D Full(x, z, poi
Page 218 and 219: function [ ] = Cavity2D(r, r0, pois
Page 220 and 221: function [ ] = Point Full(pois) 209
Page 222 and 223: function Torsion Full(x, y, z, td,
Page 224 and 225: function [ ] = Cavity3D(r, pois) 21
Page 226 and 227: function [ ] = SH2D Half(xs, zs, xr
Page 228 and 229: function [T, Ux, Uz] = Garvin(x, z,
Page 230 and 231: function [T, Uxx, Uxz, Uzz] = lamb2
Page 236 and 237: function [T, Uxx, Utx, Uzz, Urz] =
Page 238 and 239: function [T, Uxx, Utx, Uzz, Urz] =
Page 240 and 241: function [ ] = Torsion Half(r, z, z
Page 242 and 243: function [ ] = Torsion Half(r, z, z
Page 244 and 245: function [ ] = SH Plate(x, z, z0) 2
Page 246 and 247: function [ ] = SH Stratum(x, z, z0)
Page 248 and 249: function [ ] = SH Stratum(x, z, z0)
Page 250 and 251: function [ ] = SVP Plate(x, z, z0,
Page 256 and 257: function [ztors, zspher] = spheroid
Page 258 and 259: function [ztors, zspher] = spheroid
Page 260 and 261: function [si] = cisib(x) 249 functi
Page 262: function [el3] = ellipint3(phi, N,
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Eduardo Kausel-Fundamental solutions in elastodynamics_ a compendium-Cambridge University Press (2006)

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