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

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function [ ] = SVP Plate(x, z, z0, poi, BC1, BC2) 243 n = length(T2); S = sqrt((T2(k:n)-tp2)); PSI = [zeros(1,k1),-S/ts2]; % yes, we must divide by ts2, not tp2 CHI = [zeros(1,k1),alfaˆ2./S]-2*PSI; if tp2==T2(k1), CHI(k1)=inf; end k = find(ts2
244 MATLAB programs function [ztors, zspher] = spheroidal (pois, m, wmin, wmax) % Computes the torsional and spheroidal modes of a solid sphere, and % plots the two determinant functions whose zero crossings define the roots % Assumes a sphere of radius R=1 and shear wave velocity Cs=1 % Note: the modes are independent of the azimuthal index n % % Input arguments: % pois = Poisson’s ratio % m = radial index % wmin = minimum frequency for search % wmax = maximum frequency for search % Output arguments: % ztors = dimensionless frequencies, torsional modes % zspher = dimensionless frequencies, spheroidal modes % Actual frequencies (rad/s) are obtained multiplying by Cs/R % where Cs is the shear wave velocity, and R is the radius % % For enhanced accuracy, it uses the Bessel functions of half order % instead of the actual spherical Bessel functions. Reason: % The factors sqrt(pi/2z) cancel out in the determinant equations % % Makes first a rough search in the search interval to determine approximate % values of the roots, then refines the results using the bisection method % % Results agree with Eringen & Suhubi, Elastodynamics, Vol. II, pp. 814,818 dz = 0.1; % initial search step if wmin0 f = dettors(m,zs); ztors = zerox(f,dz,zs(1)); nz = length(ztors); for k=1:nz z1 = ztors(k)-dz; z2 = ztors(k)+dz; ztors(k) = bisect2(‘dettors’, m, z1, z2, 1.e-5,pois); end plot(zs,f); axis([0 wmax -1 1]); grid on; pause;
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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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10.3 Stiffness matrix method in cyl
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10.4 Stiffness matrix method for la
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SECTION VI: APPENDICES 11 Basic pro
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11.2 Spherical Bessel functions 187
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11.3 Legendre polynomials 189 1.0 P
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11.4 Associated Legendre functions
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Page 206 and 207: 12.1 Fourier transforms 195 b) Wave
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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 216 and 217: function [ ] = Blast2D(pois) 205 Ur
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 252 and 253: 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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