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 |  موضوع: كتاب Vibration of Laminated Shells and Plates - Mohamad S. Qatu الأحد 28 أبريل 2013 - 19:36 | |
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Vibration of Laminated Shells and Plates - Mohamad S. Qatu
ويتناول الموضوعات الأتية :
Algebraic polynomials 63, 66, 204
Angle of twist 224–231
Anisotropic 48
Approximate solutions 60
Arc length 24, 28, 185
Bars 75
Beams
Curved 75–105
Laminated 75–105
Sandwich 75
Straight 75
Thick 82–87
Thin 76–81
Bending 109, 114, 189, 263
Cylindrical 78
Bending modes (see Mode shapes)
Bending stretching coupling 115, 167, 189,
263
Boundary conditions
Forced 62
Geometric 62
Thick beams 86
Thick plates 119
Thick shallow shells 193
Thick shells 44
Thin beams 81
Thin plates 112
Thin shallow shells 186
Thin shells 51
Three dimensional 12–14
Boundary element methods 72
Boundary terms 178
Cantilevered
Pretwisted plates 224–230
Rectangular plates 148, 152
Shallow shells 214–223
Trapezoidal plates 166
Trapezoidal shallow shells 247–249
Triangular plates 166
Triangular shallow shells 247–249
Cartesian coordinates 6, 121, 187, 193
Christoffel symbols 26
Classical beam theory 76–81
Classical plate theory 4, 109–115
Classical shallow shell theory 185–190
Classical shell theory 46–52
Closed rings 75, 91
Columns 75
Compatibility conditions 14–15, 52
Compatibility equations 14–15
Completely free
Rectangular plates 148
Shallow shells 205–213
Trapezoidal plates 163
Trapezoidal shallow shells 241–247
Triangular plates 163
Triangular shallow shells 241–247
Composite (see Laminated)
Constitutive equations (see Stress-strain
relations)
Continuous systems 64, 99
Convergence 64, 67, 99, 144, 161, 168, 205,
216, 225, 232, 241, 247
Cross-ply lamination (see Lamination)
Curvature changes
Thick beams 82
Thick cylindrical shells 265
Thick plates 110, 113
Thick shallow shells 190
Thick shells 35
Thin beams 77
Thin cylindrical shells 262
405
Thin plates 117, 119
Thin shallow shells 186
Thin shells 47
Curved plates 183
Damped ring 75
Damped shells 360
Deformation 7, 28
Degrees of freedom (DOF) 67, 69, 75, 99,
147–149, 217
Differential quadratures 72, 179
Displacement field 64, 69
Doubly cantilevered 231–235
Dynamic loading 358
Elastic constraints 81, 142
Elastic foundation 360
Elasticity
Theory of 19, 260
Three dimensional (3D) 6, 12–14, 17,
23–28, 32, 54, 55, 116, 178
Elements
Brick 67
Eight noded 67
Rectangular 67
Shell 67
Solid 67
Triangular 67
Energy
Kinetic energy 16, 42, 80, 86, 114,
189, 263
Potential energy 16, 41, 80, 86, 114,
189, 263
Strain energy
Thick beams 86
Thick shells 41
Thin barrel shells 301
Thin beams 80
Thin conical shells 331
Thin cylindrical shells 263
Thin plates 114–115
Thin shallow shells 189–190
Thin shells 49
Three dimensional 16
Energy functionals (see Energy) 61, 63
Epoxy resin 8
Equations of motion
Thick barrel shells 308
Thick beams 84
Thick conical shells 334
Thick cylindrical shells 266
Thick plates 118, 119, 177
Thick shallow shells 193, 194, 254
Thick shells 42
Thick spherical shells 351
Thin barrel shells 299
Thin beams 78
Thin conical shells 325
Thin cylindrical shells 262
Thin plates 111, 112, 176
Thin shallow shells 186, 188, 253
Thin shells 50
Thin spherical shells 348
Three dimensional 12, 32
Exact solutions 60, 88, 93, 195–201,
268–284, 303, 309
Existence of a solution 15
Experimental methods 59
External work 41
Fiber 8, 31, 172
Fiber orientation 8
Finite differences 184
Finite element methods 54, 66–72, 140, 146,
148, 149, 169, 184
First fundamental form 24
Fluid media 360
Flutter 5
Force resultants (see Stress resultants)
Fourier analysis 72
Fourier series 197
Frenet’s formula 25
Galerkin method 65–66, 179, 184
Gauss characteristic equation 27
Geometric series 40
406 Subject Index
Hamilton’s principle 15–19, 32, 43, 81, 111,
112, 262
Higher order terms 38, 40, 63
Holography 59
Homogeneous 9, 109, 112
Imperfect shells 359
Impulsive loading 358
Initial loading 358
Kinematic equations 7–8
Thick barrel shells 307
Thick beams 84
Thick conical shells 334
Thick cylindrical shells 265, 316
Thick plates 116, 177
Thick shallow shells 190, 252
Thick shells 34
Thick spherical shells 350
Thin barrel shells 298
Thin beams 78
Thin conical shells 324
Thin cylindrical shells 262, 315
Thin plates 110, 175
Thin shallow shells 186, 251–252
Thin shells 46
Thin spherical shells 348
Three dimensional 28
Kerr foundation 360
Kinetics 6
Kirchhoff hypothesis 77, 110, 111
Lagrangian 16, 17, 61, 63
Lame´ parameters 29, 111, 112, 119
Lamination
Angle-ply 129, 122, 137, 196
Antisymmetric 60, 114, 122, 130, 129,
137
Asymmetric (see Unsymmetric)
Cross-ply 60, 122, 124, 126, 133,
196–198, 200, 268–284
Sequence 60, 139
Symmetric 41, 49, 80, 85, 140, 190
Unsymmetric 60, 122, 198–199
Layer-wise theories 52
Levy solution 122, 200
Love’s approximation 4, 33, 185
Mainardi-Codazzi equations 27
Mass parameters 120
Matrix
Mass 70, 98, 198
Stiffness 69, 70, 98, 198
Transformation 10
Membrane theory 46
Midsurface strains (see Curvature changes)
Modes 102, 103
Mode shapes
Cantilevered pretwisted plates 227–231
Cantilevered shallow shells 220–223
Cylindrical shells 276
Doubly cantilevered shallow shells
234–236
Free shallow shells 212–214
Plates 150–155
Moduli of elasticity 8
Moduli of rigidity 8
Moment resultants (see Stress resultants)
Monoclinic 31
Navier solution 122, 127, 197
Newton’s second law 12, 16, 111
Nodes 66, 69
Nonlinear
Analysis 178
Geometric nonlinearity 53
Material nonlinearity 53
Terms 29
Theories 53
Orthotropy
Circular 8, 174–178, 184
Conical 324
Cylindrical 261
Diagonal 156
Elliptical 112
Rectangular 8, 112, 119, 173, 184
Spherical 348
Subject Index 407
Pasternak foundation 360
Piezoelecric shells 359
Plates 109–179
Circular 112, 172–178
Ellliptical 112, 178
Equilateral 165
Isotropic 158–159
Rectangular 121–158
Right trapezoidal 165
Right triangular 163
Symmetrical triangular 165
Thick 116–121, 126, 130, 135, 177
Thin 109–115, 124, 129, 134, 174
Trapezoidal 159–171
Triangular 159–171
Preprocessor 66
Polar coordinates 174, 253, 259
Postprocessor 70
Poisson’s ratio 9
Pretwisted (see Plates, pretwisted)
Radius of twist (see Plates, pretwisted)
Rayleigh method 61
Rectangular coordinates
(see Cartesian coordinates)
Resin 8
Rings 75
Ritz method 61–64, 95, 140–144, 146, 169,
179, 203–205, 286–297
Rods 75
Rotating shells 359
Second fundamental form 25
Shafts 75
Shallow shells
Circular planform 249–254
Cylindrical 198–248
Ellipsoidal 183
Elliptical planform 185, 241
Equilateral 244–245
Hyperbolic paraboloidal 198–248
Rectangular planform 195–240
Right triangular 244–245
Spherical 186, 198–254
Symmetrical triangular 244–245
Thick 190–195
Thin 185–190
Trapezoidal 241–248
Triangular planform 241–248
Shear deformation beam theory 82–87
Shear deformation plate theory 4, 116–121
Shear deformation shallow shell theory
190–193
Shear deformation shell theory 33–46
Shear diaphragm 51, 124, 197–203
Shear strain 8, 11, 29
Shells
(see Shallow shells)
Barrel 297–314
Circular cylindrical 261–313
Conical 324–343
Cylindrical 261–320
Non-circular cylindrical 314–318
Shells of revolution 260, 324, 348
Spherical 348–353
Similitude 59
Simply supported
Barrel shells 303, 309
Beams 88–93
Cylindrical shells 268–284
Plates 124–137
Shallow shells 193–202
Single layered bodies 14
Single layered shells 32, 259
Spherical caps 249–254
Springs 142
Stability 5
State-space 72
Stiffened shells 359
Stiffness coefficients 11, 12, 77
Strain 7
Strain displacement relations
(see Kinematic relations)
Stress resultants
Thick barrel shells 300
Thick beams 82
408 Subject Index
Thick cylindrical shells 265
Thick plates 116
Thick shallow shells 192
Thick shells 36
Thin barrel shells 308
Thin beams 77
Thin cylindrical shells 262
Thin plates 111, 113
Thin shallow shells 186
Thin shells 48
Stress-strain relations
(see Stress resultants) 36
Thin shells 47–48
Three dimensional 8–12, 31
Stretching 113, 114, 189, 263, 302, 331
Stretching bending coupling
(see Bending stretching coupling)
Superposition 72
Surface tractions 13
Surfaces, theory of 23–28
Taylor series 33
Theory of surfaces 23–28
Thermal loading 178
Three dimensional (see Elasticity)
Transformation of stress 9
Trial functions 65
Trigonometric functions 156
Twisting modes (see Mode shapes)
Twisting moments 48, 118
Undeformed surface 24
Uniqueness of a solution 15
Variable thickness 178
Variational principles 15–19
Virtual displacement 16
Viscoelastic 75, 360
Wavelength 34, 46, 110
Wave propagation 360
Weighted residual methods 65
Weight functions 65
Weingarten formulas 26
Work 41, 80, 86
Zero curvature 109
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