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| موضوع: كتاب Vibration of Laminated Shells and Plates - Mohamad S. Qatu الأحد 28 أبريل 2013, 7:36 pm | |
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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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