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Langhaar H.R. — Energy Methods in Applied Mechanics
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Íàçâàíèå: Energy Methods in Applied MechanicsÀâòîð: Langhaar H.R. Àííîòàöèÿ: Students of engineering usually receive only fragmentary instruction in the important principles of classical mechanics, stemming from the works of Huygens, Leibniz, Bernoulli, and Lagrange, which assign a central role to the concepts of work, potential energy, and kinetic energy. These laws, designated as "energy principles of mechanics" are sufficiently general to allow Newton's second Jaw to be deduced from them. An integrated and modern treatment of energy principles of mechanics, with applications to dynamics of rigid bodies, analyses of elastic frames, general elasticity theory, the theories of plates and shells, the theory of buckling, and the theory of vibrations, is undertaken in this work.
ßçûê: Ðóáðèêà: Ìåõàíèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1962Êîëè÷åñòâî ñòðàíèö: 350Äîáàâëåíà â êàòàëîã: 15.04.2007Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Plates, Airy function for 163 Plates, Airy function for 163 Plates, boundary conditions for 168—170 Plates, boundary conditions for 168—170 Plates, circular 195—198 Plates, circular 195—198 Plates, complementary energy of 173 Plates, complementary energy of 173 Plates, flexural rigidity of 162 Plates, flexural rigidity of 162 Plates, Kirchhoff assumption for 160 Plates, Kirchhoff assumption for 160 Plates, Navier's solution for 171 Plates, Navier's solution for 171 Plates, Reissner's theory of 173—177 Plates, Reissner's theory of 173—177 Plates, shear deformation of 173—177 Plates, shear deformation of 173—177 Plates, strain energy of 162 164 Plates, strain energy of 162 164 Plates, von Karman's theory of 159—164 Plates, von Karman's theory of 159—164 Poisson's ratio 125 Poisson's ratio 125 potential energy 18—33 potential energy 18—33 Potential energy due to weight 20 Potential energy of a system of particles 24—29 Potential energy of external forces 21 Potential energy of external forces 21 Potential energy of internal forces 21 Potential energy, minimum principle for 30 Potential energy, stationary principle for 23 Quadratic forms 308—327 Quadratic forms 308—327 Quadratic forms, canonical form of 309 Quadratic forms, canonical form of 309 Quadratic forms, index of 309 310 Quadratic forms, index of 309 310 Quadratic forms, pairs of 320—323 Quadratic forms, pairs of 320—323 Quadratic forms, principal axis theory of 313—318 Quadratic forms, principal axis theory of 313—318 Quadratic forms, relation to buckling theory 324—327 Quadratic forms, relation to buckling theory 324—327 Quadratic forms, singular 309 Quadratic forms, singular 309 Quadratic forms, type of 308 Quadratic forms, type of 308 Rayleigh — Ritz method 98—100 Rayleigh — Ritz method 98—100 Rayleigh's principle 276 Rayleigh's principle 276 Reference frames 2 Reference frames 2 Reference frames, Galilean, inertial, and Newtonian 8 11 Reference frames, Galilean, inertial, and Newtonian 8 11 Reissner's theorem 130—133 Reissner's theorem 130—133 Relativity theory 8 Relativity theory 8 Resonance 275 Resonance 275 Rings, analysis by Fourier series 51—52 Rings, analysis by Fourier series 51—52 Rings, analysis by unit-dummy-load method 150—152 Rings, analysis by unit-dummy-load method 150—152 Rings, strain energy of 48—50 Rings, strain energy of 48—50 Rotation 107 Rotation 107 Sets 4 Sets 4 shells 177—198 shells 177—198 Shells, axially symmetric 191—192 Shells, axially symmetric 191—192 Shells, bending moments in 190 Shells, bending moments in 190 Shells, bending of 189 Shells, bending of 189 Shells, coordinates for 180 Shells, coordinates for 180 Shells, cylindrical 192—195 Shells, cylindrical 192—195 Shells, equilibrium equations for 181—187 Shells, equilibrium equations for 181—187 Shells, geometry of 177—181 Shells, geometry of 177—181 Shells, strain energy of 187—191 Shells, strain energy of 187—191 Shells, strains in 188—189 Shells, strains in 188—189 Signum 15 146 Signum 15 146 Stability 29—33 Stability 29—33 strain 104 strain 104 Strain energy 21 Strain energy 21 Strain energy of beams, columns, and shafts 39—44 Strain energy of beams, columns, and shafts 39—44 Strain energy of plates 162 164 Strain energy of plates 162 164 Strain energy of shear 41—42 Strain energy of shear 41—42 Strain energy of shells 190 Strain energy of shells 190 Strain in plates 160 Strain in plates 160 Strain in shells 188—189 Strain in shells 188—189 Strain, compatibility of 107 Strain, compatibility of 107 Strain, ellipsoid of 105 Strain, ellipsoid of 105 Strain, invariants of 106 Strain, invariants of 106 Strain, principal axes of 106 319—320 Strain, principal values of 105 319—320 Strain, principal values of 105 319—320 Strain, shearing 105 Strain, shearing 105 Strain, tensor of 105 Strain, volumetric 107 Stress 109 Stress 109 Stress in curvilinear coordinates 115 Stress in curvilinear coordinates 115 Stress, deviator of 117 Stress, deviator of 117 Stress, equilibrium equations for 111 Stress, equilibrium equations for 111 Stress, invariants of 111 Stress, invariants of 111 Stress, principal planes of 110 Stress, principal values of 110 Stress, tensor of 109 Surface tension 31 Surface tension 31 Surfaces, area of 178 Surfaces, area of 178 Surfaces, axially symmetric 191—192 Surfaces, axially symmetric 191—192 Surfaces, Codazzi equations for 179 Surfaces, Codazzi equations for 179 Surfaces, coordinate lines of 177 Surfaces, coordinate lines of 177 Surfaces, coordinates for 177 Surfaces, coordinates for 177 Surfaces, Gauss equation for 179 Surfaces, Gauss equation for 179 Surfaces, Gaussian curvature of 179 Surfaces, Gaussian curvature of 179 Surfaces, lines of principal curvature for 179 Surfaces, lines of principal curvature for 179 Surfaces, metric coefficients for 178 Surfaces, metric coefficients for 178 Surfaces, orthogonal parametrization of 177 Surfaces, orthogonal parametrization of 177 Surfaces, principal curvatures of 178—179 Surfaces, principal curvatures of 178—179 Surfaces, Rodrigues' theorem for 179 Surfaces, Rodrigues' theorem for 179 Surfaces, second fundamental form of 178 Surfaces, second fundamental form of 178 Surfaces, triply orthogonal systems of 180 Surfaces, triply orthogonal systems of 180 Thermal expansion, coefficient of 122 125 Thermal expansion, coefficient of 122 125 Thermodynamics, first law of 11—13 115—117 Thermodynamics, first law of 11—13 115—117 Top, motion of 255—259 Top, motion of 255—259 Top, precession of 258 259 Top, precession of 258 259 Truss analyses by Castigliano's theorem 138—141 142—143 Truss analyses by Castigliano's theorem 138—141 142—143 Truss analyses by Maxwell — Mohr method 141—142 143—144 Truss analyses by stationary potential energy 52—58 Unit-dummy-load method 146—152 Unit-dummy-load method 146—152 Variations 78—83 Variations 78—83 Variations of double integrals 92—96 Variations of triple integrals 97—98 Variations of triple integrals 97—98 Variations, admissible 79 Variations, admissible 79 Variations, notation for 15 83 Variations, notation for 15 83 Velocity, generalized 234 Velocity, generalized 234 Vibration 268—304 Vibration 268—304 Vibration damping of 272 277—279 Vibration damping of 272 277—279 Vibration of an airplane wing 285—288 Vibration of an airplane wing 285—288 Vibration of beams 280—283 Vibration of beams 280—283 Vibration of rectangular plates 289—292 Vibration of rectangular plates 289—292 Vibration of undamped systems 272—277 Vibration of undamped systems 272—277 Vibration, amplitude of 270 Vibration, amplitude of 270 Vibration, free 272 Vibration, free 272 Vibration, frequency equation for 270 Vibration, frequency equation for 270 Vibration, frequency of 270 Vibration, frequency of 270 Vibration, linear 272 Vibration, linear 272 Vibration, natural frequency of 274 302 Vibration, natural frequency of 274 302 Vibration, natural modes of 274 281 302 Vibration, natural modes of 274 281 302 Vibration, normal coordinates for 275 Vibration, normal coordinates for 275 Vibration, period of 270 Virtual work principle 14—16 Virtual work principle 14—16 Vis viva 11 Vis viva 11 Wave equation 301 Wave equation 301 Wave motion 292—304 Wave motion 292—304 Wave motion in gas 292—295 Wave motion in gas 292—295 Wave motion in liquids 295—299 Wave motion in liquids 295—299 Wave motion in solids 299—304 Wave motion in solids 299—304 Wave motion of Gerstner 297 Wave motion of Gerstner 297 Wave motion, equivoluminal 300 Wave motion, equivoluminal 300 Wave motion, flux of energy in 301 Wave motion, flux of energy in 301 Wave motion, frequency of 304 Wave motion, frequency of 304 Wave motion, irrotational 300 Wave motion, irrotational 300 Wave motion, period of 304 Wave motion, period of 304 Waves, compression, progressive, and shear 303 Waves, compression, progressive, and shear 303 Whitehead, A.N. 268 Whitehead, A.N. 268 Work 9 Work 9 Work, relativity of 9 11 Work, relativity of 9 11 Work, virtual 13 Work, virtual 13 Young's modulus 125 Young's modulus 125
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