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Langhaar H.R. — Energy Methods in Applied Mechanics
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Название: Energy Methods in Applied MechanicsАвтор: Langhaar H.R. Аннотация: 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.
Язык: Рубрика: Механика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1962Количество страниц: 350Добавлена в каталог: 15.04.2007Операции: Положить на полку |
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action 239 Adiabatic process 13 14 Airy stress function 130 163 193 Atwood machine 262 Beam columns 44—48 Beams 39—44 Beams, boundary conditions for 43 Beams, cantilever 75 Beams, complementary energy of 144—146 Beams, curved 48—52 86—89 Beams, differential equation of 85—86 Beams, fixed-end deflections of 60 Beams, fixed-end moments of 60 Beams, influence function for 283—285 Beams, lateral buckling of 218—224 Beams, redundant 149—150 Beams, rotary inertia of 288—289 Beams, shear deflection of 42 288—289 Beams, shear energy of 43 Beams, stiffness factor for 59 Beams, torsion of 43 Beams, vibrations of 280—283 Bernoulli, Jean 1 bonds 25 Born, Max 75 boundary conditions 76 Boundary conditions of beams 43 Boundary conditions of plates 168—170 Boundary conditions, forced 76 Boundary conditions, linear 78 Boundary conditions, natural 77 81 British thermal unit 11 Buckling 201—228 Buckling of a linkage 207—209 Buckling of beams 218—224 Buckling of circular plate 216—218 Buckling of columns 203—206 224—228 Buckling of rectangular plate 214—216 Buckling, bifurcation theory of 202 Buckling, relation to quadratic forms 324—327 Buckling, Trefftz's criterion of 211 Buoyancy, center of 38 Calculus of variations 75—103 Calculus of variations, auxiliary differential equations in 91—92 Calculus of variations, Euler's equation of 82 84—85 96 97 Calculus of variations, isoperimetric problems of 89—90 Calorie 11 Castigliano's theorem of least work 126—130 Castigliano's theorem on deflections 133—136 Castigliano's theorem, applications of 138—144 Castigliano's theorem, corollaries to 137—138 Catenary 89—90 Column on elastic foundation 209—210 Column, Euler formula for 46 206 Column, postbuckling of 203—206 Column, shear effect in 213—214 Column, torsional-flexural buckling of 224—228 Complementary energy 127 128 Complementary energy of beams 144—146 Complementary energy of plates 173 Complementary energy, density of 119—121 Complementary energy, principles of 120 128 129 132 133 135 Configuration 2 Configuration space 3 Configuration space, connected 3 Configuration space, continuity in 5 Configuration space, coordinates in 6—8 Configuration space, distance in 4 Configuration space, neighborhood in 4 Configuration space, paths in 5 Configuration space, points in 3 Configuration space, triangle law for 4 Conservative forces 20 26 Conservative forces, external 20 Conservative forces, internal 20 Conservative systems 18—33 Conservative systems in kinetic sense 18 Conservative systems in statical sense 18 Conservative systems, Lagrange equations for 239—240 Constraints 2 Constraints, time-dependent 241—243 Coordinate lines 113 Coordinate surfaces 112 Coordinates for shells 180 Coordinates for surfaces 177 Coordinates, curvilinear 112—115 Coordinates, cylindrical 114 Coordinates, generalized 6—8 Coordinates, normal 275 Coordinates, orthogonal 112—115 177 Coordinates, spherical 114 Crystals 122—123 Crystals 122—123 D'Alembert's principle 235 D'Alembert's principle 235 Degrees of freedom 8 Degrees of freedom 8 Degrees of freedom, finite 8 21 Degrees of freedom, finite 8 21 Degrees of freedom, infinite 8 Degrees of freedom, infinite 8 Dilatation 107 Dilatation 107 Displacements of a mechanical system 2 Displacements of a mechanical system 2 Displacements, principle of 15 Displacements, principle of 15 Displacements, virtual 13 Displacements, virtual 13 Divergence theorem 111 Divergence theorem 111 Eigenfunctions 281 Eigenfunctions 281 Eigenvalues 281 Eigenvalues 281 Elastic systems 21 Elastic systems 21 Equilibrium 13 Equilibrium 13 Equilibrium, stability of 29—33 Equilibrium, stability of 29—33 Erg 11 Erg 11 Euler, L., angles of 250 252 Euler, L., angles of 250 252 Euler, L., column formula of 46 206 Euler, L., column formula of 46 206 Euler, L., dynamical equations of 253—255 Euler, L., kinematical equations of 253 Euler, L., kinematical equations of 253 Euler, L., variational equation of 82 84—85 96 97 Extremal 82 force 10 force 10 Force, conservative 20 26 Force, conservative 20 26 Force, exciting 273 Force, exciting 273 Force, external 10 17 Force, external 10 17 Force, field of 25 Force, field of 25 Force, generalized 16—18 254 Force, internal 10 Force, lines of 25 Force, lines of 25 Fourier series in beam theory 44—47 Fourier series in beam theory 44—47 Fourier series in ring theory 51—52 Fourier series in ring theory 51—52 Fourier's inequality 13—14 Fourier's inequality 13—14 Frame analysis by slope-deflection theory 59 63 Frame analysis by slope-deflection theory 59 63 Frame analysis by stationary potential energy 58—65 Frame analysis by stationary potential energy 58—65 Frame analysis by unit-dummy-load method 148—149 Frame analysis by unit-dummy-load method 148—149 frequency 270 frequency 270 Frequency, equation of 270 281 Friction, sliding and viscous 19 Friction, sliding and viscous 19 Galileo 1 Galileo 1 Generalized coordinates 6—8 Generalized coordinates 6—8 Gimbals 259 Gimbals 259 Green, G. 159 Green, G. 159 Green, G., theorem of 93 Green, G., theorem of 93 Gyro 259 Gyro 259 Gyroscope 259—261 Gyroscope 259—261 Hamilton, W.R. 233 Hamilton, W.R. 233 Hamilton, W.R., equations of 244—245 248 Hamilton, W.R., equations of 244—245 248 Hamilton, W.R., function of 243—244 Hamilton, W.R., function of 243—244 Hamilton, W.R., principle of 234—239 Hamilton, W.R., principle of 234—239 Harmonic functions 27 Harmonic functions 27 Holonomic systems 5 8 17 22 24 Holonomic systems 5 8 17 22 24 Hooke, R. 104 Hooke, R. 104 Hookean materials 121—126 Hookean materials 121—126 Hysteresis 11 Hysteresis 11 Internal energy 11 12 21 Internal energy 11 12 21 Internal energy of distortion 117 Internal energy of distortion 117 Internal energy of ideal gas 293 Internal energy, density of 117 Internal energy, density of 117 Isotropic materials 124—126 Isotropic materials 124—126 Joule 11 Joule 11 Kinematics of general mechanical systems 2—8 Kinematics of general mechanical systems 2—8 Kinematics of rigid bodies 249—253 Kinematics of rigid bodies 249—253 Kinematics of rolling sphere 8 267 Kinematics of rolling sphere 8 267 Kinematics, Euler equations in 253 Kinematics, Euler equations in 253 kinetic energy 10 11 kinetic energy 10 11 Kinetic energy of a rigid body 254 Kinetic energy of a rigid body 254 Kinetic energy of general systems 233—234 Kinetic energy of general systems 233—234 Kinetic energy, law of 10 Kinetic energy, law of 10 Lagrange multipliers 89 92 174 296 Lagrange multipliers 89 92 174 296 Lagrange, J.L. 1 2 39 272 Lagrange, J.L. 1 2 39 272 Lagrangian continuity equation 295 Lagrangian continuity equation 295 Lagrangian dynamical equations for conservative systems 239—240 Lagrangian dynamical equations for conservative systems 239—240 Lagrangian dynamical equations for nonconservative systems 247—249 Lagrangian dynamical equations for nonconservative systems 247—249 Lame, coefficients of 113 181 Lame, elastic constants of 124 Laplace's equation 27 Laplace's equation 27 Legendre transform 120 136 244 Legendre transform 120 136 244 Leibniz, G.W. 2 11 Leibniz, G.W. 2 11 Leonardo da Vinci 1 Leonardo da Vinci 1 Material points 2 Material points 2 Matrix of strain 105 Matrix of strain 105 Matrix of stress 110 Matrix of stress 110 Matrix, rank of 309 Matrix, rank of 309 Matrix, regular 312 Matrix, regular 312 Maxwell — Mohr method 141 143 Maxwell — Mohr method 141 143 Maxwell's law of reciprocity 137 284 Maxwell's law of reciprocity 137 284 Mechanical energy 23 Mechanical energy 23 Mechanical energy, conservation of 23 244 Mechanical energy, conservation of 23 244 Mechanical systems 2—8 Mechanical systems 2—8 Mechanical systems, configuration of 2 Mechanical systems, conservative 18—33 Mechanical systems, displacement of 2 Mechanical systems, geometric terminology for 3 Mechanical systems, geometric terminology for 3 Mechanical systems, holonomic 8 22 24 Mechanical systems, holonomic 8 22 24 Mechanical systems, infinite 14 Mechanical systems, infinite 14 Mechanical systems, nonholonomic 5 17 Mechanical systems, nonholonomic 5 17 Mechanical systems, unchecked 16 Mechanical systems, unchecked 16 Minimum, absolute, relative, and improper 79 Minimum, absolute, relative, and improper 79 Minimum, proper 80 Minimum, proper 80 Minimum, theorem of potential energy 30 Minimum, theorem of potential energy 30 Momentum, generalized 243 255 Momentum, generalized 243 255 Newton's Laws 8 238 Newton's Laws 8 238 Newton's laws of gravitation 20 26 Newton's laws of gravitation 20 26 Newton's laws, third 10 Newton's laws, third 10 Newtonian potential 26 27 Newtonian potential 26 27 Newtonian potential for charged sphere 28 Pendulum with flexible suspension 271 Pendulum with flexible suspension 271 Pendulum with moving pivot 249 Pendulum with moving pivot 249 Pendulum, double 240—241 Pendulum, double 240—241 Pendulum, spherical 245 Pendulum, spherical 245
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