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Langhaar H.R. — Energy Methods in Applied Mechanics
Langhaar H.R. — Energy Methods in Applied Mechanics

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Название: Energy Methods in Applied Mechanics

Автор: 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: en

Рубрика: Механика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 350

Добавлена в каталог: 15.04.2007

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
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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