Mechanics and Strength of Materials 1

Mechanics and Strength of Materials 1
اسم المؤلف
BOGDAN SKALMIERSKI
التاريخ
16 ديسمبر 2018
المشاهدات
التقييم
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Mechanics and Strength of Materials 1
BOGDAN SKALMIERSKI
Silesian Polytechnical University
Gliwice, Poland
Subject Index
Absolute derivative of a tensor, 289
Acceleration, 16
in general motion, 38
Addition of vectors, 2
d’Alembert’s principle, 257
Amplitude characteristic, 330, 398
Angular momentum, 92, 227
Angular velocity vector, 32
Articulated joint, 106
Assur’s point, 62
Asymptotically stable system, 296
Axode, 37
Average value, 376
Base resonance, 350
Bearing friction, 140
Betti’s reciprocal theorem, 185, 186
Bilateral constraints, 253
Bilinear product, 6
Binet’s equation, 78
Boltzmann’s bodies, 182
Castigliano’s theorem, 187
Central axis of a system, 98
Central axis of inertia, 164
Centre of impact, 234
Centrifugal moment, 159
Chebyshev’s inequality, 397
Christofiel’s symbol of the first order,
288
ChristoiTel’s symbol of the second order,
289
Clapeyron’s system, 185, 190
Coaxial vectors, 2
Coefficient of friction, 137
Coefficient of restriction, 91
Collinear vectors, 4
Conditions of inseparability, 151
Cone of friction, 138
Configuration of a body, 11
Configurational space, 291
Conservative system, 71, 75, 285
Constant of spring, 215
Constrained mechanical system, 250
Construction scale, 101
Continuous vector function, 9
Contravariant tensor, 286
Convergence of a vector-function, 9
Correlaton, 379
Correlation function, 382
Correlator, 385
Couple, 96
Covariant derivative, 290
Covariant tensor, 286
Crank-slide system, 55
Crank-yoke system, 59
Creep, 182
Cremona’s method, 118
Cremona’s polygon, 118
Culmann’s line, 121
Culmann’s method, 120
Cumulative distribution function, 373
Cyclic coordinates, 269
Degrees of freedom, 249
Derivative of a vector function, 10
Derivative of the Dirac delta function, 123 430 SUBJECT INDEX
Differentiable vector function, 10
Differentiable constraints, 253
Dirac delta function, 122
Dispersion, 377
Dynamically balanced body, 232
Effort hypotheses, 217
Elastic limit, 145
Elastic buckling, 199
Energy, 70
Equations of circular motions, 231
Equations of disturbances, 295
Equations of equilibrium, 95
Ergodic process, 384
Error integral, 377
Euler’s angles, 33
Euler’s equation, 231
Expected value, 376
Externally determinate static system,
114
Fokker-Planck-Kolmogorov equation,
418
Fourier transform, 329
Framework, 195
Free-ends beam, 114
Free vector, 2
Frequency, 371
Frequency characteristic, 329
Friction, 136
of a cylinder rolling, 142
of rope against wheel, 141
on an inclined plane, 138
Friction angle, 138
Funicular polygon, 103
Hamilton function, 283
Hamilton’s canonical equations, 284
Hamilton’s principle, 258
Harmonic oscillator, 310
Heaviside distribution, 121
Helical motion, 40
Hodograph, 15
Holonomic system, 252
Homeomorphism, 11
Homogeneous body, 81
Hooke’s law, 147
Horse power, 72
Huber-Mises-Hencky hypothesis, 217
Hyperharmonic resonance, 350
Ideal constraints, 256
Inertia ellipsoid, 226
Influence function, 324
Influence matrix, 185
Instantaneous centre of acceleration, 52
Instantaneous centre of velocities, 49
Instantaneous helical axis, 39
Instantaneous power of a force, 71
Instantaneous rotational axis, 36
Internal magnitudes, 129
Intervally linear system, 337
Isotropic space, 11
Joule, 70
k-fold statically indeterminate system, 151
Kinetic energy, 70, 71
Kronecker’s symbol, 6
Krylov’s method, 341
Gauss normal distribution, 377
Gaussian process, 382
Generalized coordinates, 20
Geometric constraints, 252
Geometrical statical moment, 81, 82
Lagrange equations
of impulsive motion, 275
of the first order, 262
of the second order, 268
Lagrange kinetic function, 269 SUBJECT INDEX 431
Lagrange kinetic potential function, 260
Lagrange multipliers, 262
Lagrange-Dirichlet criterion, 297
Laplace’s transform, 318
Lapunov function, 299
Lapunov’s theorem, 299
Law, 255
if action and reaction, 70, 274
of conservation of mechanical energy,
71, 75
of conservation of angular momentum,
93
of variation of angular momentum,
92
of variation of momentum, 87
Linear dependence of vectors, 6
Logarithmic decrement, 321
Matrix of transmittance, 367
Matrix of velocity gradient, 27
Menabrea’s theorem, 190
Mean quadratic deviation, 377, 379
Modulus, 2
of rigidity, 149
of section, 166
of a vector, 9
Mohr’s analogy, 173
Mohr-Maxwell canonical system of equa-
tions, 192
Mohr-Maxwell equations, 212
Moment of deviation, 159
Moment of momentum, 92
Moment of a vector, 8
Momentum of a system, 86
Motion, 11
Newton, 69
Newton’s second law, 69
Newton’s third law, 69
Non-dilatation strain, 148
Non-holonomic system, 253
Non-oscillatory system, 308
Norm of a vector, 295
Normal stochastic process, 382
Node separation method, 118
Oblique bending, 159
Operator transfer function, 324
Orientation of a space, 8
Orthogonal coordinate system, 24
Orthogonal vectors, 4
Oscillatory system, 308
Parallel vectors, 2
Permutation symbol, 7
Phase characteristic, 330, 398
Phase plane, 308
Phase space, 352
Phase trajectory, 308, 352
Phase trajectory problem, 322
Plane truss, 117
Plastic limit, 145
Poisson number, 148
Polygon of forces, 101
Position of a body, 11
Position vector, 2
of the centre of mass, 80
Postelastic buckling, 199, 201
Potential, 70
Potential energy, 75
Principal axes of inertia, 164
Principal central axes of inertia, 226
Principal moment, 98
Principle, 255
Probability density, 375
Quantificator, 9
Quasi-harmonic system, 340
Radial velocity, 22
Random variable, 372
Radius of gyration, 225
Rayleigh’s dissipation function, 277
Reduced moment, 218
Relative frequency, 371 432 SUBJECT INDEX
Relative motion, 45
Relaxation, 182
Resultant vector, 98
Rheonomic constraints, 252
Right-hand screw rule, 32
Safety factor, 149
Scalar product, 5
Scleronomic constraints, 252
Self-locking inclined plane, 139
Sensitivity of a thermal bi-metal, 181
Simple bending, 159
Slenderness ratio of a rod, 201
Smoluchowski’s equation, 420
Solidification hypothesis, 145
Spectral density, 392, 396
Stable solution, 296
Stable system, 293, 296
Standard equations, 340
Standard deviation, 377
Statical moment, 80
Statical-dynamical analogy, 369
Statically balanced body, 232
Statically indeterminate system, 151
Stationary motion, 303
Stationary process, 383
Steiner’s equation, 162, 223
Stochastic process, 381
of the first order, 382
of the second order, 383
Strain of a rod, 147
Stress, 146
Subharmonic resonance, 350
Subtraction of vectors, 3
Tapering spring, 213
Tensile rigidity, 146
Tensor multiplication, 286
Tensor of velocity gradient, 27
Tetmajer’s line, 202
Theorem on statical moments, 80
Time function of transmittance, 324
Torsional rigidity, 210
Transmittance, 324
Transportation, 45
Transverse component, 22
Triple-jointed system, 106
Truss, 117
Uniform space, 11
Unilateral constraints, 253
Unit vector, 4
Uncorrelated variables, 379
Variance 377, 379
Vector, 1
Vector function, 8
Vector product, 6
Velocity, 14
of a moving space, 41
of transportation, 41
Velocity tensor of a strain, 29
Velocity vector, 14
Vibration frequency of a harmonic oscilla-
tor, 319
Virtual displacement, 254
Voight’s model, 184
Watt, 72
White noise, 393
Work, 70
Wrench, 98
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