Admin مدير المنتدى
عدد المساهمات : 19001 التقييم : 35505 تاريخ التسجيل : 01/07/2009 الدولة : مصر العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
| موضوع: كتاب Computational Methods in Structural Dynamics السبت 03 أغسطس 2019, 3:11 pm | |
|
أخواني في الله أحضرت لكم كتاب Computational Methods in Structural Dynamics Leonard Meirovitch Reynolds Metals Professor Department of Engineering Science and Mechanics Virginia Polytechnic Institute and State University
و المحتوى كما يلي :
Contents Chapter 1. Concepts from linear algebra 1.1 Introduction 1.2 Linear vector spaces 1.3 Linear dependence 1.4 Bases and dimension of a vector space 1.5 Inner products and orthogonal vectors 1.6 The Gram Schmidt orthogonalization process 1.7 Matrices 1.8 Basic matrix operations 1.9 Determinants 1.10 Inverse of a matrix 1.11 Partitioned matrices 1.12 Systems of linear equations 1.13 Matrix norms Chapter 2. Free vibration of discrete systems 29 2.1 Introduction 2.2 The system equations of motion 2.3 Small motions about equilibrium points 2.4 Energy considerations 2.5 Free vibration and the eigenvalue problem Chapter 3. The eigenvalue problem 3.1 General discussion 3.2 The general eigenvalue problem 3.3 The eigenvalue problem for real symmetric matrices 3.4 Geometric interpretation of the eigenvalue problem 3.5 Hermitian matrices 3.6 The eigenvalue problem for two nonpositive definite real symmetric matrices 3.7 The eigenvalue problem for real nonsymmetric matrices XIContents Contents 6.8 Response of general dynamical systems 217 6.9 Discrete-time model for general dynamical systems 6.10 Stability of motion in the neighborhood of equilibrium 223 Chapter 4. Qualitative behavior of the cigensolution 4.1 Introduction 4.2 The Rayleigh principle 4.3 Rayleigh's theorem for systems with constraints 4.4 Maximum-minimum characterization of eigenvalues 4.5 The inclusion principle 4.6 A criterion for the positive definiteness of a Hcrmitian matrix 4.7 Eigenvalues of the sum of two Hcrmitian matrices 4.8 Gerschgorin’s theorems 4.9 First-order perturbation of the eigenvalue problem Chapter 7. Vibration of continuous systems 229 7.1 Introduction 7.2 Lagrange’s equation for continuous systems. Boundaryvalue problem 7.3 The eigenvalue problem 7.4 Self-adjoint systems 7.5 Non-self-adjoint systems 7.6 Vibration of rods, shafts and strings 7.7 Bending vibration of bars 7.8 Two-dimensional problems 7.9 Variational characterization of the eigenvalues 7.10 Integral formulation of the eigenvalue problem 7.11 The response problem Chapter 5. Computational methods for the eigensolution 261 5.1 General discussion 5.2 Gaussian elimination 5.3 Reduction to triangular form by elementary row operations 5.4 Computation of eigenvectors belonging to known eigenvalues 5.5 Matrix iteration by the power method 5.6 Hotelling’s deflation 5.7 Wielandt’s deflation 5.8 The Cholesky decomposition 5.9 The Jacobi method 5.10 Givens’ method 5.11 Householder's method 5.12 Eigenvalues of a tridiagonal symmetric matrix. Sturm’s theorem 5.13 The QR method 5.14 The Cholesky algorithm 5.15 Eigenvectors of a tridiagonal matrix 5.16 Inverse iteration Chapter 8. Discretization of continuous systems 285 8.1 Introduction 8.2 The Rayleigh-Ritz method 8.3 The assumed-modes method 8.4 The method of weighted residuals 8.5 Flutter of a cantilever aircraft wing 8.6 Integral formulation of the method of weighted residuals 319 8.7 Lumped-parameter method employing influence coefficients 8.8 System response by approximate methods Chapter 9. The finite element method 328 9.1 Introduction 9.2 Second-order problems. Linear elements 9.3 Higher-degree elements. Interpolation functions 9.4 Fourth-order problems 9.5 Two-dimensional domains 9.6 Errors in the eigenvalues and eigenfunctions 9.7 Inconsistent mass matrices Chapter 6. Response of discrete systems 6.1 Introduction 6.2 Linear systems. The superposition principle 6.3 Impulse response. The convolution integral 6.4 Discrete-time systems 6.5 Response of undamped nongyroscopic systems 6.6 Response of undamped gyroscopic systems 6.7 Response of damped systems Chapter 10. Systems with a large number of degrees of freedom 368 10.1 Introduction 10.2 Static condensation XII XIIIContents 10.3 Mass condensation 10.4 Simultaneous iteration 10.5 Subspace iteration 10.6 The method of sectioning Chapter 11. Substructure synthesis 11.1 General discussion 11.2 Component-mode synthesis 11.3 Branch-mode analysis 11.4 Component-mode substitution 11.5 Substructure synthesis Bibliography 410 Suggested problems 415 Author index 432 Subject index 434 XIVAuthor index Smolitskiy, K. L., 413 Stahle, C. V., 391, 412 Stewart, G. W., 167, 414 Stoker , J. R., 371, 414 Strang, G., 266, 336, 365, 367, 414 Wilkinson, J. H„ 142, 149, 152, 155, 163. 164, 165, 166, 167, 414 Wilson, W. L., 378, 410 Wright, G. C., 372, 414 Author index Topp, L. J., 328, 414 Ziegler, H., 34, 414 Turner, M. J., 328, 414 Huebner. K. H., 339, 359, 363, 411 Hurty, W. C., 82, 384, 391, 411. 412 Huseyin, K., 34, 412 Bajan, R. L., 391, 410 Bamford , R. M., 391, 410 Bampton, M. C. C., 390, 410 Bathe , K. J., 378, 410 Bell, K., 355, 411 Benfield, W. A., 384, 395, 401, 410 Bolotin, V. V., 34, 410 Bowman , F., 272, 410 Irons , B., 370, 412 Issid , N. T., 30, 413 Jaszlics, 1. J., 391, 410 Jennings, A., 373, 374, 412 Jensen, P. S„ 380, 381, 382, 412 Kublanovskaya, V. N., 163, 412 Kuhar, E. J., 391, 412 Carey, G. F., 412 Caughey, T. L., 211, 410 Clint , M., 373, 374, 410 Clough, R. W., 328, 414 Courant, R., 245, 271, 279, 280, 293, 328, 350 , 410 Craig, R. R., 390, 410 Lancaster, P., 82, 412 Likins. P. W., 34, 412 Martin, H. C., 328, 412 Meirovitch, L., 30, 31, 38, 40, 45, 46, 47, 81, 146, 189, 190, 192, 202, 205, 207, 208, 212, 215, 225, 231, 232, 244, 248, 255 , 265, 269, 271, 274, 280, 299, 384, 402, 403, 405, 407, 409, 412, 413, 414 Melosh, R. J.. 328, 413 Mikhlin, S. G., 413 Miles , G. A., 372, 414 Mingori, D. L., 34, 413 Murdoch, D. C., 20, 24, 55, 58, 413 Daniel, J. W., 9, 10, 28, 152, 413 Dowell, E. H., 319, 391, 410, 411 Feng, C. G, 391, 410 Finlayson, B. A., 411 Fix, G. J., 266, 336, 365, 367. 414 Francis , J. G. F., 163, 411 Franklin, J. N.. 55, 67, 100, 121, 129, 411 Friedman, B., 253, 411 Fung, Y. C„ 253, 313, 316, 411 Gallagher, R. H„ 364, 411 Noble, B., 9, 10, 28. 152, 413 Gladwell , G. M. L., 384, 391, 411 Goldman, R. L., 391, 411 Gould, S. H , 411 Guyan, R. J., 371, 411 Paidoussis, M . P., 30, 413 Przemieniecki, J. S., 371, 414 Ralston, A., 162, 414 Ramsden, J. N., 371, 413 Rayleigh (Lord). 288, 414 Reinsch, C., 167, 414 Rubin, S., 391, 414 Rutishauser, H., 163, 414 Ryland , G., 202, 414 Hale, A. L„ 384, 402. 407, 409, 411, 413 Hilbert, D., 245, 271, 279, 280, 293, 410 Hintz , R. M., 391 , 411 Holland, I., 355, 411 Hou , S. N., 391, 411 Hruda, R. F., 384, 395, 401, 410 432 433Subject index Damping forces, 30 Damping matrix, 35 hysteretic, 212 Deflation (matrix): Hotelling’s, 128-134 Wielandt’s , 134-135 Degenerate system, 270, 272 Degrees of freedom, 29 Determinant(s), 16-19 cofactor, 17 Gramian, 26 minor, 17 Dirac delta function, 186 spatial, 282 Discrete-time systems, 192-199, 221-223 Dissipation function; general, 35 Rayleigh’s, 30 Dual expansion theorem, 72 Dynamic potential, 32 Element stiffness matrix, 335, 341 Energy functions, 249 Energy inner product, 249 Energy space, 249 Equilibrium point: nontrivial, 32 trivial, 32 Errors (in eigensolution), 364 Expansion theorem: continuous systems, non-self-adjoint, 254 self-adjoint, 252 discrete systems, damped, 69 dual, see non-self-adjoint Hermitian, 67 non-self-adjoint, 72 real symmetric, 60 Subject index Adjoint eigenvalue problem : algebraic, 72 differential , 253 Adjoint operator, 253 Admissible functions, 249 Amplitude, 44 Approximation in the mean, 247 Area coordinates, 353 Asymptotically stable equilibrium, Characteristic values, see eigenvalues Characteristic vectors, see eigenvectors Cholesky algorithm, 172-176 Cholesky decomposition, 135-138 Circulatory forces, 34 Circulatory matrix, 35 Classical modal analysis, 201 for damped systems, 210 Collocation method, 304-306 Comparison functions, 247 Complete set, 247 in energy, 250 Complex stiffness matrix, 213 Component modes, 385 Condensed eigenvalue problem, 370 Condensed mass matrix, 372 Configuration space, 31 Conservation of energy, 41 Conservative forces, 41 Conservative systems, 40 gyroscopic, 45 nongyroscopic, 41 Consistent mass matrix, 366 Constraint damping forces, 34 Convergence: in energy, 250 in the mean , 247 Convolution integral, 189 Convolution sum, 197 Coriolis forces, 30 Coriolis matrix, 35 Critical behavior, 225 225, 226 Finite element method, 328-367 Finite elements: one-dimensional, cubic, 342 linear, 332, 339 quadratic. 339 two-dimensional, quadrilateral, 359 rectangular, 359 triangular, 351 Flapping mode, 263 Flutter , 312-319 Free vibration: continuous systems, 239 discrete systems, 29-49 distributed systems, see continuous systems Frequency equation: continuous systems, 241 discrete systems, 42 distributed systems, see continuous systems Back substitution , 112 Bandwidth of matrix, 336 Bessel inequality, 246 Bilinear elements, 359 Biorthogonality: of functions, 253 of vectors, 71 Biorthonormality: of functions, 254 of vectors, 71 Bisection method , 160 Boundary conditions, 234 dynamic, 238 essential, 238 geometric, 237 natural, 238 Boundary-value problem 234 Branch modes , 392 Eigenfunctions, 242 Eigensolutions, 43 Eigenvalue problem: continuous systems, 241 integral form, 280 discrete systems, conservative gyroscopic, 45 conservative nongyroscopic, 42 damped nongyroscopic, 47 general dynamical, 48 distributed systems, see continuous systems Eigenvalue problem (algebraic): adjoint, 72 damped systems, 68-70 general, 50 for Hermitian matrices , 65-68 for real nonsymmetric matrices, 70-72 for real symmetric matrices, 56-65 self -adjoint, 72 Eigenvalues, 42. 50, 242 multiplicity, 51 repeated, 46, 51 shift in. 52 Eigenvectors, 42, 50 left , 70 right, 71 Element mass matrix, 335. 341 Centrifugal forces, 30 Characteristic determinant, 42, 51 Characteristic equation: continuous systems, 241 discrete systems, 42, 51 distributed systems, see continuous Characteristic functions, see eigenfunctions Characteristic polynomial, 51 Characteristic value problem, see eigenvalue problem Galerkin equations, 289 Galerkin method, 303-304 Gaussian elimination , 1 11-115 Gauss-Jordan reduction, 114 Generalized coordinates, 30 Generalized forces , 31 Generalized momenta , 31 Damping: constraint, 34 proportional, 211 structural , 212 viscous, 30 Damping coefficients, 30 434 435r Subject index Subject index Generalized velocities, 30 Generalized virtual displacements, 31 Gerschgorin theorems, 99-101 Givens’ method, 146-151 Global mass matrix, 336 Global stiffness matrix, 336 Gram-Schmidt orthogonalization, 8-11 modified , 9 Green’s function, 279 Group property, 221 Gyroscopic coefficients, 34 Gyroscopic forces, 30 Gyroscopic matrix, 35 nonnatural systems, 30 Kinetic energy density, 231 Modal Modal truncation vectors, 44, 201 Moments, method of, 308 normal, 66 null, or zero, 13 nullity of, 24 orthonormal, 58 partitioned, 21 permutation, 16, 116 positive definite, 36 positive semidefinite, 36 rank of, 23 rectangular, 11 rotation, 139 row, 13 sign-variable, 36 similar, 53 singular, 18 skew symmetric, 13 square, 12 order of, 12 symmetric, 13 trace of, 56 transpose of, 12 tridiagonal, 12 unit , or identity, 12 unitary, 66 Matrix(ces), special: circulatory, 35 Coriolis, see gyroscopic damping, 35 gyroscopic, 35 inertia, 35 mass, 35 stiffness, 35 Matrix diagonalization, 140 Matrix iteration (power method), 123-128 Maximum-minimum theorem: continuous systems, 277 discrete systems, 89 Maxwell’s reciprocity theorem, 279 Mean square error, 246 Minimax theorem, 90 Modal analysis: continuous systems, 281-284 discrete systems, damped systems, 210-217 general dynamical systems, 217-221 undamped gyroscopic systems, 204-210 undamped nongyroscopic systems, 199- 204 Modal matrix , 62 Lagrange’s equations: discrete systems, 31 distributed systems, 233 Lagrangian, 31 Lagrangian density, 232 Laplace operator, 268, 271 Least squares method, 306-308 Linear combination: of functions, 245 of vectors, 3 Linear transformation, 52 Linearized system, 224 Linearly dependent: functions, 245 vectors, 4 Linearly independent: functions, 245 vectors, 3 Local basis , 332 Local coordinates , 334 Lumped-parameter method, 321-322 Natural coordinates, 201 Natural coordinates (in finite element method), 334, 352 Natural frequencies, 44, 242 Natural modes, 44, 242 Natural systems, 40 Newton-Raphson method, 162 Nodal vector, 336 Nodes , 271 Nodes (in finite element method), 332 external, 340 internal, 340, 342 Nonconservative forces, 41 Nonnatural system, 30 Non-self-adjoint systems: continuous, 252-255, 312-319 discrete, 316 Norm: energy, 249 Euclidean, 7 of functions, 245 of vectors, 7 Normal coordinates, 201, 283 Normal modes, 61, 242 Normalization: of functions, 242 of vectors, 7, 58, 61 Half-bandwidth, 358 Hamiltonian , 40 Hermite cubics , 347 Hotelling deflation, 128-134 Householder method, 151-157 Hysteretic damping matrix, 212 Impulse response, 187 Inclusion principle, 90-94 Inconsistent mass matrix, 366 Inertia coefficients , 33 Inertia matrix, 35 Influence function , 279 Initial value problem, 234 Inner product: energy, 249 of functions, 244 of vectors, 6 Integral operator, 279 Intermediate structure, 407 Interpolation functions: cubic, 342 linear, 335, 339 quadratic, 339 Inverse iteration , 177-182 Isoparametric elements, 364 Mass coefficients , 33, 288 Mass condensation , 370 Mass matrix , 35, 289 Matrix(ces): adjoint, 13 adjoint of, 20 augmented, 24 banded, 19 block-diagonal, 22 cofactor, 19 column, 13 determinant of, 16, 56 diagonal, 12 dimensions of, 12 Gramian , 26 Hermitian, 13 Hessenberg, 12 identity, or unit, 12 inverse of , 19 negative definite, 36 negative semidefinite, 36 nonsingular, 18 norm of, 27 Euclidean , 28 Orthogonal functions, 245 Orthogonal matrices, 58 Orthogonalization: of functions, 293 of vectors, 8-11 Orthonormal functions, 245 Orthonormal vectors, 8 Perturbation of eigenvalue problem, 102- Jacobi integral, 40 Jacobi method, 138-146 Jordan form, 55 109 Phase angle, 44 Positive definite system: continuous, 250 discrete, 44 distributed, see continuous Positive, semidefinite system: continuous, 250 Kinetic energy: discrete systems, 30 distributed systems, 231 natural systems, 40 436 437Subject index Subject index Positive, semidefinite system: (Corct.) discrete, 44 distributed, see continuous Potential energy: discrete systems, 30 distributed systems, 235 Potential energy density, 231 Principal coordinates, 201 Proportional damping, 211, 327 Pyramid functions, 350 QL method, 167 OR method, 162-172 Quadrilateral elements, 359 Sampler, 194 Sampling period, 194 Sectioning, method of , 380 Self-adjoint eigenvalue problem: algebraic, 72 differential, 248 Self -adjoint systems: continuous, 248 discrete, 72 distributed , see continuous Shape functions, 335 Shift in eigenvalues, 52, 166 Significant behavior, 225 Similarity transformation, 53 Simultaneous iteration, 373 Space: configuration, 31 phase, 32 state, 32, 45 vector, see vector space Spatial Dirac delta function, 282 Square summable functions, 245 Stability of motion, 223-228 Stable equilibrium, 225, 226 State vector , 32, 45 Static condensation, 369 Stiffness coefficients: elastic, 34, 288 geometric, 34 Stiffness matrix, 35, 289 complex, 212 Structural damping, 212 Structural damping factor, 212 Sturm sequence, 158 Sturm theorem, 159 Subdomains, method of, 308 Subspace iteration, 377 Superposition principle, 185 Sylvester’s criterion, 95 Synchronous motion: continuous systems, 239 discrete systems, 41 System: conservative, 41 damped, 47 gyroscopic, 40 linear, 35 linearized, 33 natural, 40 linearly independent, 3, 52 modal, 44 orthogonal, 8 orthonormal, 8 space(s), see vector space(s) state , 32 unit, 7 Vector space(s), 1-11 basis for, 5 column, 23 dimension of, 5 generating system of, 5 null, 24 row, 23 spanned, 4 standard basis for, 6 subspace, 3 Virtual work, 31 Virtual work density, 231 Viscous damping, 30 nonconservative, 41 nonlinear , 38 nonnatural , 30 unrestrained, 44 Test functions, 301 Test space, 302 Transformation: linear, 52 orthonormal, 64 similarity, 53 unitary, 67 Transition matrix , 220, 222 Trial functions, 274, 301 Trial space, 302 Triangular decomposition , 118 Rayleigh dissipation function, 30 Rayleigh energy method , 292 Rayleigh principle, 74-84 Rayleigh quotient: continuous systems, 274 discrete systems, 74 conservative gyroscopic, 81 conservative nongyroscopic, 80 distributed systems, see continuous Rayleigh-Ritz method, 286-298 Rayleigh theorem, 84-88 Rectangular elements, 359 Response: continuous systems, 281-284 discrete systems, conservative gyroscopic, 204-210 conservative nongyroscopic, 199-204 damped nongyroscopic, 210-217 general dynamical, 217-221 discrete-time systems, 192-199, 221-223 discretized systems, damped nongyroscopic, 326-327 undamped gyroscopic, 324-326 undamped nongyroscopic, 322-324 distributed systems, see continuous systems Unit impulse, 186 Unit step function, 187 Unitary transformation, 67 Unstable equilibrium, 225, 226 Weighted residuals method, 301-312 integral formulation, 319-321 Weighting functions, 301 Weyl’s theorem, 97 Wielandt deflation, 134-135 Vector(s): characteristic, 42 configuration, 35 displacement, see configuration force, 35 linearly dependent, 4 Zero-order hold, 195 single-degree-of-freedom systems, 186- 192 Ritz system, 289 eigenfunctions, 290 eigenvalues, 290 Rigid-body modes, 44 Roof functions, 332 Rotary inertia, 248 Rotation matrix
كلمة سر فك الضغط : books-world.net The Unzip Password : books-world.net أتمنى أن تستفيدوا من محتوى الموضوع وأن ينال إعجابكم رابط من موقع عالم الكتب لتنزيل كتاب Computational Methods in Structural Dynamics رابط مباشر لتنزيل كتاب Computational Methods in Structural Dynamics
|
|