Stochastic Dynamics of Structures

1 - Cover [Seite 1]
2 - Title Page [Seite 5]
3 - Copyright [Seite 6]
4 - Contents [Seite 7]
5 - Preface [Seite 13]
6 - 1. Introduction to Structural Dynamics [Seite 17]
6.1 - 1.1. Composition of problems relating to dynamic structures [Seite 18]
6.1.1 - 1.1.1. Finite element method [Seite 20]
6.1.2 - 1.1.2. Modal superposition method [Seite 21]
6.1.3 - 1.1.3. Direct integration [Seite 22]
6.2 - 1.2. Structural optimization [Seite 24]
6.2.1 - 1.2.1. Design optimization [Seite 25]
6.2.2 - 1.2.2. Shape optimization [Seite 25]
6.2.3 - 1.2.3. Topological optimization [Seite 26]
6.2.4 - 1.2.4. Definitions and formulation of an optimization problem [Seite 28]
6.3 - 1.3. Structures with uncertain parameters [Seite 29]
6.3.1 - 1.3.1. Monte Carlo simulation [Seite 30]
6.3.2 - 1.3.2. Analytic method [Seite 31]
6.3.3 - 1.3.3. Stochastic finite element method [Seite 31]
6.3.4 - 1.3.4. Fluid logic method [Seite 32]
6.3.5 - 1.3.5. Reliability method [Seite 33]
6.3.6 - 1.3.6. Reliability optimization [Seite 37]
6.4 - 1.4. Conclusion [Seite 39]
7 - 2. Decoupled Systems [Seite 41]
7.1 - 2.1. Introduction [Seite 41]
7.2 - 2.2. Problems with structural dynamics [Seite 41]
7.2.1 - 2.2.1. Movement equation [Seite 41]
7.2.2 - 2.2.2. Hooke's law [Seite 42]
7.2.3 - 2.2.3. Variational formulation [Seite 43]
7.2.4 - 2.2.4. Estimation by finite elements [Seite 43]
7.2.5 - 2.2.5. Resolution in the frequency domain [Seite 44]
7.2.6 - 2.2.6. Solution in the temporal domain [Seite 45]
7.2.7 - 2.2.7. Reduction of the model [Seite 47]
7.3 - 2.3. Acoustic problems [Seite 58]
7.3.1 - 2.3.1. Wave equation: formulation pressure [Seite 58]
7.3.2 - 2.3.2. Variational formulation [Seite 59]
7.3.3 - 2.3.3. Estimation by finite elements [Seite 59]
7.3.4 - 2.3.4. Solution in the frequency domain [Seite 60]
7.3.5 - 2.3.5. Model fluid reduction [Seite 61]
7.4 - 2.4. Conclusion [Seite 71]
8 - 3. Coupled Systems [Seite 73]
8.1 - 3.1. Introduction [Seite 73]
8.2 - 3.2. Mathematical formulation [Seite 73]
8.2.1 - 3.2.1. Behavior equations [Seite 73]
8.2.2 - 3.2.2. Conditions for fluid-structure coupling [Seite 74]
8.3 - 3.3. Variational formulation [Seite 75]
8.4 - 3.4. Estimation by finite elements [Seite 75]
8.4.1 - 3.4.1. Estimation of unknown physical values [Seite 75]
8.4.2 - 3.4.2. Integration of variational forms [Seite 76]
8.5 - 3.5. Vibro-acoustic problem [Seite 76]
8.6 - 3.6. Hydro-elastic problem [Seite 77]
8.6.1 - 3.6.1. Calculation of the elementary matrix of the fluid-structure interaction [Seite 80]
8.6.2 - 3.6.2. Dynamic study [Seite 81]
8.7 - 3.7. Reduction of the model [Seite 83]
8.7.1 - 3.7.1. Modal superposition method for the paired system [Seite 83]
8.7.2 - 3.7.2. Direct calculation [Seite 87]
8.7.3 - 3.7.3. Calculation with modal reduction [Seite 88]
8.7.4 - 3.7.4. Modal synthesis method for paired systems [Seite 90]
8.7.5 - 3.7.5. Direct numerical calculation [Seite 97]
8.7.6 - 3.7.6. Numerical calculation with modal superposition [Seite 99]
8.8 - 3.8. Conclusion [Seite 100]
9 - 4. Reliability and Meshless Methods in Mechanics [Seite 101]
9.1 - 4.1. Introduction to non-networking methods [Seite 101]
9.2 - 4.2. Moving least squares [Seite 104]
9.2.1 - 4.2.1. Properties of MLS form function [Seite 110]
9.2.2 - 4.2.2. Base functions [Seite 111]
9.2.3 - 4.2.3. Weight functions [Seite 112]
9.3 - 4.3. Galarkin mesh-free method [Seite 114]
9.4 - 4.4. Imposition of essential limiting conditions [Seite 119]
9.4.1 - 4.4.1. Variational principle modified with Lagrange multipliers [Seite 119]
9.4.2 - 4.4.2. Variational principle modified without Lagrange multipliers [Seite 120]
9.4.3 - 4.4.3. Variational principle with a charge [Seite 121]
9.4.4 - 4.4.4. Connection with meshing of finite elements [Seite 122]
9.5 - 4.5. Integration in the EFG method [Seite 123]
9.6 - 4.6. Description of EFG method algorithms [Seite 125]
10 - 5. Mechanical Systems with Uncertain Parameters [Seite 131]
10.1 - 5.1. Introduction [Seite 131]
10.2 - 5.2. Monte Carlo simulation [Seite 132]
10.3 - 5.3. Disturbance methods [Seite 132]
10.3.1 - 5.3.1. Expansion into a second-order Taylor series [Seite 134]
10.3.2 - 5.3.2. Muscolino distortion method [Seite 140]
10.3.3 - 5.3.3. Disturbance methods and modal reduction methods [Seite 143]
10.4 - 5.4. Projection onto polynomial chaos [Seite 147]
10.4.1 - 5.4.1. Moments of the response function in frequency [Seite 150]
10.4.2 - 5.4.2. Moments of dynamic response [Seite 151]
10.4.3 - 5.4.3. Projection onto polynomial chaos with modal reduction [Seite 153]
10.5 - 5.5. Conclusion [Seite 165]
11 - 6. Modal Synthesis Methods and Stochastic Finite Element Methods [Seite 167]
11.1 - 6.1. Introduction [Seite 167]
11.2 - 6.2. Linear dynamic problems [Seite 168]
11.2.1 - 6.2.1. Equations of motion [Seite 168]
11.2.2 - 6.2.2. Solutions in the transient regime [Seite 169]
11.2.3 - 6.2.3. Solutions in the harmonic regime [Seite 170]
11.3 - 6.3. Modal synthesis methods [Seite 171]
11.3.1 - 6.3.1. Introduction [Seite 171]
11.3.2 - 6.3.2. Sub-structure assembly technique [Seite 173]
11.3.3 - 6.3.3. Fixed interface method [Seite 174]
11.3.4 - 6.3.4. MacNeal's free interface method [Seite 177]
11.3.5 - 6.3.5. Free interface method [Seite 179]
11.3.6 - 6.3.6. Hybrid method [Seite 182]
11.3.7 - 6.3.7. Reduction in degrees of freedom of the interface [Seite 182]
11.4 - 6.4. Stochastic finite element methods [Seite 184]
11.4.1 - 6.4.1. Introduction [Seite 184]
11.4.2 - 6.4.2. Discretization of random fields [Seite 185]
11.4.3 - 6.4.3. Methods of moments [Seite 187]
11.5 - 6.5. Conclusion [Seite 195]
12 - 7. Stochastic Modal Synthesis Methods [Seite 197]
12.1 - 7.1. Introduction [Seite 197]
12.2 - 7.2. Taylor series expansion of the modal equations of a stochastic structure [Seite 197]
12.2.1 - 7.2.1. Expression of the mean values and covariances [Seite 200]
12.3 - 7.3. Muscolino perturbation method [Seite 200]
12.3.1 - 7.3.1. Expansion of the modal equations of a stochastic structure [Seite 201]
12.4 - 7.4. Stochastic fixed interface method [Seite 202]
12.4.1 - 7.4.1. Taylor series expansion [Seite 202]
12.5 - 7.5. Stochastic modal synthesis method [Seite 207]
12.5.1 - 7.5.1. Introduction [Seite 207]
12.6 - 7.6. Conclusion [Seite 252]
13 - 8. Dynamic Response of a Structure with Uncertain Variables to a Given Excitation [Seite 253]
13.1 - 8.1. Introduction [Seite 253]
13.2 - 8.2. Perturbation method [Seite 254]
13.2.1 - 8.2.1. Taylor series expansion of the equations of motion [Seite 254]
13.2.2 - 8.2.2. Muscolino perturbation method [Seite 257]
13.3 - 8.3. Stochastic modal synthesis method [Seite 258]
13.4 - 8.4. Projection onto homogeneous chaos [Seite 261]
13.5 - 8.5. Coupling modal synthesis methods with projection onto homogeneous chaos [Seite 264]
13.6 - 8.6. Conclusion [Seite 280]
14 - 9. Stochastic Frequency Response Function [Seite 281]
14.1 - 9.1. Introduction [Seite 281]
14.2 - 9.2. Calculation of the stochastic frequency response function [Seite 282]
14.3 - 9.3. Calculation of the stochastic frequency response function with modal synthesis methods [Seite 286]
14.4 - 9.4. Conclusion [Seite 297]
15 - 10. Modal Synthesis Methods and Reliability Optimization Methods [Seite 299]
15.1 - 10.1. Introduction [Seite 299]
15.2 - 10.2. Combining modal synthesis and RBDO methods [Seite 299]
15.3 - 10.3. Conclusion [Seite 310]
16 - 11. Stochastic Model of Transmission in a Wind Turbine [Seite 311]
16.1 - 11.1. Introduction [Seite 311]
16.2 - 11.2. Modeling the dynamic behavior of the gearing system in a wind turbine [Seite 311]
16.3 - 11.3. Dynamic response of a two-step gear system in a wind turbine with uncertain variables [Seite 312]
16.3.1 - 11.3.1. Dynamic model of a two-step wind turbine transmission [Seite 312]
16.3.2 - 11.3.2. Study using the polynomial chaos method [Seite 315]
16.3.3 - 11.3.3. Perturbation method study [Seite 325]
16.3.4 - 11.3.4. Comparison of the different methods [Seite 331]
16.4 - 11.4. Conclusion [Seite 333]
17 - Bibliography [Seite 335]
18 - Index [Seite 343]
19 - Other titles from iSTE in Mechanical Engineering and Solid Mechanics [Seite 347]
20 - EULA [Seite 353]