Stochastic dynamics of structures / Abdelkhalak El Hami, Bouchaib Radi.

Format:

Book

Author/Creator:

El Hami, Abdelkhalak, author.

Radi, Bouchaïb, author.

Series:

Mechanical engineering and solid mechanics series ; 2.

THEi Wiley ebooks.

Mechanical Engineering and Solid Mechanics Series ; 2

THEi Wiley ebooks

Language:

English

Subjects (All):

Dynamics.

Stochastic processes.

Physical Description:

1 online resource

Edition:

1st ed.

Place of Publication:

London, England ; Hoboken, New Jersey : Wiley : ISTE, 2016.

System Details:

Access using campus network via VPN at home (THEi Users Only).

Summary:

This book is dedicated to the general study of the dynamics of mechanical structures with consideration of uncertainties. The goal is to get the appropriate forms of a part in minimizing a given criterion. In all fields of structural mechanics, the impact of good design of a room is very important to its strength, its life and its use in service. The development of the engineer's art requires considerable effort to constantly improve structural design techniques.--Provided by publisher.

Contents:

Cover

Title Page

Copyright

Contents

Preface

1. Introduction to Structural Dynamics

1.1. Composition of problems relating to dynamic structures

1.1.1. Finite element method

1.1.2. Modal superposition method

1.1.3. Direct integration

1.2. Structural optimization

1.2.1. Design optimization

1.2.2. Shape optimization

1.2.3. Topological optimization

1.2.4. Definitions and formulation of an optimization problem

1.3. Structures with uncertain parameters

1.3.1. Monte Carlo simulation

1.3.2. Analytic method

1.3.3. Stochastic finite element method

1.3.4. Fluid logic method

1.3.5. Reliability method

1.3.6. Reliability optimization

1.4. Conclusion

2. Decoupled Systems

2.1. Introduction

2.2. Problems with structural dynamics

2.2.1. Movement equation

2.2.2. Hooke's law

2.2.3. Variational formulation

2.2.4. Estimation by finite elements

2.2.5. Resolution in the frequency domain

2.2.6. Solution in the temporal domain

2.2.7. Reduction of the model

2.3. Acoustic problems

2.3.1. Wave equation: formulation pressure

2.3.2. Variational formulation

2.3.3. Estimation by finite elements

2.3.4. Solution in the frequency domain

2.3.5. Model fluid reduction

2.4. Conclusion

3. Coupled Systems

3.1. Introduction

3.2. Mathematical formulation

3.2.1. Behavior equations

3.2.2. Conditions for fluid-structure coupling

3.3. Variational formulation

3.4. Estimation by finite elements

3.4.1. Estimation of unknown physical values

3.4.2. Integration of variational forms

3.5. Vibro-acoustic problem

3.6. Hydro-elastic problem

3.6.1. Calculation of the elementary matrix of the fluid-structure interaction

3.6.2. Dynamic study

3.7. Reduction of the model

3.7.1. Modal superposition method for the paired system.

3.7.2. Direct calculation

3.7.3. Calculation with modal reduction

3.7.4. Modal synthesis method for paired systems

3.7.5. Direct numerical calculation

3.7.6. Numerical calculation with modal superposition

3.8. Conclusion

4. Reliability and Meshless Methods in Mechanics

4.1. Introduction to non-networking methods

4.2. Moving least squares

4.2.1. Properties of MLS form function

4.2.2. Base functions

4.2.3. Weight functions

4.3. Galarkin mesh-free method

4.4. Imposition of essential limiting conditions

4.4.1. Variational principle modified with Lagrange multipliers

4.4.2. Variational principle modified without Lagrange multipliers

4.4.3. Variational principle with a charge

4.4.4. Connection with meshing of finite elements

4.5. Integration in the EFG method

4.6. Description of EFG method algorithms

5. Mechanical Systems with Uncertain Parameters

5.1. Introduction

5.2. Monte Carlo simulation

5.3. Disturbance methods

5.3.1. Expansion into a second-order Taylor series

5.3.2. Muscolino distortion method

5.3.3. Disturbance methods and modal reduction methods

5.4. Projection onto polynomial chaos

5.4.1. Moments of the response function in frequency

5.4.2. Moments of dynamic response

5.4.3. Projection onto polynomial chaos with modal reduction

5.5. Conclusion

6. Modal Synthesis Methods and Stochastic Finite Element Methods

6.1. Introduction

6.2. Linear dynamic problems

6.2.1. Equations of motion

6.2.2. Solutions in the transient regime

6.2.3. Solutions in the harmonic regime

6.3. Modal synthesis methods

6.3.1. Introduction

6.3.2. Sub-structure assembly technique

6.3.3. Fixed interface method

6.3.4. MacNeal's free interface method

6.3.5. Free interface method

6.3.6. Hybrid method.

6.3.7. Reduction in degrees of freedom of the interface

6.4. Stochastic finite element methods

6.4.1. Introduction

6.4.2. Discretization of random fields

6.4.3. Methods of moments

6.5. Conclusion

7. Stochastic Modal Synthesis Methods

7.1. Introduction

7.2. Taylor series expansion of the modal equations of a stochastic structure

7.2.1. Expression of the mean values and covariances

7.3. Muscolino perturbation method

7.3.1. Expansion of the modal equations of a stochastic structure

7.4. Stochastic fixed interface method

7.4.1. Taylor series expansion

7.5. Stochastic modal synthesis method

7.5.1. Introduction

7.6. Conclusion

8. Dynamic Response of a Structure with Uncertain Variables to a Given Excitation

8.1. Introduction

8.2. Perturbation method

8.2.1. Taylor series expansion of the equations of motion

8.2.2. Muscolino perturbation method

8.3. Stochastic modal synthesis method

8.4. Projection onto homogeneous chaos

8.5. Coupling modal synthesis methods with projection onto homogeneous chaos

8.6. Conclusion

9. Stochastic Frequency Response Function

9.1. Introduction

9.2. Calculation of the stochastic frequency response function

9.3. Calculation of the stochastic frequency response function with modal synthesis methods

9.4. Conclusion

10. Modal Synthesis Methods and Reliability Optimization Methods

10.1. Introduction

10.2. Combining modal synthesis and RBDO methods

10.3. Conclusion

11. Stochastic Model of Transmission in a Wind Turbine

11.1. Introduction

11.2. Modeling the dynamic behavior of the gearing system in a wind turbine

11.3. Dynamic response of a two-step gear system in a wind turbine with uncertain variables

11.3.1. Dynamic model of a two-step wind turbine transmission

11.3.2. Study using the polynomial chaos method.

11.3.3. Perturbation method study

11.3.4. Comparison of the different methods

11.4. Conclusion

Bibliography

Index

Other titles from iSTE in Mechanical Engineering and Solid Mechanics

EULA.

Notes:

"Mathematical and mechanical engineering set."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781119377672

1119377676

9781119377610

1119377617

9781119377658

111937765X

OCLC:

964931732