Modeling and computation in vibration problems. Volume 2, Soft computing and uncertainty. / edited by Snehashish Chakraverty, Francesco Tornabene, and J. N. Reddy.

Format:

Book

Contributor:

Chakraverty, Snehashish, editor.

Tornabene, Francesco, editor.

Reṭṭi, J. N., editor.

Series:

IOP Ebooks Series

Language:

English

Subjects (All):

Soft computing.

Physical Description:

1 online resource (296 pages)

Edition:

First edition.

Place of Publication:

Bristol, England : IOP Publishing, [2021]

Summary:

These books provide a state-of-the-art treatment of mathematical theories of vibration. The second volume covers soft computing, including machine intelligence techniques and uncertainty scenarios. It is an invaluable guide for graduate and postgraduate students, teachers and researchers in fields including applied mathematics, physics and engineering.

Contents:

Intro

Preface

Editor biographies

S Chakraverty

F Tornabene

J N Reddy

List of contributors

Chapter 1 Deep learning for solution and inversion of structural mechanics and vibrations

1.1 Introduction

1.2 Deep learning

1.3 Physics-informed neural networks

1.4 Training neural networks

1.5 Applications of deep learning for data representation

1.5.1 Polynomial regression

1.5.2 Smoothing noisy vibration measurements

1.6 Deep learning for solution and inversion of vibration problems

1.6.1 Forced vibration spring-mass problem

1.6.2 Free vibration of rectangular membrane

1.6.3 Free vibration of a rectangular plate

1.7 Discussions and final remarks

References

Chapter 2 Artificial neural network based technique for solving nonlinear eigenvalue problems of structural dynamics with fuzzy parameters

2.1 Introduction

2.2 Preliminaries

2.2.1 Nonlinear eigenvalue problems (NEPs)

2.2.2 Fuzzy nonlinear eigenvalue problems (FNEPs)

2.2.3 Linearization of FNEPs

2.2.4 Conversion of the fuzzy matrix into interval form

2.3 ANN methodology

2.4 Numerical example

2.5 Conclusion

Chapter 3 Multilayer unsupervised symplectic artificial neural network model for solving Duffing and Van der Pol-Duffing oscillator equations arising in engineering problems

3.1 Introduction

3.2 Architecture of multi-layer feed-forward neural network

3.3 Duffing oscillator equations

3.4 Van der Pol-Duffing oscillator equations

3.5 General formulation for differential equations with respect to ANN

3.5.1 Construction of symplectic neural network method for initial value problem

3.6 Numerical experiments and results

3.7 Conclusion

Acknowledgment

Chapter 4 Estimation of structural parameters using Chebyshev neural network model

4.1 Introduction.

4.2 Modelling for system identification of multistorey shear buildings

4.3 Chebyshev neural network

4.3.1 Structure of Chebyshev neural network

4.3.2 Learning algorithm of Chebyshev neural network

4.4 Results and discussion

4.5 Conclusion

Chapter 5 Inverse problems in vehicle-bridge interaction dynamics with application to bridge health monitoring

Symbols

5.1 Introduction

5.2 Part I: Roughness and vehicle parameter identification problem

5.2.1 Proposed technique

5.2.2 Unbiased minimum variance estimator for unknown input

5.2.3 Optimization scheme

5.2.4 Objective functions

5.2.5 Problem statement and state space formulation

5.2.6 Problem statement

5.2.7 State space formulation

5.2.8 Quarter car model

5.2.9 Modelling the vehicle-bridge interaction

5.2.10 Post-processing for extracting roughness profile

5.2.11 Numerical examples

5.2.12 Quarter car model

No measurement noise

Considering measurement noise

Natural frequency estimation

5.3 Part II: The damage identification problem

5.3.1 Vehicle dynamics

5.3.2 Mathematical modelling of the bridge

5.3.3 Part (a): Tyre model calibration

5.3.4 Relationship between VBI force and tyre pressure

5.3.5 Measurements used for tyre model calibration

5.3.6 Bayesian parameter estimation

5.3.7 Stein variational gradient descent (SVGD)

5.3.8 Simulation results

5.3.9 Part (b): Damage identification

5.3.10 Damage model

5.3.11 Damage scenarios considered in the study

5.3.12 Damage identification by contour plots

5.3.13 Damage indicators

5.3.14 Performance of the contour plots in assessing damage

5.3.15 Damage identification by optimization

5.4 Summary

Acknowledgements

References.

Chapter 6 Hybrid computational methods in vibration problems

6.1 Hybrid FE-SEA model

6.2 Benchmark models

6.2.1 Translational-spring-plate system

6.2.2 Torsional-spring-plate system

6.3 Linearisation techniques

6.3.1 Method of harmonic balance

6.3.2 Statistical linearisation

6.4 Numerical results

6.4.1 Gaussian orthogonal ensemble statistics

6.4.2 Built-up plate systems

6.5 Hybrid meshless-SEA formulation

6.5.1 Moving least square (MLS)

6.5.2 Element free MLS Ritz method

6.5.3 Hybrid element free MLS Ritz-SEA model

6.5.4 Numerical results for structure with continuous junction

6.6 Summary

Chapter 7 Vibration analysis of structures with uncertain parameters-an interval finite element approach

Introduction

7.1 Free vibration analysis of structures with uncertain structural parameters

7.2 Transient response of structures with uncertain structural parameters

Chapter 8 Vibrations of functionally graded structure with material uncertainties

8.1 Introduction

8.2 Preliminaries [3-5, 8, 9]

8.3 Mathematical modelling

8.4 Application of Hermite-Ritz method [13, 17, 18]

8.5 Numerical results and discussions

8.5.1 Validation

8.5.2 Propagation of uncertainties

8.6 Conclusion

Chapter 9 A new triple parametric approach to solve type-2 fuzzy structural problems with uncertain parameters in terms of interval type-2 trapezoidal fuzzy numbers

9.1 Introduction

9.2 Preliminaries

9.2.1 Interval type-2 fuzzy set

9.2.2 Interval type-2 fuzzy number

9.2.3 Interval type-2 trapezoidal fuzzy number

9.2.4 Interval type-2 trapezoidal fuzzy arithmetic

9.2.5 Perfectly normal interval type-2 trapezoidal fuzzy number

9.2.6 Type-2 fuzzy generalized eigenvalue problem

9.3 Triple parametric form of IT2TrFN.

9.4 Proposed methodology

9.5 Numerical examples

9.6 Conclusion

Chapter 10 Non-linear dynamic problems with uncertainty in type-2 fuzzy environment

10.1 Introduction

10.2 Preliminaries

10.2.1 Type-1 fuzzy numbers

10.2.2 Parametric form of fuzzy number

10.2.3 Type-2 fuzzy set

10.2.4 Vertical slice of type-2 fuzzy set

10.2.5 r1-plane of type-2 fuzzy set

10.2.6 Footprint of uncertainty

10.2.7 Lower membership function (LMF) and upper membership function (LMF) of a type-2 fuzzy set

10.2.8 Principle set of A˜ [10]

10.2.9 r2-cut of r1-plane [10]

10.2.10 Triangular perfect quasi type-2 fuzzy numbers [13]

10.3 Crisp non-linear eigenvalue problem

10.4 Type-2 fuzzy non-linear eigenvalue problem and proposed methodology

10.5 Numerical examples

10.6 Conclusion

Chapter 11 Semi-analytical methods for solving Ito stochastic models on the notion of Karhunen-Loéve Brownian motion transform

11.1 Introduction

11.2 Ito stochastic model

11.3 Stochastic/random vibration differential equations

11.4 Approximate-analytical methods of solution

11.5 Daftar-Gejii-Jafaris method

11.6 Picard iterative method [23]

11.7 Karhunen-Loéve expansion (K-L E) of Brownian motion

11.8 Application of K-L expansion to Ito SDEs

11.9 Comparison of the DJM solution and the PIM solution

11.10 Results, discussion and conclusion

Chapter 12 Arbitrary order vibration equation of large membranes with uncertainty

12.1 Introduction

12.2 Preliminaries [18-24]

12.3. Definitions and properties of Aboodh transform [25-28]

12.4 DPF of fuzzy fractional vibration equation

12.5 Basic idea of q-HAATM

12.6 Implementation of q-HAATM for solving fractional fuzzy VE

12.7 Result and discussion

Chapter 13 Fractional derivatives: a numerical insight into flow problems involving second grade fluid under fuzzy environment

13.1 Introduction

13.2 Formulation of the problem

13.3 Fuzzification of the problem

13.4 Method of solution

13.4.1 Solution with AB fractional derivatives

13.4.2 Solution with CF fractional derivatives

13.5 Results and discussion

13.5.1 Comparison of AB and CF fractional derivative methods in tabular form

13.5.2 Validation of our present scheme

13.6 Conclusion

Chapter 14 Successive approximation method based on uncertain dynamic responses of a fractionally damped beam

14.1 Introduction

14.2 Basic idea of successive approximation method [32, 33]

14.3 Implementation of SAM for the double parametric based solution of uncertain fractionally damped beam

14.4 Uncertain responses subjected to various forces

14.4.1 Unit step function response

14.4.2 Unit impulse function response

14.5 Conclusions

Chapter 15 Vibration of a cantilever beam immersed in a fluid with uncertain parameters

15.1 Introduction

15.2 Preliminaries

15.2.1 Interval

15.2.2 Parametric concept

15.3 Dynamics of a cantilever beam

15.3.1 Construction of γ(x,t) for a bending cantilever beam

15.3.2 Least square method (LSM) [19, 20]

15.4 Results and discussion

15.5 Conclusion

Acknowledgments

Notes:

Description based on publisher supplied metadata and other sources.

Description based on print version record.

Includes bibliographical references.

ISBN:

9780750344913

0750344911

OCLC:

1429741667