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Computational Methods for Nonlinear Dynamical Systems : Theory and Applications in Aerospace Engineering.
- Format:
- Book
- Author/Creator:
- Wang, Xuechuan, author.
- Yue, Xiaokui, author.
- Dai, Honghua, author.
- Feng, Haoyang, author.
- Atluri, Satya N., author.
- Language:
- English
- Subjects (All):
- Nonlinear systems.
- Differentiable dynamical systems.
- Aerospace engineering--Computer simulation.
- Aerospace engineering.
- Physical Description:
- 1 online resource (242 p.)
- Place of Publication:
- San Diego : Elsevier, 2022.
- Contents:
- Front Cover
- Computational Methods for Nonlinear Dynamical Systems
- Copyright Page
- Contents
- Preface
- 1 Introduction
- SUMMARY
- 1.1 The weighted residual methods
- 1.1.1 Problem description
- 1.1.2 Primal methods
- 1.1.2.1 Global unsymmetric weak form I
- 1.1.2.2 Global symmetric weak form
- 1.1.2.3 Global unsymmetric weak form II
- 1.1.2.4 Local weak forms
- 1.1.3 Mixed methods
- 1.2 Application of weighted residual methods
- 1.2.1 Transient motions
- 1.2.1.1 Collocation method
- 1.2.1.2 Galerkin method
- 1.2.2 Periodic motions
- 1.2.2.1 Collocation method
- 1.2.2.2 Galerkin method (harmonic balance method)
- 1.3 Finite difference methods
- 1.3.1 Explicit methods
- 1.3.2 Implicit methods
- 1.4 Asymptotic methods
- 1.4.1 Perturbation method
- 1.4.2 Adomian decomposition method
- 1.4.3 Picard iteration method
- References
- 2 Harmonic balance method and time domain collocation method
- 2.1 Time Collocation in a period of oscillation
- 2.2 Relationship between collocation and harmonic balance
- 2.2.1 Harmonic balance method
- 2.2.2 High dimensional harmonic balance method
- 2.2.3 Equivalence between HDHB and collocation
- 2.3 Initialization of Newton-Raphson method
- 2.3.1 Initial values for undamped system
- 2.3.1.1 Initial values for the iterative solution of NAEs for capturing the 1/3 subharmonic solution of the undamped system
- 2.3.1.2 Initial values for the iterative solution of NAEs for capturing the harmonic solution of the undamped system
- 2.3.2 Initial values for damped system
- 2.3.2.1 Initial values for the iterative solution of NAEs for capturing the 1/3 subharmonic solution of the damped system
- 3.2.1 Numerical approximation of Jacobian matrix
- 3.2.2 Explicit Jacobian matrix of HB
- 3.2.3 Mathematical aliasing of HB method
- 3.3 Formulation of the TDC method
- 3.3.1 Explicit Jacobian matrix of TDC
- 3.3.2 Mathematical aliasing of the TDC method
- 3.4 Reconstruction harmonic balance method
- 3.5 Numerical examples
- 3.5.1 RK4 results and spectral analysis
- 3.5.2 HBEJ vs. HBNJ
- 3.5.3 Aliasing analysis of the HB and TDC methods
- 3.5.3.1 Aliasing of the HB method
- HB3 with fully random initials
- HB9 with partially random initials
- HB9 with fully random initial guesses
- Notes:
- 3.5.3.2 Aliasing of the TDC method
- Electronic reproduction. Amsterdam Available via World Wide Web.
- Other Format:
- Print version: Wang, Xuechuan Computational Methods for Nonlinear Dynamical Systems
- ISBN:
- 9780323991148
- 0323991149
- Publisher Number:
- 99993430133
- Access Restriction:
- Restricted for use by site license.
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