Modeling of Complex Dynamic Systems
Fundamentals and Applications
- 1st Edition - April 9, 2025
- Imprint: Elsevier
- Authors: Vladimir Stojanović, Jian Deng, Marko D. Petković, Marko A. Ristić
- Language: English
- Paperback ISBN:9 7 8 - 0 - 4 4 3 - 2 3 9 4 2 - 7
- eBook ISBN:9 7 8 - 0 - 4 4 3 - 2 3 9 4 3 - 4
Motion is the essence of any mechanical system. Analyzing a system’s dynamical response to distinct motion parameters allows for increased understanding of its performance threshol… Read more
Purchase options
Institutional subscription on ScienceDirect
Request a sales quoteMotion is the essence of any mechanical system. Analyzing a system’s dynamical response to distinct motion parameters allows for increased understanding of its performance thresholds and can in turn provide clear data to inform improved system designs.
Modeling of Complex Dynamic Systems: Fundamentals and Applications equips readers with significant insights into nonlinear vibration phenomenology through a combination of advanced mathematical fundamentals and worked-through modeling experiments. To guide them in determining novel stabilization characteristics for complex moving objects, coupled structures, as well as the stochastic stability of mechanical systems, the technical and methodological analysis is accompanied by industry-relevant practical examples, contributing much sought-after applicable knowledge.
The book is intended for use by postgraduate students, academic researchers, and professional engineers alike.
- Connects three areas of theoretical and applied mechanics – nonlinear vibrations, dynamics of moving objects, and stochastic stability of structures, while also reviewing literature
- Compares classical dynamic models with the authors’ proposed modeling methodologies to analyze mechanical systems affected by parametric instabilities
- Discusses new technical solutions powered by AI and ML to introduce possible further research directions
Researchers, academics, and post-graduate students in mechanical engineering, applied mechanics, computational mechanics, aerospace engineering, railway engineering. Professional engineers looking into optimized design and operation approaches, as well as vibration/oscillation mitigation or control strategies for aircraft and spacecraft, high-speed trains, wind farms, cosmological stations, hydropower plants, etc.
- Title of Book
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- About the authors
- Preface
- Part I: Fundamental mathematical background of dynamics and vibrations: Overview of numerical methods and recent improvements
- 1. Mathematical methods and procedures in the analysis of stability of vibrations of complex moving objects
- Abstract
- 1.1 Introduction to complex numbers
- 1.2 Complex functions and their continuity and differentiability
- 1.3 Integrals of the complex functions
- 1.4 Cauchy integral theorem and formula
- 1.5 Taylor and Laurent series
- 1.6 Residues
- 1.7 The principle of argument
- 1.8 Laplace transform
- 1.9 Fourier transform
- References
- 2. Mathematical methods and applications in the analysis of nonlinear vibrations
- Abstract
- 2.1 Problem formulation
- 2.2 Numerical methods for solving general dynamical systems
- 2.3 Newmark method
- 2.4 Newmark method in the multidimensional case
- 2.5 Improvement of the accuracy by Richardson extrapolation
- 2.6 Harmonic balance method
- References
- 3. Mathematical methods in stochastic stability of mechanical systems
- Abstract
- 3.1 Introduction to probability space and random variables
- 3.2 Random processes
- 3.3 Wiener and white noise process
- 3.4 Markov and diffusion processes
- 3.5 Stochastic integrals and differential equations
- 3.6 Orstein–Uhlenbeck and bounded noise process
- 3.7 Moment Lyapunov exponent and stability
- 3.8 Perturbation method
- 3.9 New generalized transformations for multiple degrees of freedom mechanical systems
- References
- Part II: Stability of vibrations of complex moving objects: Modeling and applications
- 4. Stabilization and critical velocity of a moving mass
- Abstract
- 4.1 Introduction
- 4.2 Model and solution of free waves propagation
- 4.3 Response of the double-supported beam system subjected to a moving constant vertical force P
- 4.4 Stability of vibrations of a complex double-supported beam system
- 4.5 Influence of a compressive axial force on harmonic vibrations of the moving mass subjected to a constant vertical force
- 4.6 Conclusion
- References
- 5. Stability of vibrations of a system of discrete oscillators that are moving at an overcritical velocity
- Abstract
- 5.1 Introduction
- 5.2 Dispersion of complex model and characteristic equation
- 5.3 Determination of stable regions
- 5.4 Conclusion
- References
- 6. Vibrational benefits of the new stabilizer in moving coupled vehicles
- Abstract
- 6.1 Introduction
- 6.2 Mathematical model and critical velocity
- 6.3 Dynamic stability analysis
- 6.4 Influence of the elastic coupling on dynamic stability
- 6.5 Influence of the mass ratio between the connected rail cars on dynamic stability
- 6.6 Influence of the wheelbases on dynamic stability
- 6.7 Conclusion
- Appendix A 6.1
- References
- 7. Dynamics and stability of a complex rail vehicle system
- Abstract
- 7.1 Introduction
- 7.2 Dispersion relation and critical velocity
- 7.3 Modeling of the complex rail vehicle systems and the characteristic equations
- 7.4 Dynamic stability analysis
- 7.5 Influence of the viscoelastic coupling on dynamic stability of a triple vehicle system
- 7.6 Influence of the secondary suspension on dynamic stability of a vehicle that has four contact points with the rail
- 7.7 Influence of the supercritical velocity and varying parameters of the secondary suspension on boundaries of the stability domain
- 7.8 Conclusion
- References
- 8. Modeling of a three-part viscoelastic foundation and its effect on dynamic stability
- Abstract
- 8.1 Introduction
- 8.2 Dispersion relation and critical velocity
- 8.3 Modeling of railway vehicle system and characteristic equation
- 8.4 Dynamic stability analysis
- 8.5 Parametric study
- 8.6 Influence of the secondary suspension stiffness on the stability domain
- 8.7 Influence of the bogie’s mass on dynamic stability
- 8.8 Influence of the wheelbase size on dynamic stability
- 8.9 Influence of the position of the supports on dynamic stability
- 8.10 Conclusion
- References
- 9. Vibrational instability in a complex moving object: innovative approaches to elastically damped connections between car body components and supports
- Abstract
- 9.1 Introduction
- 9.2 Modeling of the complex coupled models and characteristic equation
- 9.3 Solution method and stability criteria
- 9.4 Results and discussion
- 9.5 Conclusion
- References
- Part III: Linear and nonlinear vibrations: Stabilizing phenomena and applications
- 10. Nonlinear amplitude analysis of shear deformable beams supported by an elastic foundation with variable discontinuity
- Abstract
- 10.1 Introduction
- 10.2 Mathematical model and equations of motion
- 10.3 Natural frequencies and general modes of vibration
- 10.4 Geometric nonlinear vibrations
- 10.5 Conclusions
- References
- 11. Nonlinear vibrational characteristics of damaged beams resting on a Pasternak foundation
- Abstract
- 11.1 Introduction
- 11.2 Mathematical model of intact Reddy–Bickford beam on nonlinear Pasternak foundation
- 11.3 Modeling of damage and the p-FEM formulation
- 11.4 Natural frequencies and the stiffness function
- 11.5 Forced geometrically nonlinear vibrations in the time domain and the Newmark method
- 11.6 Geometrically nonlinear free vibrations in the frequency domain and the Continuation method
- 11.7 Conclusions
- Appendix 1
- Appendix 2
- References
- 12. The purpose of an arch in the stability of nonlinear vibrations of coupled structures
- Abstract
- 12.1 Introduction
- 12.2 Problem statement and modeling of a geometrically nonlinear beam–arch coupled system using the p-FEM
- 12.3 Convergence study
- 12.4 Time-domain analysis and improvement of the Newmark method
- 12.5 Harmonic balance and continuation methods in frequency domain analysis
- 12.6 Applications
- 12.7 Conclusion
- Appendix A 12.1
- References
- 13. Quantitative effect of an axial load on the amplitude stability of rotating nano-beams
- Abstract
- 13.1 Introduction
- 13.2 Nonlocal elastic constitutive relations
- 13.3 Mathematical formulations of the equations of motion
- 13.4 Solution methodology
- 13.5 Natural frequencies of the rotating nonlocal cantilever nano-beam
- 13.6 Forced vibration of the undamped system
- 13.7 Forced vibration of the damped system
- 13.8 Results and discussion
- 13.9 Numerical discussion of the forced vibration of the undamped system
- 13.10 Numerical discussion of the forced vibration of the damped system
- 13.11 Conclusion
- References
- 14. Coupled multiple plate systems and their stability characteristics
- Abstract
- 14.1 Introduction
- 14.2 Theoretical formulation
- 14.3 Natural frequencies
- 14.4 Stability analysis of the multiplate system using CPT, FSDT, and HSDT
- 14.5 General natural mode shapes of multiplate systems
- 14.6 Numerical analysis
- 14.7 Conclusion
- References
- Part IV: Stochastic stability of structures and mechanical systems: Methodology and examples
- 15. Moment Lyapunov exponents and stochastic stability of the vibrationally isolated laminated plates
- Abstract
- 15.1 Introduction
- 15.2 Problem formulation
- 15.3 Stochastic stability analysis
- 15.4 Averaged equations in the general case of a three-degree-of-freedom-stochastic-system
- 15.5 Moment Lyapunov exponents
- 15.6 Zeroth order perturbation
- 15.7 First-order perturbation
- 15.8 Second-order perturbation
- 15.9 Stochastic stability conditions and discussion
- 15.10 Conclusions
- References
- 16. Higher-order stochastic averaging method in fractional stochastic dynamics
- Abstract
- 16.1 Introduction
- 16.2 Stochastic averaging
- 16.3 Results and discussions
- 16.4 Conclusions
- Appendix A1 Fractional calculus
- Appendix A2 Fractional viscoelasticity
- References
- 17. Parametric stochastic stability of viscoelastic rotating shafts
- Abstract
- 17.1 Introduction
- 17.2 Vibration of a rotating shaft
- 17.3 Stochastic averaging
- 17.4 Moment Lyapunov exponents
- 17.5 Conclusion
- References
- 18. Stochastic stability of circular cylindrical shells
- Abstract
- 18.1 Introduction
- 18.2 Problem formulation and deterministic vibrations
- 18.3 Stochastic vibration analysis
- 18.4 Moment Lyapunov exponents
- 18.5 Stochastic stability conditions and discussion
- 18.6 Conclusions
- Appendix A18.1
- Appendix A18.2
- Appendix A18.3
- References
- 19. Generalized transformations for MDOF stochastic systems
- Abstract
- 19.1 Introduction
- 19.2 Stochastic stability of MDOF systems
- 19.3 Stochastic stability of a coupled rotating shaft system
- 19.4 Conclusions
- Appendix A19
- References
- Part V: From traditional methods to Artificial Intelligence
- 20. Modeling and applications of markers in machine learning and technical practice
- Abstract
- 20.1 Formulation of the problem
- 20.2 Neural networks
- 20.3 Training and validation of the neural network
- 20.4 Application on the two simple mechanical systems
- 20.5 Application to the design of the advanced mechanical system for wave energy extraction
- 20.6 Conclusions
- References
- Index
- Edition: 1
- Published: April 9, 2025
- Imprint: Elsevier
- No. of pages: 556
- Language: English
- Paperback ISBN: 9780443239427
- eBook ISBN: 9780443239434
VS
Vladimir Stojanović
Dr. Stojanović currently holds an Associate Professor position at the Faculty of Mechanical Engineering, University of Niš, Serbia, and a Visiting Professor position at Lakehead University, Ontario, Canada. Since 2011, he has published numerous papers in prestigious scientific journals, where he also serves as a reviewer. As an internationally recognized scientist, he has been invited to lecture at universities worldwide and has participated in the most significant conferences in the field of theoretical and applied mechanics. His research interests primarily focus on the modeling of complex linear and nonlinear continuous and discrete dynamical systems, analytical and numerical methods for solving MDOF-based models, and the application of dynamic and stochastic stability principles to engineering problems in vibration.
Affiliations and expertise
Associate Professor, Faculty of Mechanical Engineering, University of Niš, Niš, Serbia; Visiting Professor, Dept. of Civil Engineering, Faculty of Engineering, Lakehead University, Thunder Bay, Ontario, CanadaJD
Jian Deng
Dr. Deng is currently Chair and Associate Professor in the Department of Civil Engineering at Lakehead University, Canada. He is a licensed professional engineer in Ontario and has over 20 years of research, education, and industry experience. Dr. Deng’s research group is developing theories and techniques to better understand dynamic instability, geohazards, and the reliability of structures in civil and mining engineering, especially in geotechnical engineering. His excellence in research has been recognized through several awards, including the Best Paper Award, the Research Excellence Award, and the Best Presentation Award. These accolades underscore the impact of Dr. Deng’s guidance and contributions to both research excellence and student development.
Affiliations and expertise
Chair and Associate Professor, Dept. of Civil Engineering, Faculty of Engineering, Lakehead University, Thunder Bay, Ontario, CanadaMP
Marko D. Petković
Dr. Petković received a PhD in Computer Science in 2008 from the University of Niš, Serbia. He is a prolific author, the editor-in-chief of the Facta Universitatis, Series: Mathematics and Informatics, and section editor for three other recognized journals. He is the author of more than 15 software solutions, both commercial and non-commercial scientific software. His research interests include numerical linear algebra, neural networks, source and channel coding, and optimization methods.
Affiliations and expertise
Full Professor, Dept. of Computer Science, Faculty of Sciences and Mathematics, University of Niš, Niš, SerbiaMR
Marko A. Ristić
Marko A. Ristić received his MSc degree in Mechanical Design and Mechanization in 2009 from the University of Niš. Currently, he works as a Researcher at the Faculty of Mechanical Engineering, University of Niš, to complete his doctoral thesis. His research interests include machine component design, finite element analysis, computational fluid dynamics, gear design, planetary gear trains, and high-conformal gearing.
Affiliations and expertise
Researcher and PhD Candidate, Faculty of Mechanical Engineering, University of Niš, Niš, SerbiaRead Modeling of Complex Dynamic Systems on ScienceDirect