Long description:

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 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

Table of Contents:

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
2. Mathematical methods and applications in the analysis of nonlinear vibrations
3. Mathematical methods in stochastic stability of mechanical systems

Part II: Stability of vibrations of complex moving objects: Modeling and applications
4. Stabilization and critical velocity of a moving mass
5. Stability of vibration of a complex discrete oscillator moving at an overcritical speed
6. Vibrational benefits of a new stabilizer in moving coupled vehicles
7. Dynamics and stability of a complex rail vehicle system
8. Modeling of a three-part viscoelastic foundation and its effect on dynamic stability
9. Vibrational instability in a complex moving object: Innovative approaches to elastically damped connections between car body components and supports

Part III: Nonlinear vibrations: Stabilizing phenomena and applications
10. Nonlinear amplitude analysis of shear deformable beams supported by an elastic foundation with variable discontinuity
11. Nonlinear vibrational characteristics of damaged beams resting on a Pasternak foundation
12. The purpose of an arch in the stability of nonlinear vibrations of coupled structures
13. Quantitative effect of an axial load on the amplitude stability of rotating nano-beams
14. Coupled multiple plate systems and their stability characteristics

Part IV: Stochastic stability of structures and mechanical systems: Methodology and examples
15. Moment Lyapunov exponents and stochastic stability of vibrationally isolated laminated plates
16. Higher-order stochastic averaging method in fractional stochastic dynamics
17. Parametric stochastic stability of viscoelastic rotating shafts
18. Stochastic stability of circular cylindrical shells
19. Generalized transformations for MDOF stochastic systems

Part V: From traditional methods to Artificial Intelligence
20. Modeling and applications of markers in machine learning and technical practice