Dynamics and Vibrations

1. Front Matter

   Pages i-xvii

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2. Introduction to Nonlinear Vibrations and Dynamics

   • Sayyid Habibollah Hashemi Kachapi, Davood Domairry Ganji

   Pages 1-48

3. Perturbation and Variational Methods

   • Sayyid Habibollah Hashemi Kachapi, Davood Domairry Ganji

   Pages 49-132

4. Considerable Analytical Methods

   • Sayyid Habibollah Hashemi Kachapi, Davood Domairry Ganji

   Pages 133-183

5. Introduction of Considerable Oscillatory Systems

   • Sayyid Habibollah Hashemi Kachapi, Davood Domairry Ganji

   Pages 185-247

6. Applied Problems in Dynamical Systems

   • Sayyid Habibollah Hashemi Kachapi, Davood Domairry Ganji

   Pages 249-338

Dynamical and vibratory systems are basically an application of mathematics and applied sciences to the solution of real world problems. Before being able to solve real world problems, it is necessary to carefully study dynamical and vibratory systems and solve all available problems in case of linear and nonlinear equations using analytical and numerical methods. It is of great importance to study nonlinearity in dynamics and vibration; because almost all applied processes act nonlinearly, and on the other hand, nonlinear analysis of complex systems is one of the most important and complicated tasks, especially in engineering and applied sciences problems.
There are probably a handful of books on nonlinear dynamics and vibrations analysis. Some of these books are written at a fundamental level that may not meet ambitious engineering program requirements. Others are specialized in certain fields of oscillatory systems, including modeling and simulations. In this book, we attempt to strike a balance between theory and practice, fundamentals and advanced subjects, and generality and specialization.
None of the books in this area have completely studied and analyzed nonlinear equation in dynamical and vibratory systems using the latest analytical and numerical methods, so that the user can solve the problems without the need of studying too many different references. Thereby in this book, by the use of the latest analytic, numeric laboratorial methods and using more than 300 references like books, papers and the researches done by the authors and by considering almost all possible processes and situation, new theories has been proposed to encounter applied problems in engineering and applied sciences. In this way, the user (bachelor’s, master’s and PhD students, university teachers and even in research centers in different fields of mechanical, civil, aerospace, electrical, chemical, applied mathematics, physics, and etc.) can encounter suchsystems confidently. In the different chapters of the book, not only are the linear and especially nonlinear problems with oscillatory form broadly discussed, but also applied examples are practically solved by the proposed methodology.

• Adomian’s Decomposition Method
• Duffing oscillation
• D’Alembert’s Principle
• Hamiltonian oscillation
• He’s Amplitude-Frequency formulation
• He’s Parameter Expansion Method
• Hill’s oscillation
• Homotopy perturbation method
• Mathieu oscillation
• Van der Pol oscillation

From the book reviews:

“The text is aimed to undergraduate students, scientists working in various branches of engineering, and to natural scientists or applied mathematicians. In different chapters, the authors provide an abundance of examples and homework problems. The active reader of this collection can achieve a strong understanding of the nonlinearity of dynamical equations of motion of oscillatory systems, of the required numerical and analytical methods, and the ability to interpret an engineering model and solve the governing equations describing its vibrations.” (Vasile Marinca, zbMATH, Vol.1305, 2015)

• , Department of Mechanical Engineering, Babol University of Technology, Babol, Iran

  Seyed Habibollah Hashemi Kachapi, Davood Domairry Ganji

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