Dynamics and Vibrations

This book examines nonlinear equations in dynamical and vibratory systems using the latest analytical and numerical methods. It strikes a balance between theory and practice, fundamentals and advanced subjects, and generality and specialization.

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.

A comprehensive, self-contained and complete text on dynamical and vibratory motions and analytical and numerical methods in applied problems Strikes a balance between theory and practice, fundamentals and advanced subjects, and generality and specialization Applied examples are practically solved by the use of the latest analytical and numerical methods Includes supplementary material: sn.pub/extras

Inhalt
Introduction to Nonlinear Vibrations & Oscillations and Dynamics.- Usual Sources of Nonlinearity in Mechanical and other Engineering.- Formulation of Equations.- Applied examples.- Problems.- References.- Perturbation and Variational Methods.- Introduction.- The Basic Ideas of the Perturbation Analysis.- Parameterized Perturbation Method.- Singular Perturbation Method.- Homotopy Perturbation Method and its Modified.- Variational Iteration Method.- Variational approach.- Couple Variational Method.- Energy Balance Method.- Coupled Method of Homotopy Perturbation Method and Variational Method.- Problems.- References.- Considerable Analytical Methods.- Harmonic Balance Method.- He's Parameter Expansion Method.- Differential Transformation Method and its Modified.- Adomian's decomposition method.- He's Amplitude-Frequency formulation.- Problems.- References.- Introduction of Considerable Oscillatory Systems.- Duffing's Oscillation Systems.- The Van der Pol Oscillator Systems.- Mathieu's Equation.- Ince's Equation.- Applied Problems in Dynamically Systems.- Displacement of human eardrum.- Slides motion along a bending wire.- Movement a mass along a circle.- Rolling a cylinder on a cylindrical surface.- Movement of Rigid rocks on a circular surface.- Application of two degrees of freedom viscously damped.- Application of viscously damped with a nonlinear spring.- Application of cubic nonlinearity.- Van der Pol oscillator.- Application of a slender, elastic cantilever beam.- Dynamic behavior of a flexible beam attached to rotating rigid hub.- The motion of a ring sliding freely on the rotating wire.- Application of rotating rigid frame under force.- Application of nonlinear oscillator in automobile design.