Dynamics and Vibrations Progress in Nonlinear Analysis /

• Main Authors: Kachapi, Seyed Habibollah Hashemi (Author), Ganji, Davood Domairry (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Dordrecht : Springer Netherlands : Imprint: Springer, 2014.
• Series: Solid Mechanics and Its Applications, 202
• Subjects: Engineering.; Continuum physics.; Physics.; Statistical physics.; Continuum mechanics.; Vibration.; Dynamical systems.; Dynamics.; Vibration, Dynamical Systems, Control.; Continuum Mechanics and Mechanics of Materials.; Classical Continuum Physics.; Applied and Technical Physics.; Nonlinear Dynamics.

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 line...

Table of Contents:

• 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.