Dynamics and Vibrations

• 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.

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)