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Vibration Analysis is an exciting and challenging field and is a multidisciplinary subject. This
book is designed and organized around the concepts of Vibration Analysis of Mechanical Systems
as they have been developed for senior undergraduate course or graduate course for engineering students of all disciplines.
This book includes the coverage of classical methods of vibration analysis: matrix analysis,
Laplace transforms and transfer functions. With this foundation of basic principles, the book
provides opportunities to explore advanced topics in mechanical vibration analysis.
Chapter 1 presents a brief introduction to vibration analysis, and a review of the abstract
concepts of analytical dynamics including the degrees of freedom, generalized coordinates,
constraints, principle of virtual work and D’Alembert’s principle for formulating the equations
of motion for systems are introduced. Energy and momentum from both the Newtonian and
analytical point of view are presented. The basic concepts and terminology used in mechanical
vibration analysis, classification of vibration and elements of vibrating systems are discussed.
The free vibration analysis of single degree of freedom of undamped translational and torsional
systems, the concept of damping in mechanical systems, including viscous, structural, and
Coulomb damping, the response to harmonic excitations are discussed. Chapter 1 also discusses
the application such as systems with rotating eccentric masses systems with harmonically
moving support and vibration isolation  and the response of a single degree of freedom system
under general forcing functions are briefly introduced. Methods discussed include Fourier series,
the convolution integral, Laplace transform, and numerical solution. The linear theory of free
and forced vibration of two degree of freedom systems, matrix methods is introduced to study
the multiple degrees of freedom systems. Coordinate coupling and principal coordinates,
orthogonality of modes, and beat phenomenon are also discussed. The modal analysis procedure
is used for the solution of forced vibration problems. A brief introduction to Lagrangian dynamics
is presented. Using the concepts of generalized coordinates, principle of virtual work, and
generalized forces, Lagrange's equations of motion are then derived for single and multi degree
of freedom systems in terms of scalar energy and work quantities.
An introduction to MATLAB basics is presented in Chapter 2