Mechanical Vibrations Singh

The Aim ofthe Book. This book is concerned with the subjects of vibrations and system dynamics on an integrated basis. Design engineers find themselves confronted with demands made on machin­ ery, structures and dynamic systems which are increasing at such a rate that dy­ namic performance requirements are always rising. Hence, advances in analysis and design techniques have to keep pace with recent developments in strong lightweight materials, more extensive knowledge of materials properties and structural loading. Whereas the excitation applied to structures is always increas­ ing, the machine mass and damping is reduced. Consequently, unwanted vibra­ tions can have very serious effects on dynamic systems.

''There is always a delightful sense of movement, vibration and life"". Theodore Robinson (1852-1896) "/ have never solved a major mechanical or interpretive problem at the keyboard. I have always solved it in my mind". Jorge Bolet (1914-1990) The idea of this book stems from the realization that scientists, not unlike laymen, should occasionally interrupt their regular work and reflect on the past, to see both the accomplishments and the drawbacks, so as to be able to plan for future research in the "proper" perspective. But an inquisitive reader may ask: Can one really document in any field, let alone mechanical vibrations (whose very name signifies change), ''where do we stand"? Did not a Greek philosopher famously claim that one cannot enter a river twice? Another, on an even more sophisticated note, added that actually it is impossible to enter a river even once!

The book first introduces the concept of nonlinear normal modes (NNMs) and their two main definitions. The fundamental differences between classical linear normal modes (LNMs) and NNMs are explained and illustrated using simple examples. Different methods for computing NNMs from a mathematical model are presented. Both advanced analytical and numerical methods are described. Particular attention is devoted to the invariant manifold and normal form theories. The book also discusses nonlinear system identification.

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From the First Elementary Step Through To the Expert Level in Mechanical Vibrations