Vibrations and Stability of Complex Beam Systems

verfasst von: Vladimir Stojanović, Predrag Kozić

Verlag: Springer International Publishing

Buchreihe : Springer Tracts in Mechanical Engineering

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This book reports on solved problems concerning vibrations and stability of complex beam systems. The complexity of a system is considered from two points of view: the complexity originating from the nature of the structure, in the case of two or more elastically connected beams; and the complexity derived from the dynamic behavior of the system, in the case of a damaged single beam, resulting from the harm done to its simple structure. Furthermore, the book describes the analytical derivation of equations of two or more elastically connected beams, using four different theories (Euler, Rayleigh, Timoshenko and Reddy-Bickford). It also reports on a new, improved p-version of the finite element method for geometrically nonlinear vibrations. The new method provides more accurate approximations of solutions, while also allowing us to analyze geometrically nonlinear vibrations. The book describes the appearance of longitudinal vibrations of damaged clamped-clamped beams as a result of discontinuity (damage). It describes the cases of stability in detail, employing all four theories, and provides the readers with practical examples of stochastic stability. Overall, the book succeeds in collecting in one place theoretical analyses, mathematical modeling and validation approaches based on various methods, thus providing the readers with a comprehensive toolkit for performing vibration analysis on complex beam systems.

Inhaltsverzeichnis

Frontmatter

Introductory Remarks

Abstract

A great number of mechanical systems are complex structures composed of two or more basic mechanical systems whose dynamic behavior is conditioned by their interaction. The systems connected by an elastic layer constitute one group of such mechanical structures which are commonly encountered in mechanical, construction and aeronautical industry. Mechanical systems formed by elastic connection of their members, due to the nature of the dynamic interaction conditioned by elastic connections are characterized by complex vibration and a higher number of natural frequencies. Since the number of natural frequencies depends on the number of basic elements joint together, such mechanical systems are exposed to an increased likelihood of creating resonance conditions which can cause breakage and damage. With the view to putting theoretical research into engineering practice, a great number of linear dynamic models describing the motion of a system were created. Such models are important as they give the initial approximation of the solution and a general insight into a dynamic behavior of the system at slight motion. If technical practice requires further investigation of system behavior, these dynamic models provide solid ground for the continuation of research with non-linearity effects.