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This 2007 book concerns the vibration and the stability of slender structural components. The loss of stability of structures is an important aspect of structural mechanics and is presented here in terms of dynamic behavior. A variety of structural components are analyzed with a view to predicting their response to various (primarily axial) loading conditions. A number of different techniques are presented, with experimental verification from the laboratory. Practical applications are widespread, ranging from cables to space structures. The book presents methods by which the combined effects of vibration and buckling on various structures can be assessed. Vibrations and buckling are usually treated separately, but in this book their influence on each other is examined together, with examples when a combined approach is necessary. The avoidance of instability is the primary goal of this material.

A novel feature extracted from a nonlinear time series is presented within the context of vibration-based damage detection in a system. An eight-degree-of-freedom spring-mass-damper 'structure' is considered with damage incurred by a stiffness degradation in one spring. The system is excited with a chaotic input, and by tuning the Lyapunov exponents of the chaotic excitation to the dominant eigenvalue of the structure the dimensionality of the entire system is effectively controlled. Both the input and output are viewed in state space as geometric objects, and the effect of the damage is shown to alter the geometric properties of the corresponding attractors at a local level, which may be captured in construction of the feature. The utility of the feature is compared with that of a number of modal-based features and shown to be superior in resolving capability and in robustness.

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