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This paper presents our study of dynamics of fractal solids. Concepts of fractal continuum and time had been used in definitions of a fractal body deformation and motion, formulation of conservation of mass, balance of momentum, and constitutive relationships. A linearized model, which was written in terms of fractal time and spatial derivatives, has been employed to study the elastic vibrations of fractal circular cylinders. Fractal differential equations of torsional, longitudinal and transverse fractal wave equations have been obtained and solution properties such as size and time dependence have been revealed.

Thin-walled cylindrical structures have been found to display three distinctly different stability failure modes under wind loading, depending on their geometric and material properties. In low cylinders the radial compression at the meridian facing the wind causes a buckling mode similar to that for cylinders under constant radial compression, while very long cylinders display a failure mode characterized by buckling in the lower third of the structure at the side which faces away from the wind. The failure of medium height cylinders is characterized by a number of horizontal, ripple-like buckles in an area around the upper half of the meridian which faces the wind. In an ongoing experimental study, a series of small-scale specimens with a wide range of geometric parameters is being tested in a wind tunnel. To the knowledge of the authors, this is the first time that the particular buckling mode for medium height cylinders has been documented in an experiment. The present paper gives a summary of the results gained from this study so far and compares them qualitatively to those of a previous numerical study.

An analytical model has been developed that can predict the scattering of irregular waves normally incident upon an array of vertical cylinders. To examine the predictability of the developed model, laboratory experiments have been made for the reflection and transmission of irregular waves from arrays of circular cylinders with various diameters and gap widths. Though the overall agreement between measurement and calculation is fairly good, the model tends to over- and under-predict the reflection and transmission coefficients, respectively, as the gap width decreases. The model also underestimates the energy loss coefficients for small gap widths because it neglects the evanescent waves near the cylinders. The peaks of the measured spectra of the reflected and transmitted waves slightly shift towards higher frequencies compared with that of the incident wave spectrum probably because of the generation of shorter period waves due to the interference of the cylinders. Both model and experimental data show that the wave reflection and transmission become larger and smaller, respectively, as the wave steepness increases, which is a desirable feature of the cylinder breakwaters.