Dynamics of axisymmetric hyperbolic shell structures

Shell structures have many applications including cooling towers, liquid-retaining structures and roofs where large uninterrupted space is required. These structures are aesthetically pleasing, make efficient use of construction materials and can economically meet design criteria. A number of serious failures of shell structures during the last century has led to significant research into their behaviour, analysis, design and construction. Despite this, further research is still required to improve design, especially with respect to shell dynamics. While some research on free vibration has been carried out, very little or none has been documented to date on the response to earthquake loading. In earlier research carried out by the authors, it has been shown that the hyperbolic shape is very efficient for use as an axisymmetric shell. In view of this and other existing information, this paper treats the free vibration and seismic response of hyperbolic shells, and examines the influence of thickness, height and curvature on this response. It is found that the period of vibration decreases approximately linearly with increasing curvature, but at high curvatures this trend reverses. The early periods of the circumferential mode of vibration are also found to vary linearly with changes of height and thickness, with increasing thickness reducing the period and increasing height increasing the period. The response of the first lateral mode is also significantly affected by a change in the parameters. Transient earthquake analysis shows that height is the most important factor governing the dynamic response. However, significant changes in hoop and meridional stresses are also observed for structures with different shell thickness and curvature. Analysis has been undertaken using the finite element method, and results are presented in tabular and graphical format.