Free Vibration of Light Roofs Backed by Cavities

Abstract

Modal properties of light roofs such as cable roofs backed by cavities with openings are theoretically investigated. Taken into account are the interaction between the roof and the air enclosed by the cavity, the air outside the roof, and air leakage through the openings in the building walls. Both the structural and acoustical damping are considered for the roof as well as for the wall openings. The outside air is assumed to be still. An approximate formula for the evaluation of roof model damping is derived using an energy consideration, and its accuracy is assessed by comparison with complex eigenvalue analysis and an exact solution for the circular membrane backed by a cavity. Comparison with experimental data is made. The theoretical approaches are used in a parametric study of two roofs with prototype properties. The first roof has the basic parameters of the Calgary Olympic Coliseum. The second roof is similar but features lighter mass per unit area.