Analytical Solutions For A Cable Net Over A Rectangular Plan

This paper is concerned with the analytical solution of the integro-differential equation governing the behaviour of an elastic cable net. It is here assumed that in the initial state the cables are in vertical planes the projections of which on the horizontal plane form a net of rectangular mesh. The structure is treated as a continuous system, and the equations are linearized.

A complete analytical solution is derived for a cable net over a rectangular plan with the cables located on a hyperbolic paraboloid in the initial state. Small vibrations about an equilibrium configuration are first studied, and expressions derived for the natural frequencies and normal modes. The normal modes (eigenfunctions) are then used to derive Levy-type analytical solutions for various important cases of static loading. The exact analytical solution is also used to establish simple approximate formulae for the static loading cases. Numerical examples are presented in which the results of the analytical solution are compared with those of a calculation of the same structure treated as a discrete system (the latter type of analysis, which accounts for the non-linear effects, has also been carried out by the writer).