THEORETICAL EQUATIONS OF IN-PLANE NATURAL VIBRATION FOR CABLES CONSIDERING BENDING STIFFNESS

In order to obtain the theoretical equations of in-plane modes for cables considering bending stiffness and sag effect, the equations of motion for inclined cable considered bending stiffness is derived in the local coordinate system first. Then, based on the assumption of flat-sag cable and the initial shape function of cable suggested by Irvine, the theoretical calculation equations for in-plane natural frequencies and modal shapes of flat-sag inclined cables are derived. Compared with the exact results obtained by finite difference method, the proposed formulas can be reliably applied to calculate the in-plane frequencies and mode shapes of natural vibration, both for horizontal cable and inclined cable.