Static and dynamic response of elastic suspended cables with thermal effects

Cable structures are often subjected to severe and variable environmental conditions, and their mechanical behavior is known to be particularly sensitive to different ambient factors. The paper analyzes temperature effects on the static and dynamic response of suspended inclined cables through a continuous monodimensional model including geometric nonlinearities. Uniform temperature changes are introduced through a non-homogeneous constitutive law for the material linear elasticity. Exact and approximate solutions of the equations governing the cable static equilibrium under self-weight are achieved, and the significance of the temperature-dependent variation of tension and sag are parametrically investigated. The spectral properties characterizing the free dynamics are obtained in a closed-form fashion for shallow parabolic cables within the low frequency vibration range. The sensitivity of the linear frequencies to temperature changes is discussed, outlining two thermal effects, which are distinguished by their different origins, geometric or static. For a generic temperature change, the geometric effect produces a systematic increment or reduction of all the frequencies, for both symmetric and anti-symmetric modes. The static effect stiffens or softens only the symmetric modes, and may prevail over the competing geometric effect, depending on the cable Irvine parameter. Finally, the thermal effects on the frequency veering and modal hybridization phenomena, which characterize quasi-resonant shallow cubic cables, are analyzed.