Vibration analysis of horizontal self-weighted beams and cables with bending stiffness subjected to thermal loads

This paper aims at proposing an analytical model for the vibration analysis of horizontal beams that are self-weighted and thermally stressed. Geometrical nonlinearities are taken into account on the basis of large displacement and small rotation. Natural frequencies are obtained from a linearization of equilibrium equations. Thermal force and thermal bending moment are both included in the analysis. Torsional and axial springs are considered at beam ends, allowing various boundary conditions. A dimensionless analysis is performed leading to only four parameters, respectively, related to the self-weight, thermal force, thermal bending moment and torsional spring stiffness. It is shown that the proposed model can be efficiently used for cable problems with small sag-to-span ratios (typically <18, as in Irvine's theory). For beam problems, the model is validated thanks to finite element solutions and a parametric study is conducted in order to highlight the combined effects of thermal loads and self-weight on natural frequencies. For cable problems, solutions are first compared with existing results in the literature obtained without thermal effects or bending stiffness. Good agreement is found. A parametric study combining the effects of sag-extensibility, thermal change and bending stiffness is finally given.