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摘要
The aim of this paper is to investigate temperature effects on the nonlinear vibration behaviors of suspended cables under two-frequency excitation. For this purpose, two combination and simultaneous resonances are chosen and studied in detail. First of all, based on the assumptions of the temperature effects, the partial differential equations of the in-plane and out-of-plane motions with thermal effects under multi-frequency excitations are obtained. The Galerkin method is adopted to discretize the nonlinear dynamic equations, and the single-mode planar discretization is considered. Then, in the absence of the primary and internal resonances, the frequency response equations are obtained by using the multiple scalesmethod. The stability analyses are conducted via investigating the nature of the singular points of equations. After that, temperature effects on nonlinear vibration characteristics of the first symmetric mode are studied. Parametric investigations of temperature effects on corresponding non-dimensional factors and coefficients of linear and nonlinear terms are performed. Numerical results are presented to show the temperature effects via the frequency-response curves and detuning-phase curves of four different sag-to-span ratios. It is found out that effects of temperature variations would lead to significant quantitative and/or qualitative changes of the nonlinear vibration properties, and these effects are closely related to the sag-to-span ratio and the degree of the temperature variation. Specifically, the softening/hardening-type spring behaviors, the response amplitude, the range of the resonance, the intersection and number of branches, the number and phase of the steady-state solutions are all affected by the temperature changes.
