As a classical flexible structure with quadratic and cubic nonlinearities, the suspended cables′ multi-type internal resonances are very easily excited. The paper aims at investigating influences of temperature on nonlinear dynamic behaviors of suspended cables considering simultaneous primary and two-to-one internal resonances. A kinematically condensed nonlinear model of a suspended cable considering temperature effects was introduced for the in-plane displacements by introducing a tension variation factor. Applying the Galerkin method and following the multiple scales procedure as to a weakly nonlinear system, both the polar and Cartesian forms of modulation equations were obtained when the higher/lower mode was excited directly. A complete dynamic scenario of vibration behaviors with thermal effects was presented quantitatively and qualitatively, e.g., force/frequency-response curves, periodic dynamic solutions, time displacement curves, phase plane diagrams, frequency spectrum, as well as Poincare sections. Numerical examples show that: the mode frequencies were affected by temperature changes significantly, and then the internal resonance would be changed induced by thermal effects. With an increase in temperature, the suspended cable with a smaller Irvine parameter would exhibit internal resonant responses. No matter the higher or the lower order was excited directly, the influence of temperature on the direct and internal excited response amplitudes were different. Temperature effects on the dynamic bifurcations (Hopf and periodic-doubling bifurcations) are much more apparent than the ones on the static bifurcations (saddle-node and pitck-fork bifurcations). The dynamic solutions as well as periodic motions are closely related to thermal effects, and significant different periodic motions were observed due to temperature changes. Besides, a good agreement between the perturbation solutions and the direct numerical integration ones could be observed.
林恒辉,赵珧冰. 温度变化对悬索非线性内共振响应特性影响[J]. 振动与冲击, 2021, 40(8): 165-172.
LIN Henghui,ZHAO Yaobing. Influences of temperature on suspended cables′ nonlinear vibration characteristics considering internal resonances. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(8): 165-172.
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