Analysis of in-plane 1:1:1 internal resonance of a double cable-stayed shallow arch model with cables' external excitations

doi:10.1007/s10483-019-2497-8

摘要/Abstract

摘要： The nonlinear dynamic behaviors of a double cable-stayed shallow arch model are investigated under the one-to-one-to-one internal resonance among the lowest modes of cables and the shallow arch and external primary resonance of cables. The in-plane governing equations of the system are obtained when the harmonic excitation is applied to cables. The excitation mechanism due to the angle-variation of cable tension during motion is newly introduced. Galerkin's method and the multi-scale method are used to obtain ordinary differential equations (ODEs) of the system and their modulation equations, respectively. Frequency- and force-response curves are used to explore dynamic behaviors of the system when harmonic excitations are symmetrically and asymmetrically applied to cables. More importantly, comparisons of frequency-response curves of the system obtained by two types of trial functions, namely, a common sine function and an exact piecewise function, of the shallow arch in Galerkin's integration are conducted. The analysis shows that the two results have a slight difference; however, they both have sufficient accuracy to solve the proposed dynamic system.

关键词: singularity, velocity potential, the transient problem, the harmonic problem, nonlinear dynamics, cable-stayed system, multi-scale method, internal resonance, primary resonance

Abstract: The nonlinear dynamic behaviors of a double cable-stayed shallow arch model are investigated under the one-to-one-to-one internal resonance among the lowest modes of cables and the shallow arch and external primary resonance of cables. The in-plane governing equations of the system are obtained when the harmonic excitation is applied to cables. The excitation mechanism due to the angle-variation of cable tension during motion is newly introduced. Galerkin's method and the multi-scale method are used to obtain ordinary differential equations (ODEs) of the system and their modulation equations, respectively. Frequency- and force-response curves are used to explore dynamic behaviors of the system when harmonic excitations are symmetrically and asymmetrically applied to cables. More importantly, comparisons of frequency-response curves of the system obtained by two types of trial functions, namely, a common sine function and an exact piecewise function, of the shallow arch in Galerkin's integration are conducted. The analysis shows that the two results have a slight difference; however, they both have sufficient accuracy to solve the proposed dynamic system.

Key words: singularity, velocity potential, the transient problem, the harmonic problem, internal resonance, multi-scale method, nonlinear dynamics, primary resonance, cable-stayed system

中图分类号:

65P40

Yunyue CONG, Houjun KANG, Tieding GUO. Analysis of in-plane 1:1:1 internal resonance of a double cable-stayed shallow arch model with cables' external excitations[J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 977-1000.

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