Stochastic stability control analysis of an inclined stay cable under random and periodic support motion excitations

Z. G. Ying, Y. Q. Ni, Y. F. Duan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

3 Citations (Scopus)

Abstract

The stochastic stability control of the parameter-excited vibration of an inclined stay cable with multiple modes coupling under random and periodic combined support disturbances is studied by using the direct eigenvalue analysis approach based on the response moment stability, Floquet theorem, Fourier series and matrix eigenvalue analysis. The differential equation with time-varying parameters for the transverse vibration of the inclined cable with control under random and deterministic support disturbances is derived and converted into the randomly and deterministically parameter-excited multidegree-of-freedom vibration equations. As the stochastic stability of the parameter-excited vibration is mainly determined by the characteristics of perturbation moment, the differential equation with only deterministic parameters for the perturbation second moment is derived based on the Itô stochastic differential rule. The stochastically and deterministically parameter-excited vibration stability is then determined by the deterministic parameter-varying response moment stability. Based on the Floquet theorem, expanding the periodic parameters of the perturbation moment equation and the periodic component of the characteristic perturbation moment expression into the Fourier series yields the eigenvalue equation which determines the perturbation moment behavior. Thus the stochastic stability of the parameter-excited cable vibration under the random and periodic combined support disturbances is determined directly by the matrix eigenvalues. The direct eigenvalue analysis approach is applicable to the stochastic stability of the control cable with multiple modes coupling under various periodic and/or random support disturbances. Numerical results illustrate that the multiple cable modes need to be considered for the stochastic stability of the parameter-excited cable vibration under the random and periodic support disturbances, and the increase of the control damping rather than control stiffness can greatly enhance the stochastic stability of the parameter-excited cable vibration including the frequency width increase of the periodic disturbance and the critical value increase of the random disturbance amplitude.

Original languageEnglish
Pages (from-to)641-651
Number of pages11
JournalSmart Structures and Systems
Volume23
Issue number6
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Inclined cable
  • Matrix eigenvalue
  • Parametric excitation
  • Random disturbance
  • Stability control

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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