Space-time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables

Narakorn Srinil, Giuseppe Rega

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This paper presents space-time numerical simulation and validation of analytical predictions for the finite-amplitude forced dynamics of suspended cables. The main goal is to complement analytical and numerical solutions, accomplishing overall quantitative/qualitative comparisons of nonlinear response characteristics. By relying on an approximate, kinematically non-condensed, planar modeling, a simply supported horizontal cable subject to a primary external resonance and a 1:1, or 1:1 vs. 2:1, internal resonance is analyzed. To obtain analytical solution, a second-order multiple scales approach is applied to a complete eigenfunction-based series of nonlinear ordinary-differential equations of cable damped forced motion. Accounting for both quadratic/cubic geometric nonlinearities and multiple modal contributions, local scenarios of cable uncoupled/coupled responses and associated stability are predicted, based on chosen reduced-order models. As a cross-checking tool, numerical simulation of the associated nonlinear partial-differential equations describing the dynamics of the actual infinite-dimensional system is carried out using a finite difference technique employing a hybrid explicit-implicit integration scheme. Based on system control parameters and initial conditions, cable amplitude, displacement and tension responses are numerically assessed, thoroughly validating the analytically predicted solutions as regards the actual existence, the meaningful role and the predominating internal resonance of coexisting/competing dynamics. Some methodological aspects are noticed, along with a discussion on the kinematically approximate versus exact, as well as planar versus non-planar, cable modeling.
LanguageEnglish
Pages394-413
Number of pages19
JournalJournal of Sound and Vibration
Volume315
Issue number3
DOIs
Publication statusPublished - 19 Aug 2008

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cables
Cables
Computer simulation
predictions
simulation
Ordinary differential equations
Eigenvalues and eigenfunctions
partial differential equations
complement
Partial differential equations
eigenvectors
differential equations
nonlinearity
Control systems

Keywords

  • suspended cable
  • direct numerical simulation
  • analytical prediction
  • reduced-order model
  • internal resonance
  • nonlinear forced vibration

Cite this

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title = "Space-time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables",
abstract = "This paper presents space-time numerical simulation and validation of analytical predictions for the finite-amplitude forced dynamics of suspended cables. The main goal is to complement analytical and numerical solutions, accomplishing overall quantitative/qualitative comparisons of nonlinear response characteristics. By relying on an approximate, kinematically non-condensed, planar modeling, a simply supported horizontal cable subject to a primary external resonance and a 1:1, or 1:1 vs. 2:1, internal resonance is analyzed. To obtain analytical solution, a second-order multiple scales approach is applied to a complete eigenfunction-based series of nonlinear ordinary-differential equations of cable damped forced motion. Accounting for both quadratic/cubic geometric nonlinearities and multiple modal contributions, local scenarios of cable uncoupled/coupled responses and associated stability are predicted, based on chosen reduced-order models. As a cross-checking tool, numerical simulation of the associated nonlinear partial-differential equations describing the dynamics of the actual infinite-dimensional system is carried out using a finite difference technique employing a hybrid explicit-implicit integration scheme. Based on system control parameters and initial conditions, cable amplitude, displacement and tension responses are numerically assessed, thoroughly validating the analytically predicted solutions as regards the actual existence, the meaningful role and the predominating internal resonance of coexisting/competing dynamics. Some methodological aspects are noticed, along with a discussion on the kinematically approximate versus exact, as well as planar versus non-planar, cable modeling.",
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Space-time numerical simulation and validation of analytical predictions for nonlinear forced dynamics of suspended cables. / Srinil, Narakorn; Rega, Giuseppe.

In: Journal of Sound and Vibration, Vol. 315, No. 3, 19.08.2008, p. 394-413.

Research output: Contribution to journalArticle

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