Narakorn Srinil. Large-amplitude three-dimensional dynamic analysis of arbitrarily inclined sagged extensible cables. Doctoral Degree(Civil Engineering). King Mongkut's University Technology Thonburi. Library. : King Mongkut's University of Technology Thonburi, 2004.
Large-amplitude three-dimensional dynamic analysis of arbitrarily inclined sagged extensible cables
Abstract:
This dissertation presents a general, theoretical model, which is capable of analyzing geometrically nonlinear, three-dimensional motion with large-amplitude dynamicdisplacements of arbitrarily inclined, sagged and extensible cables. Based on the virtual work-energy functional, the governing nonlinear equations of motion of the generalmodel are derived, accounting for the extensibility (axial deformation) effects. To allow the analytical perturbation-based solution, a consistent approximate version of thegeneral model is then developed, which relies on the small sag assumption of both horizontal and inclined cables. Contrary to the current literature model of horizontalcable, which neglects the longitudinal displacement (initial term) effects according to a condensation procedure, these effects are here accounted for. The approximate, noncondensedmodel still reveals the quadratic and cubic nonlinear terms due to cable axial stretching, and captures the spatio-temporal development of cable nonlinear dynamictension as well as the asymmetric feature of cable hybrid modes due to inclination effects. To highlight the longitudinal displacement effects, the condensed model ofhorizontal cables is also addressed with respect to the non-condensed model. Analytical closed-form and direct numerical solutions governing the static and lineardynamic equations of the cable are presented and their cross-checked sample results are verified to guarantee the correctness and validity of the developed model. As regardsnonlinear dynamics, the cable nonlinear characteristics in the large-amplitude free vibration response are investigated. In pursu.it of this, the system equations of theapproximate model is analytically investigated by means of a multi-mode Galerkin discretization and a second-order multiple scales, whereas the general model isnumerically investigated based on a finite difference discretization in the case of a specified end tension. In both investigations, three-dimensional or two-dimensionalnonlinear couplings and multi-modal interactions due to various activated internal resonances are highlighted, and their role in system dynamics is distinguished fordifferent horizontal (crossover) and inclined (avoidance) cables. A phenomenon of modal transition and the significance of cable nonlinear dynamic tensions aredemonstrated. In addition, the effects of cable inclination and cable sag on system nonlinear behaviors are evaluated. A remarkable difference in nonlinear dynamicsbetween horizontal and inclined cables is observed, which is influenced by the system high modal density and by the ensuing hybrid modal character of inclined cables. Someinteresting nonlinear interaction behaviors between low-order vertical and elastic modes of highly extensible horizontal cables are then exemplified.Experiments are also performed on a large-scale, inclined and highly extensible sagged cable. Measurement of response results of the fundamental linear free vibrations andnonlinear forced vibrations subject to cable longitudinal end-support excitation highlights and confirms the existence of lowest frequency avoidance phenomenon,associated hybrid in-plane modes, and multi-modal interactions due to simultaneous external and internal resonance conditions, respectively.The combination of analytical, numerical and experimental investigations carried out on different cable models in this dissertation provides satisfactory qualitative agreementand extensive findings on the main features of multi-modal interaction due to internal resonance phenomena.
King Mongkut's University Technology Thonburi. Library