Dynamic tension of cables in a random sea: analytic approximation for the envelope probability density function

Tension during parametric excitation in submerged vertical taut tethers

“…In addition, the wave loading on the bridge towers or the tube of the tunnel depends on the random sea state. However, due to the transfer function from wave action to structural movements, this random process leads to a narrow banded excitation of the mooring line [13,24]. Thus, the waveinduced motion is represented as a sinusoidal imposed vertical displacement of the upper beam support.…”

“…Other examples in the literature study the cable tension, but they do not consider the particular case of parametric excitation. For instance, [23] derives an approximate analytical expression of dynamic cable tension, and [24] obtains an analytical approximation of the probability distribution of the dynamic tension envelope for a random sea state. Therefore, even though some investigations have considered tether tension, additional studies are needed to characterize parametrically excited taut mooring systems.…”

Análise dinâmica não-linear de viga esbelta semi-infinita sob flexão composta com contato unilateral em apoio elástico: uma aplicação ao estudo de vibrações de risers em catenária.

“…O presente estudo teve como base o trabalho de As análises contidas em Aranha et al [1], [2] e [3], Chatjigeorgiou [7], [8], [9], Chatjigeorgiu [10], Fujarra [17], Josefsson [19], Pesce et al [28], Ramos e Pesce [30], Sanches et al [32], Silveira [35], Simos e Fujarra [36], e Takafuji [39], permitiram conhecer a ordem de grandeza de alguns dados de entrada do problema, como características físicas do riser e diferentes abordagens já propostas.…”

“…Note-se no caso T1 indícios de "traveling wave", que pode ser verificado com a forma do histórico do deslocamento na forma de pulsos. Caso T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 φ i (N/m³) R elação entre frequências 0.48 0.48 0.41 0.49 0.37 0.39 0.39 0.36 0.36 0.36 0.36 conforme Aranha e Pinto [1], e para os cinco últimos casos, P7 a P12, taxa de amortecimento de ߦ =30%, conforme Sanches [31].…”