Computation of Rayleigh damping coefficient of a rectangular submerged floating tunnel (SFT)
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Computation of Rayleigh damping coefficient of a rectangular submerged floating tunnel (SFT) Md. Hafizur Rahman1,2 · Chhavi Gupta1 Received: 28 December 2019 / Accepted: 30 March 2020 © The Author(s) 2020 OPEN
Abstract The dynamic behaviors of the submerged floating tunnel, a buoyant structure of high slenderness, are a matter of concern since it is surrounded by the huge hazardous effects called hydrodynamic, seismic and functional action. Modal analysis and Rayleigh damping coefficients play a significant role in dynamic analysis, but it is not sufficiently simple to predict the reasonable damping coefficients named α and β. The present paper outlines the modal analysis and the calculation of Rayleigh damping coefficients that provide the natural frequencies, mode shapes, mode’s motion as well as coefficients α and β. To compute the Rayleigh damping coefficients, 2–10% damping to the critical damping has been assumed for this analytical study. For the analysis, an FEA-based software ANSYS is utilized successfully. It has been seen that the fundamental frequency and Rayleigh damping coefficients (α = 0.946 and β = 0.00022) of the SFT are reasonably high and it is under noticeable damping. Keywords Buoyant · Slenderness · Rayleigh damping coefficients · Mode’s motion
1 Introduction With the racing era of modern science and technology, structural engineering is going ahead to rescue the new challenges. The waterway crossing is one of them, and usually, a bridge is used, but a submerged floating tunnel (SFT) can be used for coming out of this challenge [1–5]. Though immersed tunnel, undersea tunnel, and bridge of long span have been being used for decades ago, now the curious concentrations are focused on the submerged floating tunnel as it is the new one and it gets the popularity day by day due to its interests [2]. Among the possibilities of waterway crossings, the SFT is chosen when the length and depth of the waterway are excessively high. The SFT can easily solve the concerning environmental problems; lesser project costs and can be introduced for its anti-vibrational behaviors [1–4, 6]. Being a slender structure, the perspective proportion of SFT, which
is characterized as the proportion of span to the characteristic length of tube cross section, is as a rule as huge as 102–103. It implies that the energetic behavior of SFT would like a slim bar limited by ties. Hence, the interaction between SFT and encompassing liquid is noteworthy. Here, due to the slenderness of SFT, the deformation of SFT beneath hydrodynamic loads composes distinctive vibration modes. In this way, it is not fitting to accept that SFT is inflexible when we compute the liquid strengths applying to it. SFT tube is by and large inundated within the profundity of 20–30 m beneath the water, once collision mishaps or fear-based oppressor assaults happen amid its operation; the result is more genuine [7]. Even though SFT is put beneath the water surface at a certain profundity, the surface wave has an imperative impact on its energetic r
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