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In this paper, unified practical formulas are proposed to estimate cable tension for vibrations under different boundaries. Correction coefficients are applied to the cable tensions calculated from the taut string theory. In these formulas, a dimensionless parameter η is introduced to represent the relative bending stiffness of the cable in lieu of the dimensionless parameter ξ in the previous formulas found in practice. Results have shown that the proposed formulas are accurate. For the fixed-fixed boundaries, the error in the estimated cable tensions for various frequencies is less than 3% for η ≤ 0.88, and less than 1% for η ≤ 0.55. For the fixed-hinged boundaries, the error in the estimated cable tensions for various frequencies is less than 1% for η ≤ 0.9. If there are multiple frequencies in the in-situ measurement, the proposed formulas can be used to identify the cable tension and bending stiffness simultaneously by solving a quadratic equation. The proposed formulas have been validated against several numerical examples as well as practical test cases.

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The buckling behavior of functionally graded graphene platelet-reinforced composite (FG-GPLRC) shallow arches with elastic rotational constraints under uniform radial load is investigated in this paper. The nonlinear equilibrium equation of the FG-GPLRC shallow arch with elastic rotational constraints under uniform radial load is established using the Halpin-Tsai micromechanics model and the principle of virtual work, from which the critical buckling load of FG-GPLRC shallow arches with elastic rotational constraints can be obtained. This paper gives special attention to the effect of the GPL distribution pattern, weight fraction, geometric parameters, and the constraint stiffness on the buckling load. The numerical results show that all of the FG-GPLRC shallow arches with elastic rotational constraints have a higher buckling load-carrying capacity compared to the pure epoxy arch, and arches of the distribution pattern X have the highest buckling load among four distribution patterns. When the GPL weight fraction is constant, the thinner and larger GPL can provide the better reinforcing effect to the FG-GPLRC shallow arch. However, when the value of the aspect ratio is greater than 4, the flakiness ratio is greater than 103, and the effect of GPL’s dimensions on the buckling load of the FG-GPLRC shallow arch is less significant. In addition, the buckling model of FG-GPLRC shallow arch with elastic rotational constraints is changed as the GPL distribution patterns or the constraint stiffness changes. It is expected that the method and the results that are presented in this paper will be useful as a reference for the stability design of this type of arch in the future.

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