Natural frequencies, mode shapes and modal damping ratios must be estimated to assess subsea pipeline spans for vortex-induced vibrations (VIV) and response to direct wave loading. Several approximate solutions exist for a linearly elastic pipe under constant axial force supported by linearly elastic springs beyond the span's shoulders. An exact analytical solution has only recently been published. That solution is used here in a Rayleigh-Ritz approximation to account for arch action arising from combined effects of sag under gravity loads and axial restraint at the shoulders. The method allows survey data to be used directly to quantify arch action. Its accuracy is confirmed by finite element analysis. Further, the modal damping ratio is estimated based on the fractions of the potential energy in bending, the axial force, and the soil springs, all of which are determined analytically. Thus, it is found that the effective modal damping ratio increases without a bound as the axial load approaches the buckling load in compression.

必须估算固有频率，模态形状和模态阻尼比，以评估海底管道跨度的涡流振动（VIV）和对直接波载荷的响应。对于线性弹性管，在恒定轴向力的作用下，存在几种近似解决方案，这些线性弹性由跨度跨度的线性弹性弹簧支撑。确切的分析解决方案直到最近才发布。该解决方案在此处以瑞利-里兹近似法使用，以说明由于重力载荷和肩部轴向约束而下垂的综合作用所引起的足弓作用。该方法允许将调查数据直接用于量化足弓动作。其准确性已通过有限元分析得到确认。此外，模态阻尼比是基于弯曲中的势能，轴向力和土弹簧的分数来估算的，所有这些都是通过分析确定的。因此，发现有效模态阻尼比随着轴向载荷接近压缩中的屈曲载荷而无限制地增加。