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.

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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.