When an offshore cylindrical pile is impacted axially, the resulting wall vibration and underwater radiated sound pressure are insensitive to which thin shell theory is selected

Abstract

When a pile is impacted axially, a pulse of axial and radial vibration travels downwards and undergoes continued reflections at the toe and head. If a pile is to be treated as a thin cylindrical shell then producing a model for radiated sound pressure requires a particular “thin shell theory” to be selected. There are 12 such theories, as catalogued in Leissa’s monograph “Vibration of shells.” Four have been selected: the Membrane, Donnell-Mushtari, Flugge, and Epstein-Kennard theories (the last is the most intricate of the 12). An offshore pile with 25.4-mm wall thickness and 381-mm radius (6.7%-ratio) is modeled. Since the pile head is above the water surface, aerial radiation strongly attenuates the vibration of the immersed pile near the pile’s ring frequency (2.1 kHz). Spectra of radial vibration and underwater radiated sound pressure are computed up to 10 kHz using each of the four theories and found to be the same, except near the ring frequency. When the calculations are repeated for a similar pile with a wall three times thicker (no longer a thin shell), the Flugge results are higher than the other three by an amount that increases to 2 dB as frequency increases to 10 kHz.