Hull vibration mode

A hull vibration mode is a natural vibration shape of the global hull girder, where the whole ship flexes as a free-free beam with nodes and antinodes along its length. The lowest modes are the 2-node vertical (and horizontal) bending modes, whose eigenfrequencies follow f proportional to sqrt(EI / (m * L^4)) for a free-free beam, with m the mass per unit length including added mass of water. Higher modes add nodes (3-node, 4-node) and torsional and coupled forms. Design avoids resonance between these natural frequencies and the main excitation orders: propeller blade-rate, shaft rotational frequency, and main-engine firing frequency, which is why blade number and engine RPM are chosen against the computed hull modes.