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The classical continuous beam model with steady state response to periodic excitation is presented first. This includes natural frequencies, mode shapes and modal expansion. Discrete analysis is next presented based upon finite element principles. Examples are discussed involving analysis of the entire ship and component parts, e.g., the deckhouse. There are sections on vibration surveys, sea trials, acceptable vibration standards and criteria. Concluding sections treat methods of remediation of vibration problems that are found after the ship is completed, including modifications to propeller design, structure and machinery.