In this article, the frequency, mode and dynamic response of the high-speed underwater free beam are studied. Based on the Hamiltonian Principle, the governing equations for the lateral vibration and longitudinal vibration of the free beam are derived. The Galerkin method is used to discretize the continuous beam and the discrete control equations. The software calculation program is processed by the differential equations, and the fourth-order Runge-Kutta method is used to solve the numerical solution. The dynamic water pressure of the free beam subjected to underwater motion is theoretically deduced, and the modal analysis is carried out with the submarine-launched missile as an example. The analysis shows that the faster the speed, the lower the frequency of longitudinal vibration and lateral vibration, the larger the amplitude, the damping is sub-critical damping, and the vibration is attenuated. The numerical calculation result of displacement response of lateral vibration and the current period of water flow force are the most. The proximity of a certain mode is dominant. The calculation step size is reduced, and the displacement-time curve is smooth and flat when the step size is increased. However, when the calculation order is high, the matrix becomes a metamorphic matrix, and the high-order vibration image is distorted, and a jagged curve segment appears.
