Damping Mechanisms and Their Effects on the Whipping Response of a SubmergedSubmarine Subjected to an Underwater Explosion

摘要

An analytical approach to the solution of the whipping response of a submergedsubmarine to the pulsation of a nearby explosion bubble is presented. Particular aspects of energy dissipation (damping) are addressed in regards to their effects on the overall loading forces and dynamic response of the submarine. Particular damping mechanisms discussed include hull damping (hull material and structural), internal damping (internal structures and sloshing liquids), and external damping (hydrodynamic damping including wave radiation and viscous fluid effects). A flexible analytic model is developed, using the fundamentals of vibration and hydromechanics. A finite-element beam model is used to represent the flexural structure of the hull. Internal structures are modeled as separate dynamic systems, using both discrete and modal superposition approaches. Onboard liquids are modeled using a mechanical-equivalent system based upon a potential flow solution of the liquid free-surface. External hydrodynamic forces are modeled using a modified Morison formulation, with fluid velocities and accelerations calculated based upon a popular explosion bubble model. The equations of motion for the composite dynamic systems are solved in the time-domain using a modified Newmark direct time integration scheme, with iterations at each time step accomplished using a modified Newton-Raphson method. (MM).