Energy finite element method for vibration analysis of stiffened plates under fluid loading

Formulations for New Energy Finite Element Analysis (EFEA) are developed for high frequency vibration analysis of stiffened plates and stiffened cylindrical shells under heavy fluid loading. An alternative approach is presented for deriving the EFEA governing differential equations without a lossy plane approximation. Instead, the EFEA differential equations are derived by considering the response of a plate as a linear superposition of orthogonal waves. The added mass effect and radiation damping effect due to heavy fluid are incorporated in the derivation of the EFEA governing differential equations. The fluid loading effect and the presence of stiffeners are accounted in the computation of the power transfer coefficients through plate/stiffener joints. In addition, Periodic Structure (PS) theory is employed for predicting the high frequency vibration of fluid-loaded cylindrical shells with periodic circumferential stiffeners. The periodicity effects such as the pass/stop characteristics are accounted in the EFEA solution. The new formulation is validated through comparison of EFEA results to solutions by very dense finite element model, the solutions by classical techniques such as Statistical Energy Analysis (SEA) method, and results by the modal decomposition method for bodies of revolution. The energy ratios between the receiving members and the excited members are compared. The good correlation indicates that the new EFEA formulations capture properly the heavy fluid loading effects of the exterior fluid medium, the stiffener effects, and the periodicity characteristics due to periodic stiffeners. The real marine structures are analyzed by the new formulations. The effects of heavy fluid loading on vibration response are discussed and the advantages of the new formulation are identified.