Semi-Analytical Modeling and Vibration Characteristics of U-Shaped Stiffened Plates

Abstract

The U-shaped stiffened plates are widely used in construction, machinery, ships and other fields. It will inevitably lead to structural vibration problems due to its various loads in engineering applications. The aim of this study is to establish a semi-analytical model for evaluating the vibration characteristics of U-shaped stiffened plates. To begin with, the energy expressions of the plate are derived by incorporating the domain decomposition approach, artificial spring method and shear deformation plate theory. It is assumed that the plate and stiffener are rigidly connected in this study. Kinematic admissible functions are constructed via superposition of characteristic orthogonal polynomials and trigonometric series. Subsequent implementation of the Rayleigh-Ritz variational principle enables systematic resolution of vibrational behaviors, while validation studies demonstrate exceptional consistency with benchmark solutions from FEM simulations. Ultimately, the influence of the characteristic parameters such as the number and size of the stiffeners, the structural parameters of the plate on the dynamic behavior is investigated.