Dynamic boundary equivalence for the truncated V-shaped plate model: a new method and study on the effects of aligned plates

To conduct numerical analysis and experimental testing on the dynamic performance of stiffened plates truncated from naval and marine structures, it is necessary to address dynamic boundary equivalence to simulate the effects of surrounding coupled structures on the dynamic characteristics of the truncated structure.

The finite element method is used to analyze the effects of the coupling angle and length of aligned plates on the free vibration behavior of a V-shaped stiffened plate, as well as the effects of elastic support stiffness on the free vibration behavior of an orthogonally stiffened plate with one elastically supported edge and three free edges. A comparison of the vibration characteristics between V-shaped stiffened plates with different coupling angles and aligned plate lengths and orthogonally stiffened plates with appropriate elastic support stiffness is conducted to establish a simulation method for achieving dynamic boundary equivalence of truncated stiffened plates.

The results show that for the first four modes, the sensitivity range of the coupling angle of the V-shaped stiffened plate is between 140° and 180°, while the stable length range of the aligned plate is between 0.60 and 0.90 m. When the elastic support stiffness is small, the additional mass significantly decreases the natural frequencies of the orthogonally stiffened plate, increases sensitivity to stiffness and narrows the frequency range over which the system is sensitive to stiffness variations. When the elastic support stiffness is large, the additional mass has little effect on the natural frequencies of the orthogonally stiffened plate. The equivalent elastic support stiffness of the first four modes of the V-shaped stiffened plate decreases as the coupling angle increases. Changes in the length of the aligned plate of the V-shaped stiffened plate lead to modal differentiation and distortion of the mode shapes.

The use of the elastic support boundaries to simulate the dynamic coupling conditions of the V-shaped stiffened plates, despite minor deficiencies during inherent mode transitions, can still achieve overall effective equivalence. This strategy not only provides a new approach for simulating truncated model boundaries but also improves calculation efficiency while maintaining high accuracy.