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.

To investigate the dynamic characteristics of local structures in naval architecture and ocean engineering, the dynamic boundary equivalence method between truncated model and original model is proposed.

The finite element method is used to calculate the natural frequencies and vibration modes of the V-shaped plate model with one side elastically supported under free boundary conditions, and the isolated plate model with three sides under free boundary conditions. The natural frequencies and vibration modes of the V-shaped plate model are compared with those of the isolated plate model to investigate the dynamic boundary equivalence of the truncated plate model.

The research shows that with an increase in the thickness of the attached plate, the half-wave number m of the (m, n) order of the main plate of the V-shaped plate is constant along the coupled edge direction, and the half wave number n perpendicular to the coupled edge direction increases; with the increase of the length of the attached plate, the half wave number m of the (m, n) order of V-shaped plates mode is constant along the coupled edge direction, while the half-wave number n perpendicular to the coupled edge direction decreases. When the coupling angle α between the main plate and the attached plate is between 40° and 90°, the attached plate of the V-shaped plate provides a fixed support boundary condition for the main plate.

A fast prediction method for the natural frequency of partial modes of the V-shaped plate is proposed.

In order to design and optimize the typical orthogonally stiffened plates commonly used in naval architecture and ocean engineering, it is necessary to investigate the influence of different stiffener configurations on the intrinsic dynamic characteristics of orthogonally stiffened plates.

The natural frequencies and mode shapes of orthogonally, obliquely and curvilinearly stiffened plates are calculated using the finite element method under clamped boundary conditions. Comparative and analogy analyses of the intrinsic dynamic characteristics of the three types of stiffened plates reveals the influence of stiffener configurations on their dynamic coupling behavior and intrinsic dynamic characteristics.

The numerical results show that the natural frequency of obliquely stiffened plates can be increased by 9% compared to that of orthogonally stiffened plates, while the stiffness distributions of obliquely stiffened plates and curvilinearly stiffened plates are more homogeneous than that of orthogonally stiffened plates, and the dynamic stiffness homogenization effect of curvilinearly stiffened plates is more significant. In the frequency range below 900 Hz, the stronger the reinforcement, the greater the influence of the stiffener configuration on the dynamic characteristics of stiffened plates.

The results of this study can provide valuable references for the design of structures composed of orthogonally stiffened plates.

In order to explore the relationship and difference between the intrinsic dynamic characteristics of the orthogonally stiffened plate of different dimensions, the scale effect of the intrinsic dynamic characteristics of the construction members, such as the beam and the plate, as well as the dynamically coupled structure of the two construction members, the orthogonally stiffened plate, was analyzed and discussed.

Taking the models of the beam, the plate and the orthogonally stiffened plate as research objects, the natural frequencies and mode shapes of the above-mentioned models of different sizes were calculated by the finite element method. The influence of boundary conditions on the scale effect is discussed in terms of the similarities and differences between the natural frequencies of the beam model and the plate model of the unit scale under the free boundary conditions with those of the models under the simply supported boundary conditions. The influence of dynamic coupling between the construction members of the beam and the plate on the size effect of the intrinsic dynamic characteristics of the orthogonally stiffened plate was investigated by discussing the similarities and differences between the natural frequencies and mode shapes of the orthogonally stiffened plate of unit scale with those of the beam model and the plate model of unit scale.

Numerical results show that the variation of the natural frequencies of the model of unit scale against the size of the model under free boundary conditions no longer strictly follows the law that the natural frequencies are inversely proportional to the square of the size, but it is generally similar, or close to, the law.

The dynamic coupling between the construction members of the beam and the plate, results in the transformation of the variation of the natural frequencies against the size of the orthogonally stiffened plate of unit scale from a rapid decrease to a gradual increase. It also leads to dislocation and distortion of the mode shape of specified orders of the orthogonally stiffened plate, which contrasts with the classical pattern and regular lattice distribution of mode shapes of the unstiffened plate.