[Objective] Orthogonally stiffened plates with different plate-to-beam bending stiffness ratios are taken as the research objects to uncover the dynamic coupling characteristics of the beam and plate components of orthogonally stiffened plates, and reveal the mechanism and influence of dynamic coupling between the construction members on their intrinsic dynamic characteristics. [Method] The natural frequencies and mode shapes of numerical models under free boundary conditions and clamped boundary conditions are calculated using the finite element method. Through an analysis of variations in the natural frequencies and mode shapes of an orthogonally stiffened plate against the plate-to-beam bending stiffness ratio, the intrinsic dynamic characteristics of an orthogonally stiffened plate with different bending stiffness ratios are discussed, and the dynamic coupling characteristics between the beam and plate are analyzed. [Results] The numerical results show that with the variation of the plate-to-beam bending stiffness ratios, the dynamic behaviour of the orthogonally stiffened plate transforms between two kinds of characteristics: one dominated by the plate and the other one coupled by the beam and plate. The critical plate-to-beam bending stiffness ratios and the criterion for determining them are presented in this paper. [Conclusion] The dynamic coupling between the beam and plate changes the variation rate of the natural frequencies with the plate-to-beam bending stiffness ratio, leading to the dislocation and distortion of the mode shapes of orthogonally stiffened plates.
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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.
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