Size effect on the intrinsic dynamic characteristics of the orthogonally stiffened plate

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.