Similitude and Physical Modeling for Buckling and Vibration of Symmetric Cross-Ply Laminated Circular Cylindrical Shells

Abstract

The similitude invariant and the scaling laws of the symmetric cross-ply laminated circular cylindrical shells for buckling and free vibration problems are derived by applying the similitude transformation to the governing differential equations directly. The scaling laws obtained by this approach are unique because they are forced by the governing differential equations. In the absence of the experimental data, the validity of the scaling laws is verified by numerical experiments. This is done by calculating theoretically the buckling loads and fundamental frequencies for free vibration of the model and substituting into the scaling laws. The predicted values of the prototype from the scaling laws are then compared with those values from the closed-form solution. Examples for the complete similitude cases with various stacking sequences, number of plies, and radius ratios show exact agreement. The presented relationships between the model and prototype will greatly facilitate and reduce the costly experiment. In reality, it may not be feasible to construct the model to fulfill the similarity requirements completely. Several cases of partial similitude are investigated and verified numerically. Modeling with distortion in stacking sequences is recommended, but model with distortion in material properties yields moderately high percent of discrepancy.