### New approach to establish similitude invariant for vibration experiment of symmetrically laminated plates.

Pairod Singhatanadgid, Variddhi Ungbhakorn

#### Аннотация:

Similitude theory is a powerful tool to establish the sufficient and necessary conditions of similarity between the model and prototype. Recently there were several published papers on laminated plates and shells to develop the similarity conditions for the buckling and vibration problems. However, those authors have applied the similitude transformation to the solutions of the governing differential equations instead of to the governing differential equations directly. This causes serious limitation on the applicability of the similitude theory because exact or approximate analytical solutions must be obtained before they could apply the similitude transformation. This research paper is to derive the similitude invariants, hence the scaling laws, for free vibration response of symmetric cross-ply and angle-ply laminated plates by applying the similitude transformation to the governing differential equations directly. Due to scarce test data, the fundamental frequencies of vibration obtained by this approach is theoretically verified by using data of the models from theory and make substitution into the scaling laws to predict the fundamental frequencies of the prototypes and compare to the theoretical values of the prototypes. For complete similitude cases with several aspect ratios show exact agreement between results predicting from the scaling laws and from theory. But in reality, either due to the complexity of the scaling laws, or to minimize the costly experiment, partial similitude may be required. Therefore, approximate scaling laws are investigated and recommended by considering distortion in material properties, stacking sequences and number of plies.

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