A Scaling Law for Vibration Response of Laminated Doubly Curved Shallow Shells by Energy Approach

Abstract

Abstract This research paper derives the scaling law for physical modeling of generally laminated doubly curved shallow shells for free vibration response by applying the similitude transformation to the governing total energy of the system. Validity of the scaling law is verified by numerical experiments on laminated doubly curved shallow shells. This is accomplished by calculating theoretically the natural frequencies for free vibration of the model specimen and substituting into the scaling law to obtain the corresponding values of the prototype. The predicted natural frequencies of the prototype from the scaling law are then compared with those from the theoretical solutions. Examples for the complete similitude cases with various stacking sequences, number of plies, and planform ratios show exact agreement. The derived relationships between the model and prototype will greatly facilitate and reduce the costly experiment. In practice, either due to the complexity of the similitude requirements or to reduce experimental cost and time, it may not be feasible to construct the model to fulfill the requirements completely. Thus, partial similitude models are also investigated numerically. These include models with distortion in stacking sequences and laminated material properties. Distortion model in stacking sequences is proven to be fairly accurate. However, the model with distortion in material properties yields high percent of discrepancy of the scaling natural frequencies, so it is not recommended. Keywords: scaling lawsimilitudevibrationlaminated shallow shellsdoubly curved shallow shellsenergy approach