An experimental investigation into the use of scaling laws for predicting vibration responses of rectangular thin plates

A scaling law for the vibration response of rectangular plates along with a similarity requirement was derived and validated with the experimental results in this study. The scaling law was derived from the governing equation of the problem and was found to be exact after verifying with a closed-form solution. An experimental investigation was conducted on several model and prototype specimens using an impact test method. The natural frequencies of the models were substituted into the scaling law to obtain the scaling natural frequencies of the prototypes, which were then compared with the measured natural frequencies. In the first part of the study, a total of nine aluminum rectangular plates with various boundary conditions were tested for natural frequencies to determine the size effect on the accuracy of the scaling law. From a total of 108 comparisons, the average percentage discrepancy of the scaling natural frequencies was 4.90% with a standard deviation of 6.45%. Therefore, the scaling law is satisfactorily accurate for a pair of models and prototypes of the same material but of different size. The other part of the study involved the investigation of the materialʹs effect on the accuracy of the scaling law. The experimental results showed that, unlike theoretical verification, using model and prototype systems with different materials resulted in an erroneous scaling natural frequency. The predicted natural frequency was inaccurate in this case because the boundary conditions enforced by the supports on the models and prototypes of different materials were significantly different. Consequently, the similarity requirement between the model and prototype is violated in the case of this study. With an additional experiment, the scaling law was found to be practically accurate for model–prototype pairs of different materials if their similitude requirements were fulfilled. The possible sources of discrepancy of the scaling natural frequency include uncertainties of the experiment, incomplete similarity of plate configurations and non-identical boundary conditions between the prototype and its model.