Performance of similitude methods for structural vibration analyses of rectangular plates

Engineers often use similitude analyses to design small scale models for experimental tests or to design size ranges of mechanical structures such as drive technology systems. This paper is concerned with similitude analysis methods for vibration analyses of rectangular plates. If their geometry is scaled by different factors (distorted similitude), the scaling laws approximate the actual vibration responses with a certain accuracy only. This paper introduces a performance measure that reliably assesses how well the scaling laws approximate the actual vibration responses of rectangular plates. This measure, the so-called MAHALANOBIS distance, applies in a-posteriori analyses, where the vibration responses obtained from the scaling laws are compared to the actual ones. Numerical and experimental investigations on vibrating rectangular plates validate that the MAHALANOBIS distance is suitable to assess the performance of similitude analyses. The MAHALANOBIS distance can be linked to the geometrical properties of the rectangular plates in order to define a maximum permissible distortion of the geometry. Scaling laws approximate the vibration responses of the rectangular plates sufficiently well up to this maximum permissible distortion. Furthermore, the performance of two different state-of-the-art similitude analysis methods is compared. Both similitude analysis methods are found to perform well up to the maximum permissible amount of geometrical distortion.