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.

工程师经常使用相似性分析来设计用于实验测试的小比例模型或设计机械结构（例如驱动技术系统）的尺寸范围。本文涉及矩形板振动分析的相似分析方法。如果它们的几何形状由不同的因素（扭曲的相似性）缩放，则缩放定律仅以一定的精度近似实际的振动响应。本文介绍了一种性能度量，可以可靠地评估缩放定律与矩形板的实际振动响应的近似程度。这种措施，即所谓的马哈拉诺比斯距离，适用于后验分析，其中将从标度定律获得的振动响应与实际响应进行比较。对振动矩形板的数值和实验研究证实，马哈拉诺比斯距离适用于评估相似性分析的性能。在马氏距离可以与矩形板的几何特性相关联，以定义几何形状的最大允许变形。缩放定律足以很好地近似矩形板的振动响应，直至达到最大允许变形。此外，还比较了两种不同的最先进的相似性分析方法的性能。发现这两种相似性分析方法在几何变形的最大允许量下都表现良好。