Similitude theory has been applied to design scaled models in many fields of engineering. For laminated composite cylinders, the ply thickness is too thin to manufacture in scaled models, leading to similitude distortion. Meanwhile, this distortion problem cannot be solved with the traditional similitude method. The present study aims to propose a new similitude method to correct the distortion caused by non-scalability of ply thickness and to establish high-precision similitude of the free vibration of laminated composite cylinders. Firstly, the complete and partial similitude relationships are deduced while the similitude distortion derived from the non-scalability of ply thickness is discussed. Then, with the analysis of similitude for energy, a new similitude method named the energy similitude correction method is proposed. Finally, this method is verified through numerical examples of various cylinders. The results show that the proposed method can solve the similitude distortion of ply thickness with high accuracy, and it can be applied to various cylinders with different ply thickness, stacking sequences and materials.

在许多工程领域中，相似性理论已应用于设计缩放模型。对于层压复合材料圆柱体，帘布层的厚度太薄，无法在比例模型中制造，从而导致相似度失真。同时，这种失真问题不能用传统的相似度方法解决。本研究旨在提出一种新的相似性方法，以纠正由层厚度不可缩放性引起的变形，并建立层压复合材料圆柱体自由振动的高精度相似性。首先，推导了完整的和部分的相似度关系，同时讨论了由层厚度不可缩放性引起的相似度失真。然后，通过对能量相似性的分析，提出了一种新的相似性方法，即能量相似性校正方法。最后，通过各种气缸的数值实例验证了该方法。结果表明，所提出的方法可以高精度地解决板层厚度的相似性变形，可应用于具有不同板层厚度，堆垛顺序和材料的各种圆柱体。