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该文基于结构体系的总能量进行相似转换,导出了大型加筋扁球壳轴对称振动时模型需满足的广义相似条件和缩尺原理。在此基础上,创新性地引入结构刚度参数公式,重点研究了不完全相似缩尺振动。以正交加强(径-环向加筋)扁球壳为例,基于线性几何方程和壳体最大动能,应用里兹法建立结构的频率方程,分析了模型与原型的完全和不完全相似。结果表明:完全相似缩尺模型能准确地预测原型。不完全相似分析中,当模型与原型的加筋肋满足截面积、一阶矩和二阶矩与对应加筋肋间距比值相似时,模型加筋肋截面可采用与原型不同的形式,为试验模型的设计提供了方便;当模型与原型的材料泊松比相等或相近时,推导的缩尺原理能较好的预测原型结构的动力特性。该文采用的方法和给出的结论对于相关试验和设计具有很好的实用价值。
Based on the similar transformation of the total energy of the structural system, the generalized similarity conditions and scaling principle that the model needs to satisfy in the case of axisymmetric vibration of large-scale stiffened spherical shells are derived. On this basis, the structural stiffness parameter formula is introduced creatively, focusing on the incompletely similar scaling vibration. Taking the orthogonally reinforced (radial - circumferential reinforcement) flat spherical shell as an example, based on the linear geometric equation and the maximum kinetic energy of the shell, the frequency equation of the structure is established by using the Ritz method. The complete and incomplete similarity between the model and the prototype is analyzed. The results show that the exact scale model can accurately predict the prototype. In the incomplete similarity analysis, when the model rib and the prototype stiffener satisfy the cross-sectional area, the first moment and the second moment are similar to the corresponding stiffener rib spacing ratio, the model stiffened rib section can adopt different forms from the prototype. The design of the model provides convenience. When the Poisson’s ratio of the model and the prototype is equal or similar, the deduced scale principle can better predict the dynamic characteristics of the prototype structure. The method and the conclusion given in this paper have good practical value for the related experiments and designs.