预应力索杆结构模型相似理论及其验证

缩尺模型试验可用于评估大型预应力索杆结构的静动力性能，而按照相似理论设计的缩尺模型、施加外荷载和边界条件等均对静动力试验结果的准确性至关重要。为此，对需要考虑几何大变形的预应力索杆结构的静力、动力相似理论进行研究。采用方程分析法建立了索杆结构的静力非线性相似准则，进一步研究了自振频率与振动模态的相似性关系。采用量纲分析法建立了索杆结构时程分析相似性条件，并结合算例进行了验证。结果表明：当杆件长度、截面积、内力、外力以及材料弹性模量等存在相似性，且外力、轴向刚度、内力相似比相同时，缩尺模型与实际结构的静力非线性变形具备相似性；材料弹性模量、质量密度、杆件长度、截面积、内力存在相似性，且内力与轴向刚度相似比相同时，缩尺模型与实际结构的振型相同、频率满足相似性；要达到索杆结构的时程分析相似性，需考虑时间、杆件长度、截面积、外力、内力、材料弹性模量以及边界条件的相似性。

Validation of similitude laws for prestressed cable-strut structures

The static and dynamic properties of large prestressed cable-strut structures can be measured by the experiment of scale models. The design of scale models, external force and boundary conditions based on similitude laws are vital for the accuracy of the experiment. In this paper, the static and dynamic similitude laws of prestressed cable-strut structures were studied. The nonlinear static similitude laws were derived by equation analysis. The similarity of undamped natural frequency and mode shapes were studied by analyzing the dynamic equations. Similitude laws of dynamical time-history analysis of prestressed cable-strut structures were studied by dimensional analysis. Two numerical examples were given to demonstrate the accuracy of the similitude laws. The results show that the nonlinear static similarity of structures are guaranteed by the similarity of member length, cross-sectional area, external force and internal force, Young’s modulus, as well as the equality of the similarity coefficients among external force, axial stiffness and internal force. If the similarity of Young’s modulus, density, member length, cross-sectional area and internal force exists and the similarity coefficients of axial stiffness and internal force are equal, the undamped mode shape is the same and the natural frequency is similar. To guarantee the similarity in dynamical time-history analysis, the similarity in time, member length, cross-sectional area, external force, internal force, Young’s modulus and boundary condition should be considered.