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基于匀直剪切梁横向自由振动微分方程和刚性半空间上的直立悬臂剪切梁模型,考虑半空间弹性,发展和建立了弹簧-剪切梁模型,并获得了单层以及任意多层覆盖情况下的隐式解析解和递推公式。以弹簧-剪切梁模型分析了传统半空间刚性假设对场地自振频率计算结果的影响。结果表明,半空间刚性假设引起的计算误差随着剪模比和覆盖层厚度的增大而减小。对于一般实际场地,在覆盖层厚度不是很小的情况下,采用传统刚性假设剪切梁法计算场地自振频率可获得比较满意的精度。
Based on the transverse free vibration differential equation of uniform shear beam and the erected cantilever beam model in rigid half space, considering the half-space elasticity, the spring-shear beam model is developed and established, and single layer and arbitrary multi-layer coverage Implicit Analytic Solutions and Recursion Formulas in Case. The influence of the traditional half-space rigid assumption on the natural frequencies of the site is analyzed by the spring-shear beam model. The results show that the calculation error caused by the half-space rigid assumption decreases with the increase of the shear modulus and the thickness of the overburden. For general practical site, if the cover thickness is not very small, the traditional rigid assumption shear beam method can be used to calculate the natural frequency of the site to obtain satisfactory accuracy.