基于membrane理论,推导出一组完全满足抛物薄壳自由边界条件的模态振型函数.通过模态分析实验得到自由边界抛物薄壳的低阶模态实验振型,将实验振型与有限元分析振型及依据模态振型函数所得到的理论振型进行对比,三者能够较好的吻合,表明所推导的模态振型函数可正确描述抛物薄壳的模态形状. Based on the membrane theory, a set of modal shape functions that fully satisfy the free boundary conditions of the parabolic shell are deduced. The modal analysis of the low-order modes of the parabolic shell with free boundary is obtained by modal analysis, The analysis of the mode shapes and the comparison of the theoretical mode shapes obtained from the mode shapes show that the three modes can be well fitted, which shows that the modal shape functions derived can describe the modal shapes of parabolic shells properly.