球壳和柱壳振动中一类方程组的求解<sup>*</sup>

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球壳和柱壳振动中一类方程组的求解^*

基金项目: *国家自然科学基金

摘要: 本文利用矩阵型式的Frobenius级数方法求解了球壳和柱壳振动中一类含正则奇点的常微分方程组.考虑了指标方程根的相互关系,从而全面地得到了不同情况下解的表达形式,为解析求解工作奠定了基础.
- 振动 /
- 方程组 /
- Frobenius级数 /
- 球壳 /
- 柱壳
Abstract: The governing equations of the free vibrations of spherical and cylindrical shells with a regular singularity are solved by Frobenius Series Method in the form of matrix.Considering the relationship of the roots of the indicial equation,we get somevarious expressions of solutions according to different cases.This work lays a foundation of solving certain elastic problems by analytical method.
- vibration /
- equations /
- Frobenius Sories /
- spherical shell /
- cylindrical shell

[1]	Mirsky,I.,Axisymmetric vibrations of orthotropic cylinders,J.Acoust.Soc.Am.,36(1964),2106-2112.
[2]	Cohen,H.and A.H.Shan,Free vibrations of a spherically isotropic hollow sphere,Acustica,26(1972),329-333.