Abstract: A self-adjoint method is proposed to derive the guided?wave restriction condition. After finding the orthogonal sets corresponding to the guided?wave restriction condition, the analytic dispersive equation, group velocity equation and steady response are obtained simultaneously. It is found that the propagating stress waves are classified by the kinds of the quasi-P, quasi?SV and quasi-SH waves, and are arranged by the standing wave number; the spectrum, the group velocity curve and the steady response have the same regularity. In the end, a calculation is represented, and the spectrum, the group velocity curve and the steady response are plotted of the transversely isotropic square columns.

Key words: square column, self?adjoint method, frequency equation, group velocity equation, spectrum, group velocity curve, steady response

摘要： 提出自结合方法，导出波传播的限定条件，在找到相应的正交序列后，完全得到弹性波导系统中解析形式的频散方程、群速度方程和稳态响应。发现弹性波按照拟P波、拟SV波和拟SH波的形式进行分类，根据驻波波数进行排序；频谱、群速度曲线和稳态响应具有同样的规律。最后以横观各向同性弹性方柱为例，具体绘制出波导系统的频谱、群速度曲线和稳态响应图。

关键词: 方柱, 自结合方法, 频散方程, 群速度方程, 频谱, 群速度曲线, 稳态响应