锚杆动测问题的解析解

岩石声波测试技术应用于锚固工程的无损检测中，其基本原理是采用动力瞬态激振使锚杆引起弹性振动，通过测定锚杆的振动响应来估计和推断锚杆中的缺陷。应用弹性动力学的基本理论，建立了锚杆动测问题的物理模型，在力学上表现为给定扰动源信息及边界条件、初始条件，建立描述介质运动的支配方程，归结为双曲型或双曲—扩散型方程的初值或初值—边值问题，由此求解其动力响应，推导了一维非齐次波动方程在有界域情况下的解析解。

Analytic Solution of Anchor Bolts with Dynamic Detection

Sonoprobe method has been applied in non-destructive inspection of anchorage project. Its fundament is that to use dynamic transient excitation for inducing anchor bar's elastic vibration. The flaws in the bar can be estimated or deduced by determining transient response of anchor bar. Based on the theory of elasto-dynamics, in this paper, a theoretical model of acoustic detection of anchor bar has been built up. On the mechanics field, this method means that if information of disturbance resource, boundary conditions and initial conditions has been given, the dominant equation describing medium motion would be established. That is, it leads to the problem of initial value or initial boundary value of hyperbolic type or hyperbolic-diffusibility type equation. Thereby the dynamic response could be solved. As an example, analytic solution of heterogeneous wave equation is deduced in case of bounded region.