## 1 Introduction  
We are interested in the use of guided wave techniques in non-destructive testing, applied specifically to the problem of hidden tamper detection in an arms control context. In arms control it is essential to ensure that all parties are in compliance with the terms of a treaty. A problem arising from this necessity is tamper detection [1]. The competent authorities wish to ensure that items of interest cannot be accessed for long periods of time and to this end they are sealed in freight-like containers. However, with sufficient time and effort any container can be breached, hence we will focus on the problem of making these containers 'tamper indicating'. This means that if a container is breached, it should be impossible to hide the evidence of this from a verification process, even if the breach has been deliberately concealed. Such a deliberately concealed breach is known as a 'hidden tamper'. We wish to apply a well known, non-destructive testing method to tamper detection, i.e., that of guided elastic waves. This has been motivated by experimental evidence [2] that tampers can be detected easily, even by non-specialist technicians, by scanning for mode conversion of elastic waves. Refraction and reflection of the guided wave, or excitation of additional modes, may occur due to welds [3], cracks [4], or other inhomogenous imperfections at the boundary of the tamper; however, we are mainly interested in mode conversion due to asymmetry introduced by the tamper itself. In elastic plates, there are two types of modes that propagate, symmetric and antisymmetric, and these modes travel at different speeds. For a plate of given thickness and material properties, the number of cut on (i.e., propagating) symmetric and antisymmetric modes depends on the frequency, with the lowest antisymmetric mode, \(A_{0}\), moving more slowly than its symmetric counterpart, \(S_{0}\). When elastic waves are initially generated from a known source location, the region where the slower modes are present at any given time is bounded. Any slower modes found outside this region must therefore be caused by mode conversion from the faster waves interacting with a hidden tamper. Due to the symmetric and antisymmetric nature of the two types of modes, converting between the two requires some asymmetry around the mid-plane of the plate. An example of how a tamper could introduce asymmetry is as follows: a section of the container could be removed to gain internal access, and later replaced by a plate of slightly greater thickness; it could then be polished flat on the outside wall to hide it from detection. However, it cannot be polished on the inside wall as the container is sealed, hence there will exist an indentation or protrusion on the inaccessible inner side; this feature is asymmetric and induces mode conversion. A schematic diagram of such a hidden tamper is given in Figure 1, which shows that the tamper is asymmetric about the mid-plane. It has been shown [5] that the stress field near traction-free elastic corners with an internal angle greater than \(\pi\) are locally singular; in Figure 1, two such corners are present. This leads us to believe that the corners could have a large effect on the solution of the problem and their asymmetric positioning about the mid-plane implies that this effect will include mode conversion. The local stress fields near a traction-free corner of internal angle less than \(\pi\) are not singular, but are irregular. This means that they are bounded in the vicinity of the corner, but behave locally as a non-integer power of the distance from the corner.