A rod can be fastened in a number of ways. If the rod ends are inaccessible to visual observation, the question arises of whether it is possible to determine the type and parameters of their fastening from sound vibrations induced by an impact on the rod. In this connection, a possible statement of the problem is as follows: to identify the type and parameters of fastening on both ends of a homogeneous rod from its natural frequencies. In other words, it is necessary to determine the type of fastening of each of the ends of a homogeneous rod (clamping, free support, elastic support, elastic fixing, floating fixing, or free end) and its parameters (the stiffness coefficients of springs for elastic fixing). The duality and stability of the solution to this problem is demonstrated. A method of solving this problem with the use of 9 natural frequencies is proposed. The results of numerical experiments on reconstructing various types of fastening from 9 natural frequencies are presented.
展开▼
