Eigenvalues and eigenvectors of the transfer matrix

The work presents theoretical and experimental studies on the binary and ternary solid elastic systems, with the aim to give a method for the determination of the elastic constants of the materials, especially for small ceramic samples. The built-in systems contain a gauge material and the sample of interest. The idea of the work starts from the properties of the intrinsic transfer matrix of the system, which share the same kind of eigenvalues in the resonance case. By explicit computation of the intrinsic transfer matrix of the system it is possible to find the eigenvalues and eigenvectors, and finally by measuring the frequency of the system's eigenmodes it is possible to elaborate a numerical method to compute the phase velocity and consequently the elastic constant of the material. To find experimentally the frequency of the eigenmodes, we used an experimental setup based on the Laser Doppler Interferometry and a measuring chain containing preamplifiers, filters and FFT signal analyzers.