In this report, the authors propose the addition of constraints between variable elements of spatial matrices on the experimental spatial matrix identification technique which they previously proposed, in order to enable the identification of physically meaningful spatial matrices by using a single-point excitation FRFs. Additional constraints are introduced by modelling an objective structure's dynamics, shape specifications, frequency ranges of interest, etc. After an explanation of the theory and its usefulness, an example is shown by using experimental FRFs of an actual beam structure on a free-free boundary condition. Three sets of physically meaningful spatial matrices of the specimen are obtained and studied by changing the modelling with respect to damping terms. In addition, two applicational simulations are carried out by using the identified spatial matrices