Identification of beam boundary conditions in ill-posed problem

The purpose of the study is demonstration of the possibility of identification of boundary conditions in an ill-posed problem. The problem is understood as determination of four constants necessary for a description of functions of forced vibration amplitudes from three equations. To this end, the Singular Value Decomposition (SVD) algorithm is used. After determining the amplitudes of forced vibration, elasticity coefficients of supports can be calculated from the equations describing the boundary conditions. Verification of the obtained mathematical model (elastically supported Bernoulli-Euler's beam) was done by comparing natural frequencies obtained from analytical and numerical models, and analysing the correlation of forced vibration amplitude vectors for different excitation frequencies.