Finite element method for calculation of dynamic stresses in the continuous beam on elastic supports

We study a damping beam construction on elastic supports. For this kind of a construction a general mathematical model is deduced. The external load is a time-depending harmonic function. The corresponding spectral problem contains the eigenvalue parameter in the boundary conditions. The variational formulations of the considered boundary value problems are obtained. The dynamic stresses of the constructions are determined using the finite element method and the method of normal shapes. Finally, the numerical results related to the problem with practical applications are presented.