The synthesis of an inhomogeneous elastic system with a boundary load

For an adequate description of free and controlled movements of one-dimensional elastic systems with distributed parameters, we consider a suitable model described by a linear boundary value problem with boundary conditions of the third kind. It is assumed that the control action enters additively in the equation of motion and in the boundary conditions. The coefficients of the equation of state and the boundary conditions may depend on the spectral parameter (frequency), which allows one to take into account the inertial and/or force load at one or both ends as well as the elastic properties (the Rayleigh correction) and other imperfections.