The synthesis of an inhomogeneous elastic system with a boundary load

Abstract

For an adequate description of free and controlled motions of one-dimensional elastic systems with distributed parameters, we consider a suitable model expressed by a linear problem with Robin boundary conditions. It is assumed that the control action is used additively in the equation of motion and in the boundary conditions. The coefficients used in the equation of state and in 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 of the boundary as well as the elastic properties (the Rayleigh correction) and other imperfections.