The displacements solution for steady-state longitudinal vibrations of segment-wise inhomogeneous elastic rods (Q1094918)

The Laplace integral transform is used to construct the displacements solution for steady-state vibrations of an inhomogeneous elastic rod made up of n (n\(\geq 2)\) homogeneous elastic segments of the same cross- section. The method consists in determining the displacements function of the inhomogeneous rod for zero initial conditions and for displacements type superimposed boundary conditions, with the residuals calculated for the poles of the Laplace images of the ends boundary conditions. The accuracy of the constructed solution is then proved and several examples are given to illustrate the method (harmonic end excitations are included).