Analytical solutions for the resonance response of Goupillaud-type elastic media using z-transform methods

►z-transform methods are used to derive exact stress solutions in Goupillaud media. ► The determinant of the z-space global system matrix is a palindromic polynomial. ► The zeros of the determinant are on the unit circle for media with up to five layers. ► Natural frequencies are described analytically for the given boundary conditions. ► Universal resonance frequencies are found for designs with an odd number of layers.