Spin waves are promising candidates for information carriers in advanced technology. The interactions between spin waves and acoustic waves in magnetic nanostructures are of much interest because of their potential application for spin-wave generation, amplification, and transduction. We investigate numerically the dynamics of magnetoelastic excitations in a one-dimensional magnonic-phononic crystal consisting of alternating layers of permalloy and cobalt. We use the plane-wave method and the finite-element method for frequency- and time-domain simulations, respectively. The studied structure is optimized for hybridization of specific spin-wave and acoustic dispersion branches in the entire Brillouin zone in a broad frequency range. We show that this type of periodic structure can be used for efficient generation of high-frequency spin waves.