Vibration reduction in piecewise bi-coupled periodic structures

The problem of minimizing transmitted vibrations through finitely long periodic structures is addressed. Bi-coupled periodic element properties and arrangement are tailored to localize the response around the excitation source within any assigned frequency range. Bi-dimensional analytical maps of the single unit free-wave propagation domains (stop, pass and complex domains) provide the optimal choice of the cell properties and ordering. Moreover, the amount of vibration suppression along the periodic structure is also controlled as it can be described through iso-attenuation curves representing the contour plot of the real part of the propagation constants. Applications to both undamped and damped beams resting on elastic supports are illustrated. The response of the periodic structures to harmonic excitations is expressed through the wave vector method taking into account the effects of wave reflection due to changes in the cell properties along the structure and boundary conditions. Such computational schemes enables one to overcome numerical difficulties arising in the transfer matrix formulation for structures with a large number of periodic units.