ON THE MODAL DENSITY AND ENERGY-FLOW CHARACTERISTICS OF PERIODIC STRUCTURES

General expressions for the modal density of one- and two-dimensional periodic structures are derived in terms of the phase constants which are associated with propagating wave motion. The energy flow in such structures is then considered, and it is formally proved that the energy velocity is always equal to the group velocity for an undamped system. Although this results may be expected from basic physical principles, the present approach provides an explicit confirmation within the framework of an existing general theory of harmonic wave motion in periodic structures. A graphical technique is developed whereby the direction of the Poynting vector which is associated with wave motion in a two-dimensional periodic structures may readily be visualized. The theory is applied to a periodic beam system, a panel row and a two-dimensional plate system. In the first two cases the forced response of a 20-bay structure is calculated by using the dynamics stiffness method, and a comparison is made with approximate response predictions which are based on the modal density. © 1994 Academic Press Limited.