10Vibration Control with Periodic Structures

10.1 Introduction

Periodic structures, whether passive or active, are structures that consist of identical substructures, or cells, connected in an identical manner as shown in Figures 10.1 and 10.2. Because of their periodic nature, these structures exhibit unique dynamic characteristics that make them act as mechanical filters for wave propagation. As a result, waves can propagate along the periodic structures only within specific frequency bands called the “pass bands” and wave propagation is completely blocked within other frequency bands called the “stop bands” as shown in Figure 10.3a. The spectral width and location of these bands are fixed for passive periodic structures, and are tunable in response to the structural vibration for active periodic structures as indicated in Figure 10.3b (Baz 2001).

2 Diagrams displaying passive periodic structures with geometrical discontinuity (left) and with material discontinuity (right), both depicted by a horizontal shaded bar with 6 section. Each section represents a cell.

Figure 10.1 Typical examples of passive periodic structures: (a) with geometrical discontinuity and (b) with material discontinuity.

Left: Diagram of a horizontal shaded bar with protruding dark shaded box for piezoelectric patches and section labeled cell. Right: A horizontal shaded bar labeled base structure with dark bars for shape memory inserts.

Figure 10.2 Typical examples of active periodic structures: (a) with active piezoelectric patches and (b) with active shape memory inserts.

Left: Graph of passive with fixed bands displaying 2 adjacent bars for pass and stop. Right: Graph of active with tunable bands displaying 3 discrete adjacent bars pass between two bars for stop.

Figure 10.3 Pass and stop bands of passive and active ...

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