Active and Passive Vibration Damping

12Power Flow in Damped Structures

12.1 Introduction

Extensive efforts have been exerted recently to quantify the power flow and energy transmission paths in vibrating structures. Such a quantification process is essential to the design of appropriate passive/active vibration control systems for these structures. In these control systems, the emphasis is placed on altering/confining the transmission paths to uncritical zones of the vibrating structures or minimizing the power flow across paths encircling the disturbance zones.

Several approaches have been considered for identifying the power flow, which is also known as structural or mechanical intensity, in vibrating structures. Distinct among these methods are: the Statistical Energy Analysis (SEA) method (Lyons 1975), the finite element method (FEM) (Garvic and Pavic 1993; Pavic 1987, 1990, 2005; Alfredsson 1997; Alfredsson et al. 1996), the FEM with heat conduction analogy (Nefske and Sung 1987; Wohlever and Bernhard 1992; Bouthier and Bernhard 1995), and a wide variety of experimental methods (Noiseux 1970; Pavic 1976; Williams et al. 1985; Williams 1991; Linjama and Lahti 1992; Gibbs et al. 1993; Halkyard and Mace 1995). Comprehensive and critical reviews of structural power flow are given by Mandal et al. (2003) and Mandal and Biswas (2005).

It is important here to note that the SEA is particularly suitable for computation of the average spatial power flow in the high frequency domain. The classical FEM is, however, more ...