Application of time windowing to spatial maps of damping.

Some of the most challenging vibration control problems involve the selection and placement of frequency‐dependent damping devices, such as multilayered viscoelastic materials. In complex structures involving the simultaneous use of several passive damping devices, it is difficult to determine the effectiveness of each device directly from measurements. This question motivates the present analysis, which seeks to quantify the power being dissipated by the structure at selected locations for a given force distribution. The analysis begins with an expression for power flow to the structure from a specified force distribution. This expression involves the real part of the admittance matrix looking into the structure at a set of measurement points. By expanding this matrix as a sum over damping elements that mechanically connect measurement points, one can spatially map the power flow into the structure. While thermodynamics requires that this power flow to the structure be equal to the power dissipated by th...