Abstract
The dynamic vibration absorber (DVA) is a passive vibration control device which is attached to a vibrating body (called a primary system) subjected to exciting force or motion. In this paper, we will discuss an optimization problem of the three- element-type DVA on the basis of the H<SUB>2</SUB> optimization criterion. The objective of the H<SUB>2</SUB> optimization is to reduce the total vibration energy of the system for overall frequencies; the total area under the power spectrum response curve is minimized in this criterion. If the system is subjected to random excitation instead of sinusoidal excitation, then the H<SUB>2</SUB> optimization is probably more desirable than the popular H<SUB>(infinity</SUB> ) optimization. In the past decade there has been increasing interest in the three-element type DVA. However, most previous studies on this type of DVA were based on the H<SUB>(infinity</SUB> ) optimization design, and no one has been able to find the algebraic solution as of yet. We found a closed-form exact solution for a special case where the primary system has no damping. Furthermore, the general case solution including the damped primary system is presented in the form of a numerical solution. The optimum parameters obtained here are compared to those of the conventional Voigt type DVA. They are also compared to other optimum parameters based on the H<SUB>(infinity</SUB> ) criterion.
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