Application of Sherman–Morrison matrix inversion formula to damped vibration absorbers attached to multi-degree of freedom systems

Dynamic (tuned mass) vibration absorbers are among the most commonly used devices for vibration suppression. A new method is introduced based on the Sherman–Morrison matrix inversion formula for calculation of the optimal absorber parameter values for attachment to a damped multi-degree of freedom system. The new method can be used to minimize the motion of particular physical masses or modes of vibration, regardless of their location relative to the placement of the absorber subsystem. The new method can also minimize a linear summation of the degrees of freedom. Case studies illustrate the methodʹs superior performance relative to classical analytical techniques for determining absorber parameters.