In recent years there have been rapid advances in digital computers, the miniaturization of electronic circuits and
the development of new materials. In the acoustics and vibration fields these advances have led to a continual
increase in computational power and speed, improved acoustics and vibration transducers and instrumentation
and better measurement techniques. In many cases the developments have been synergistic; new experimental
knowledge has led to improved theoretical models and approaches and vice versa. Improved computers have
allowed the development of a host of computer programs and increasing numbers have become available as
commercial acoustics and vibration software. Of particular importance has been the development of numerical
calculation schemes such as the finite element method (FEM) and the boundary element method (BEM) which
have led to much improved predictive capabilities in many fields. However, advances have been in many other
areas of acoustics as well and not confined just to such numerical prediction schemes. As examples, a few of
these advances will be concisely summarized including: increased knowledge of and use of FEM and BEM,
Computational Aeroacoustics, Sonochemistry, Thermoacoustic Engines, Active Noise and Vibration Control,
Sound Intensity Measurements and their uses, Techniques of Speech Coding and Recognition of Speech, Ultrasonics
in Medical Diagnostics, and Cochlear Mechanics.

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Finite Element Analysis of Active Vibration Isolation
Using Vibrational Power as a Cost Function

An active vibration isolation system comprised of a simply-supported beam and a rigid mass mounted on an
active isolator is analyzed using Finite Element Analysis. The cost function which is minimized is the vibrational
power transmitted from the vibrating mass into the beam. The analysis shows that moments can generate
negative power transmission values along a translational axis. It is shown that a control strategy which
minimizes the power transmission along a translational axis and neglects the power transmission due to
moments can produce higher beam vibration levels than without control. It is shown by example that the
minimization of squared acceleration or squared force in the vertical direction at the base of the isolator,
performs nearly as well as the minimization of total power transmission (along translational and rotational axes).
It is shown that the cost function of translational power transmission along the vertical axis can have negative
values, when rotational moments are present. In these situations, the cost function of squared power transmission
along the vertical axis will have a locus of filter weights where the squared power transmission is zero along the
vertical axis. The optimum set of filter weights corresponding to the minimization of squared acceleration or
squared force along a vertical axis, is a point which lies on this locus. It is shown that a point exists on this
locus, where the control effort is also minimized. At this point, the control effort is less than that required when
the squared acceleration or squared force along the vertical axis is minimized. However, at the point where
squared power transmission along the vertical axis and the control effort is minimized, the total power transmission
is not necessarily minimized and generally not as small as achieved by just minimizing squared force or
squared acceleration in the vertical Z direction at the base of the isolator. Two adaptive control algorithms are
suggested for finding the optimum filter weights which minimize the squared power transmission and the control
effort. The first algorithm uses Newton?s method to minimize the control effort by moving the filter weights
along a constant power level on the error surface without causing an increase in the residual error. A second
method is suggested which alternates the filter weight updates between a partial leaky filtered-x LMS algorithm
and the standard filtered-x LMS algorithm. This results in a zigzag path of the filter weights and a slightly