negative mass in modelling constraints

Dear friends,
If you are aware of modelling constraints such as rigid supports and
connections using penalty functions, you may be interested in this.
There may not be a "negative mass" in the universe but just as the
concept of "imaginary number" helps to solve a vast range of
mathematical problems the concept of negative mass can be used to solve
some vibration problems.
The natural frequencies of an object depend on constraints such as the
requirement that the movement of a bridge be zero at the supports. In
some computational methods, the vibratory displaced form of the object
is expressed as a series of assumed shapes, each conforming to the
support constraints. The natural frequencies and vibration modes of the
object are then determined by applying the physical law governing the
motion. In the popular energy method known as the Rayleigh-Ritz method,
this is achieved by minimising an energy function. This procedure
allows the contribution from each assumed shape to be adjusted in such
a way as to produce the best possible estimate of the natural
frequencies and modes.
This is part of a media release I prepared for one of my Royal Society
If you are interested in this please visit
Please note my site is one of the free geocities site and has a maximum
data transfer limit. Therefore, please download the interactive
programs only if you need them for teaching or research. If you are
interested in doing postgraduate or collaborative research in this area
please feel free to email me.
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