Natural Science Forum / Physics / Particle Physics / September 2005

> 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
> publications.
> If you are interested in this please visit
> <http://www.geocities.com/Ilanko/negativemass.htm> or
> <http://www.geocities.com/Ilanko/vibration.htm>
>
> 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.
>
> Regards.
> Ilanko.