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 or
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.