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Subject: New method
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Date: 01/22/02 at 5:57 PM
Posted by: Sergey Karavashkin
We suggest a new original non-matrix method to obtain exact analytical solutions for both distributed and lumped systems. Our solutions offer to calculate a 1D lumped system having any number of elastically connected elements (up to infinity), both homogeneous and heterogeneous, taking into account the resistance and different longitudinal and transversal stiffness coefficients of the material of a real-world system. The conventional methods cannot it even approximately. We already have developed this method for the line (such as mechanical shafts), kinked (as the joint of a table-land and mountain ridge, or as the mountain ridge bend being the concentrators of seismic destroying power), closed-loop systems (the analogue of a wheel) and systems having the resonance subsystems.
All our solutions show the greatly unexpected features which cannot be noted by the conventional methods. Specifically, our solutions for systems having complex resonance subsystems show basically other vibration and resonance pattern than it is thought conventionally. It may be that just here is the reason, why sometimes the ordinary-loaded constructions suddenly fall, and the check shows that the construction was designed perfectly (by the conventional methods).
Our method well deepens the insight on the vibration pattern. On distinct of the conventional methods, when one must apply the parallel computing to obtain a numerical result which cannot be predicted or corrected during the process, our method is visual at any stage of calculation and offers to choose the suitable parameters just in the course of computation. It is so easy in processing that one can calculate a problem of such kind on a very old and small computer, and if needed, even on a calculator.
We have checked our results experimentally and obtained the calculation diagrams coinciding with those experimental up to such trifles as are usually thought the noises of experiment but appeared the regular small peaks.
We also have developed a few applications of our method to some mechanical (in that number seismic) problems. In assemblage with our original Dynamical Electromechanical Analogy DEMA, we have calculated the mismatched electric ladder filter, while the conventional methods cannot calculate the mismatched filters at all.
Please visit the homepage of our laboratory at
and read more detailed proposal there.
Our electronic journal SELF Transactions can give you much additional information: http://angelfire.lycos.com/la3/SELFlab
You can find there both our mentioned and other results.
Head laboratory SELF
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