Symmetry Exploitation in the Natural Vibrations of Rod Systems

The purpose of this work was to study spectral and Cauchy problem for the mechanical system consisting of three rods, two of them being identical and connected with the third one by linear elastic elements. We stated the corresponding spectral problem and studied its spectrum. Findings of the research show that eigenfunctions of the considered spectral problem are classified according to the irreducible representations of the finite group of transformations despite the fact that the initial equations system admits continuous (Lie) transformation groups. We considered the weak solution of Cauchy problem and revealed its simplification in case of special "symmetrical" form of initial conditions and right-hand side of the corresponding operator equation system.

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