Vibrations of Self-Similar Branched Structures. Dichotomous Lattice

Vibrational properties of self-similar structures in which each cell at a certain scale follows the structure of the previous one are studied. A dichotomous lattice with different coefficients of similarity between rows is considered. A number of static and dynamic features of lattice under vibration have been found. It is shown that the lattice is a frequency bandpass filter and its bandwidth has been found. The existence of multiple natural frequencies equal to the partial frequency of forming element has been identified; the multiplicity of frequencies is determined by the number of lattice rows; conditions are found for the same static compression of each row when lattice moves as a solid body.