Correlation between properties of eigenfrequencies and eigenmodes in a chain of rigid bodies with inertialess moment connections

Abstract

A regular chain of N rigid bodies is under consideration. Each body has one degree of freedom: rotation along the axis, orthogonal to the chain axis. Bodies of the chain are connected by means of elastic inertialles Bernoulli-Euler beams. We build the analytical solution of eigenvalue problem for the chain if N is arbitrary. The properties of eigenfrequencies and eigenmodes of the chain are compared with analogical properties of the canonical Newton chain. It is shown that the correlation between properties of eigenfrequencies and eigenmodes in a rigid body chain with inertialess torque connections and the same correlation in the canonical Newton chain is principally different. The eigenmodes, corresponding to the lowest eigenfrequencies of the rigid body chain, have maximal number of nodes. The eigenmodes, corresponding to the highest eigenfrequencies of this chain are most smooth. The nontypical correlation, obtained as a result of the precise solution, goes in contradiction to the states, putted by physics into the foundation of theoretical investigations devoted to various dynamical phenomena in crystal lattices. Refs 8. Figs 7.