Forced Oscillations Investigation of Elastic Designs of Variable Cross-Section with Heavy Base on Vibration Supports

Forced oscillations of a variable cross-section elastic structure with a heavy base on vibration supports with straightened surfaces were studied using the Ritz variational method. The motion equation solutions are presented as a series expansion in fundamental functions. The study investigates resonance modes of bending vibrations of rod-shaped, wedge-shaped, pyramid-shaped, and cone-shaped elastic structures with a heavy base. The pyramid-shaped elastic structure showed amplitude times smaller than the elastic structures of other forms. The natural frequencies of wedge-shaped, pyramid-shaped or cone-shaped variable cross-section elastic structures were outside the resonant zone of the oscillatory motion of the base, and for a rod-shaped elastic structure, they were within the resonant zone.