The Theoretical Modal Analysis of a Circular Plate With a Solid Shaft

Abstract

Choosing a thick circular plate with a solid shaft as a simple model of gear blanks, the authors have developed a theoretical method for accurately estimating the noise power radiated from gear blanks during the design phase. To model analytically the natural modes of damped flexural vibration of the circular plate, a diagonal matrix equation was derived from Mindlin's equations for thick plates. Also, approximate spring constants required for an elastic boundary condition were derived in order to calculate the natural modes of flexural vibration as precisely as possible. Almost correct natural modes have been obtained: the natural frequencies and mode shapes calculated with the elastic boundary condition compare well with those obtained from experimental modal analysis and analytical modal analysis by a finite element method.