The Appropriate Lumped Constants of Vibrating Shaft Systems

Abstract

Abstract The present paper is a theoretical supplement to the descriptive article, “Static and Dynamic Spring Constants.” It is concerned with the derivation of the constants (1a) K i = k i + 1 6 m i ω 2 = k i ( 1 + 1 6 ϵ i 2 ) ( ϵ i 2 = ω 2 m i / k i ) (1b) M i = μ i + 1 2 ( m left + m right ) of the appropriately lumped shaft system (Section 1), and with an estimate of the range of the new method (Sections 2, 3, 4). Term ki denotes the distributed static spring constant, mi the total mass of the ith (uniform) shaft section of the system; μi is the ith concentrated mass, ω the frequency of vibration.