Effect of variability of parameters of cross-sections of rods on their dynamic performance

Abstract

Influence of prismatic cross-section rods surface quality on natural frequencies and mode shapes is investigated. Modified equations of Kirchhoff and Klebsh are used. These equations allow taking into account the influence of tension-compression and in-plane shear of rods. Linear initial-value boundary-value eigenvalue problem is formulated. Modeling of frequency function is carried out with the help of method of initial parameters. Existence of nonlinear dependence of natural frequencies on rod cross-section parameters changing and high sensitivity of mode shapes when changing rod cross-section parameters is confirmed, Urgency of developing special high-precision algorithms of ill-conditioned boundary problems solution for practical use of the confirmed effect is revealed.

Keywords

• vibrations of rods
• vector equation
• bend
• tension-compression
• shift
• boundary value problem
• method of initial parameters
• frequency function