Optimal Tuning of Resonant Modes of a Vibrational Technological Machine: Structural Approach

The problem of optimizing vibrational technological machines and systems operating in resonance mode is considered. The aim is to improve the dynamic quality of resonant modes. The methodology of structural mathematical modeling is employed, wherein the design scheme of a technical object represented as a mechanical oscillatory system is associated with dynamically equivalent structural diagrams of automatic control systems. A methodology for optimizing resonant modes of vibrational technological machines has been developed. A complete analytical derivation of amplitude-frequency characteristics (AFCs) for a two-mass oscillatory system with viscous damping has been performed. Based on matrix representations, expressions for transfer functions of the system are obtained, which can operate depending on parameters either as a dynamic vibration absorber formed by primary and auxiliary masses or as a vibrational test stand formed by a vibrator and a working organ. Extended analytical formulas for coordinates of invariant points independent of the damping coefficient have been derived. An analysis of structural invariance of the inter-partial transfer function, which does not depend on the mass ratio, has been conducted.