Forced harmonic vibration of rotating beam systems in space analysed by use of exact finite elements

Autor: H. Mikael Lundblad
Rok vydání: 1991
Předmět:
Zdroj: International Journal for Numerical Methods in Engineering. 32:571-594
ISSN: 1097-0207
0029-5981
DOI: 10.1002/nme.1620320308
Popis: A general computational technique is developed for the accurate analysis of forced non-synchronous harmonic vibration of linear structures rotating with constant speed about a fixed axis in the inertial space. The structures studied are built up from piecewise uniform straight Rayleigh-Timoshenko beam members having coinciding cross-sectional centres of geometry, shear and mass, and vibrating in coupled tension, torsion, bending and shearing. Hysteretic and viscous dampings in the beam material and in a Winkler-type ambient medium are considered. Rigid bodies and modal bodies and also discrete masses, springs and dampers can be included in the structure. The six coupled scalar partial linear differential equations governing the motion of a loaded beam are established in a corotating local co-ordinate system. A transcendentally frequency-dependent non-symmetric complex-valued 12 × 12 stiffness matrix is derived, over a state-space analogy and an associated eigenproblem, for a harmonically vibrating beam member non-synchronously excited at its ends. This matrix is exact in the sense that no assumed shape functions and no lumped masses are used. The general computational technique is here applied to a simple beam rotating about (1) its longitudinal axis and (2) about a transverse axis. The study clarifies the influence of gyroscopic effects and of material and support dampings on the dynamical behaviour of the beam at different rotational speeds and forcing frequencies. Resonance frequencies are found. Frequency response functions and frequency maps are plotted.
Databáze: OpenAIRE
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