Elastically restrained Bernoulli--Euler beams applied to rotary machinery modelling
Tiago A.N.Silva1,Nuno M.M.Maia2,2
1. ISEL, Polytechnic Institute of Lisbon, Department of Mechanical Engineering, Rua Conselheiro Emidio Navarro, 1959-007 Lisbon, Portugal 2. IDMEC-IST, Technical University of Lisbon, Department of Mechanical Engineering, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
Abstract Facing the lateral vibration problem of a machine rotor as a beam
on elastic supports in bending, the authors deal with the free
vibration of elastically restrained Bernoulli-Euler beams carrying
a finite number of concentrated elements along their length. Based
on Rayleigh's quotient, an iterative strategy is developed to find
the approximated torsional stiffness coefficients, which allows
the reconciliation between the theoretical model results and the
experimental ones, obtained through impact tests. The mentioned
algorithm treats the vibration of continuous beams under a
determined set of boundary and continuity conditions, including
different torsional stiffness coefficients and the effect of
attached concentrated masses and rotational inertias, not only in
the energetic terms of the Rayleigh's quotient but also on the
mode shapes, considering the shape functions defined in branches.
Several loading cases are examined and examples are given to
illustrate the validity of the model and accuracy of the obtained
natural frequencies.
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